Search Results for analysis

Biographies

1. Henrici Peter biography
   
   • Garrett Birkhoff, in Salutation to Peter Henrici on his 60th Birthday published in the SIAM Journal on Numerical Analysis, writes about Henrici's [SIAM Journal on Numerical Analysis 20 (6) (1983).',2)">2]:- .
     
   • His books and papers have helped greatly in maintaining numerical analysis as a subject with beauty, order, and structure, in the spirit of the great pioneers of the past.
     
   • There is no doubt that this book is a valuable contribution to numerical analysis, and it will certainly have an important influence on future developments in the numerical integration of ordinary differential equations.
     
   • Another impressive text by Henrici Elements of numerical analysis appeared in 1964.
     
   • This book marks a new level of excellence for introductory texts in numerical analysis.
     
   • One may perhaps quibble with the particular selection, but this approach is especially sound in numerical analysis.
     
   • These texts were rightly praise as remarkable achievements, but the high point of Henrici's writings must he the three volume work Applied and computational complex analysis.
     
   • The first volume Power series - integration - conformal mapping - location of zeros first appeared in 1974, the second volume Special functions - integral transforms - asymptotics - continued fractions first appeared in 1977, and the third and final volume Discrete Fourier analysis - Cauchy integrals - construction of conformal maps - univalent functions first appeared in 1986.
     
   • Writing this masterpiece did not fully occupy his textbook writing time, however, for between the publication of the second and third volumes he published Essentials of numerical analysis with pocket calculator demonstrations (1982).
     
   • In 1964 Henrici was an invited plenary speaker at the sixteenth British Mathematical Colloquium held in Leicester and he lectured to the Colloquium on Some applications of the quotient-difference algorithm in classical analysis.
     
   • The prize is awarded for original contributions to applied analysis and numerical analysis and/or for exposition appropriate for applied mathematics and scientific computing.
     
   • This Prize is given to honor Peter Henrici who was such an eminent figure in Applied Mathematics and Numerical Analysis.
     

2. Dahlquist biography
   
   • Bohr took the time to discuss mathematics with his young student and inspired Dahlquist's early interests, which centred on analytic number theory, complex analysis, and analytical mechanics.
     
   • This led him to a deep study of numerical analysis.
     
   • In such cases, the classic Lipschitz convergence analysis would have failed.
     
   • From 1956 to 1959 Dahlquist had been head of Mathematical Analysis and Programming Development at the Swedish Board of Computer Machinery.
     
   • He spent the rest of his career at this institution where the Department of Numerical Analysis, an offshoot the Department of Applied Mathematics, was founded in 1962.
     
   • In the following year Dahlquist became Sweden's first professorship in Numerical Analysis when he became the professorial head of the Department which at this stage had six members of the academic staff.
     
   • In the same year he published A special stability problem for linear multistep methods which introduced A-stability and became one of the most cited papers in numerical analysis.
     
   • This is a substantial, detailed and rigorous textbook of numerical analysis, in which an excellent balance is struck between the theory, on the one hand, and the needs of practitioners (i.e., the selection of the best methods - for both large-scale and small-scale computing) on the other.
     
   • The prerequisites are slight (calculus and linear algebra and preferably some acquaintance with computer programming) so that some of the finer theoretical points (those at which numerical analysis becomes applied functional analysis, for example) are outside the scope of the book.
     
   • This work is a monumental undertaking and represents the most comprehensive textbook survey of numerical analysis to date.
     
   • [The second part] is mainly concerned with the derivation, analysis and applications of a summation formula, due to Lindelof, for alternating series and complex power series, including ill-conditioned power series.
     
   • Yesterday, the Eidgenossische Technische Hochschule Zurich and Society for Industrial and Applied Mathematics presented 'The 1999 Peter Henrici Prize' to Germund Dahlquist for his outstanding research and leadership in numerical analysis.
     
   • His interests, like Henrici's, are very broad, and he contributed significantly to many parts of numerical analysis.
     

3. Hille biography
   
   • Later in his career his interests turned more towards functional analysis.
     
   • Hille was one of the few mathematicians who brought to his study of functional analysis - operator theory some twenty years experience in classical analysis.
     
   • Moreover, he was almost unique among mathematicians in applying functional analysis to investigate classical problems, rather than simply considering abstract situations for their own sake.
     
   • The first of these was Functional analysis and semigroups (1948).
     
   • Among Hille's other texts were Analytic function theory Vol 1 (1959), Vol 2 (1964); Analysis Vol 1 (1964), Vol 2 (1966); Lectures on ordinary differential equations (1969); Methods in classical and functional analysis (1972); and Ordinary differential equations in the complex domain (1976).
     
   • In the preface of Methods in classical and functional analysis Hille explains both about his aims in writing the text and his view of mathematics:- .
     
   • His problems come from analysis and his results should throw light on analysis..
     
   • The book [Einar Hille, Classical analysis and functional analysis : selected papers, Mathematicians of Our Time Vol.
     

4. Dieudonne biography
   
   • His doctoral studied were supervised by Montel and his thesis was in the area of classical analysis.
     
   • Left to myself, I would undoubtedly have remained billeted in a narrow sector of analysis my whole life.
     
   • He began his mathematical career working on the analysis of polynomials.
     
   • His best known books are La Geometrie des groupes classiques (1955), Foundations of Modern Analysis (1960), Algebre lineaire et geometrie elementaire (1964) and nine volumes of Elements d'analyse (1960-1982).
     
   • Dieudonne writes in Foundations of Modern Analysis that it is intended:- .
     
   • .to provide the necessary elementary background for all branches of modern mathematics involving 'analysis'.
     
   • The subject of study is indeed elementary analysis, and the theorems are theorems of analysis stated in geometrical terms.
     
   • He published texts such as History of functional analysis (1981), History of algebraic geometry (1985), Pour l'honneur de l'esprit humain (1987), A history of algebraic and differential topology 1900-1960 (1989), and L'ecole mathematique francaise du XXe siecle (2000).
     
   • The History of functional analysis is:- .
     
   • a detailed and absorbing account of the history and development of functional analysis, beginning with Lagrange and Daniel Bernoulli, through the work of Fredholm, Hilbert, and Frigyes Riesz at the turn of this century, and ending about 1960.
     
   • is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincare and Brouwer to Serre, Adams, and Thom.
     

5. Stampacchia biography
   
   • For three years he produced outstanding examination results in a wide range of courses such as Tutorial Sessions in Analysis and in Geometry, Calculus of Variations, Theory of Functions, and Ordinary Differential Equations.
     
   • He obtained his Laurea with distinction from the University of Naples in November 1944 with a thesis written with Renato Caccioppoli as his advisor [Variational analysis and applications, Nonconvex Optim.
     
   • At this stage he won a scholarship to enable him to continue his research at the University of Naples under the supervision of Renato Caccioppoli and Carlo Miranda, and he also undertook tutorial work to assist the Professor of Algebraic Analysis, although this was done on a voluntary basis.
     
   • He wrote [Variational analysis and applications, Nonconvex Optim.
     
   • With an impressive research record, Stampacchia was appointed as an assistant to the Professor of Mathematical Analysis at the University of Naples in July 1949.
     
   • He presented fourteen papers for his Libera Docenza (equivalent to the German Habilitation) in 1951 [Variational analysis and applications, Nonconvex Optim.
     
   • Not surprisingly, he was nominated for a chair in Rome and in November 1968 he was invited to fill the Chair of Mathematical Analysis in the Faculty of Sciences of the University of Rome "La Sapienza".
     
   • When he was invited to return to the Scuola Normale Superiore in Pisa as professor of Higher Analysis in 1970, he gladly accepted.
     
   • One of the main projects Stampacchia had undertaken during his period as professor of Higher Analysis in Pisa was to work on a book on variational inequalities.
     
   • Garroni writes a tribute to Stampacchia in [Variational analysis and applications, Nonconvex Optim.
     
   • We end this biography by quoting from Mazzone in [Variational analysis and applications, Nonconvex Optim.
     

6. Tukey biography
   
   • They show a remarkable uniformity of attitude characterised by a realistic recognition of the complexity of the situation, a consequent distrust of asymptotic theory, the use of standard statistical techniques as providing benchmarks rather than (say) precise confidence intervals, continual questioning of assumptions, emphasis on computational aspects, emphasis on ways of presenting the analysis, this presentation in ways familiar to the main users rather than in ways adopted in mathematical treatments, the early recognition of the superior qualities of digital devices for general purposes (as compared to analog devices) and a conspicuous fascination with new words and phrases, some of which have become established.
     
   • These include methods for estimating spectra, spectra of higher moments, complex demodulation, methods for determining the magnitude and sign of initial impulses observed after transmission through a (more or less) fixed linear system and the Fourier analysis of the logarithm of a spectral estimate to discern echoes.
     
   • Tukey described his development in the way he thought about his subject in the introduction to his paper The future of data analysis published in 1962:- .
     
   • And when I have pondered about why such techniques as the spectrum analysis of time series have proved so useful, it has become clear that their 'dealing with fluctuations' aspects are, in many circumstances, of lesser importance than the aspects that would already have been required to deal effectively with the simpler case of very extensive data where fluctuations would no longer be a problem.
     
   • All in all, I have come to feel that my central interest is in data analysis ..
     
   • the usefulness and limitation of mathematical statistics; the importance of having methods of statistical analysis that are robust to violations of the assumptions underlying their use; the need to amass experience of the behaviour of specific methods of analysis in order to provide guidance on their use; the importance of allowing the possibility of data's influencing the choice of method by which they are analysed; the need for statisticians to reject the role of 'guardian of proven truth', and to resist attempts to provide once-for-all solutions and tidy over-unifications of the subject; the iterative nature of data analysis; implications of the increasing power, availability and cheapness of computing facilities; the training of statisticians.
     
   • He held a senior position in the Department of Statistics and Data Analysis from the time it was set up at AT&T in 1952.
     
   • Tukey also made substantial contributions to the analysis of variance and the problem of making simultaneous inferences about a set of parameter values from a single experiment.
     

7. Zygmund biography
   
   • Zygmund worked in analysis, in particular in harmonic analysis.
     
   • Surely, Antoni Zygmund's "Trigonometric series" has been, and continues to be, one of the most influential books in the history of mathematical analysis.
     
   • Generations of mathematicians from Hardy and Littlewood to recent classes of graduate students specializing in analysis have viewed "Trigonometric series" with enormous admiration and have profited greatly from reading it.
     
   • Zygmund created one of the strongest analysis schools of the 20th century, making Chicago into a major analysis research centre (see [A century of mathematics in America III (Amer.
     
   • Their famous joint papers over the next few years on singular integrals and partial differential equations, the most significant of which appeared in 1952, have had a major impact on modern analysis.
     
   • This textbook has been conceived with the explicit intention of providing an easy and quick access to the most useful techniques of measure and integration in the modern analysis of real variables.
     
   • For outstanding contributions to Fourier analysis and its applications to partial differential equations and other branches of analysis, and for his creation and leadership of the strongest school of analytical research in the contemporary mathematical world.
     

8. Mitchell biography
   
   • Ron had developed an interest in Numerical Analysis, initially as a means of tackling fluid dynamics problems using Southwell's relaxation methods.
     
   • In 1953/54, he taught an Honours special topic in Numerical Analysis, the first time Numerical Analysis had been taught in St Andrews.
     
   • By 1965, there was a thriving numerical analysis group in St Andrews.
     
   • With a level of priority which was atypical of a classical Applied Mathematician in those days, he decided to build up Numerical Analysis, which he was far-sighted enough to see as a growth area.
     
   • In 1967, the year in which Queens College Dundee formally severed its links with St Andrews and became the University of Dundee, he obtained funds to establish a Chair of Numerical Analysis, and Ron (by that time a Reader in St Andrews) was appointed.
     
   • The academic year 1970-71 was a special one for numerical analysis in Dundee.
     
   • Ron obtained funding from the UK Science Research Council to promote the theory of numerical methods and to upgrade the study of numerical analysis in British universities and technical colleges.
     
   • He is a major figure in UK Numerical Analysis, and he has had a significant impact on the subject.
     
   • The Dundee Numerical Analysis Conferences .
     

9. Krasnosel'skii biography
   
   • Having remained at Kiev until 1952, in that year Krasnosel'skii was appointed to the Chair of Functional Analysis at Voronezh State University in Voronezh, western Russia.
     
   • It is highly recommended to those interested in the applications of functional analysis.
     
   • He was head of the Department of Mathematical Methods for Analysis of Complex Systems and, as a result, his research investigated applications to control theory as well as theoretical developments.
     
   • Such methods form an important branch of functional analysis, with various applications to numerical analysis, where they usually originated.
     
   • The richness of the methods, the clarity of the exposition and the importance of the results make this book highly valuable for those interested in functional analysis, as well as for numerical analysts.
     
   • The monograph Geometric methods of nonlinear analysis (1975):- .
     
   • is one of the best books on nonlinear analysis.
     
   • It presents a well organized and compact treatment of modern methods in nonlinear analysis.
     
   • In particular, he was responsible for opening up important new mathematical directions, the development of which created the foundations of modern nonlinear analysis.
     

10. Carleman biography
    
    • One reason was that many of his results, for instance the extension of Holmgren's uniqueness theorem, the analysis of the Schrodinger operator, and the existence theorem for Boltzmann's equation, were two decades ahead of their time and therefore not immediately appreciated.
      
    • Before his professorship in Lund he published about thirty papers, the majority treating of the problems in the theory of integral equations, and the theory of real and complex functions, where he gave extraordinary evidence of originality, penetration and capacity to use various methods of analysis.
      
    • Carleman is now remembered for remarkable results in integral equations (1923), quasi-analytic functions (1926), harmonic analysis (1944), trigonometric series (1918-23), approximation of functions (1922-27) and Boltzmann's equation (1944).
      
    • Names such as Carleman inequality, Carleman theorems (Denjoy-Carleman theorem on quasi-analytic classes of functions, Carleman theorem on conditions of well-definedness of moment problems, Carleman theorem on uniform approximation by entire functions, Carleman theorem on approximation of analytic functions by polynomials in the mean), Carleman singularity of orthogonal system, integral equation of Carleman type, Carleman operator, Carleman kernel, Carleman method of reducing an integral equation to a boundary value problem in the theory of analytic functions, Jensen-Carleman formula in complex analysis, Carleman continuum, Carleman linearization or Carleman embedding technique, Carleman polynomials, Carleman estimate in the unique continuation problem for solutions of partial differential equations and Carleman system in the kinetic theory of gas are well-known in mathematics (see [Encyclopaedia of Mathematics 2 (Kluwer 1988), 25-26.
      
    • XII.17], [Nonlinear dynamical systems and Carleman linearization (World Scientific, 1991).',12)">12], [Carleman\'s formulas in complex analysis : theory and applications (Kluwer, 1993).
      
    • In complex analysis there are Carleman formulae (proved already in 1926) which, unlike the Cauchy formula, reconstruct a function holomorphic in a domain D from its values on a part M of the boundary ∂D of a positive Lebesgue measure.
      
    • Different generalizations as well as some applications of these formulae to various problems of mathematics (problems of analytic continuation in the theory of functions), in theoretical and mathematical physics, in extrapolation and interpolation of signals having a finite Fourier spectrum, and results obtained by computer simulation on the elimination of noise in a given frequency band, are presented in the book [Carleman\'s formulas in complex analysis : theory and applications (Kluwer, 1993).
      
    • The connection of his and Schwartz's definition are nicely presented in [T Kawai and K Fujita (eds.), Microlocal Analysis and Complex Fourier Analysis (Singapore, 2002), 166-185.',23)">23].
      

11. Fox Leslie biography
    
    • In 1963 Fox was appointed as Professor of Numerical Analysis at Oxford also being elected to a professorial fellowship at Balliol College.
      
    • He contributed in many ways to promoting numerical analysis, for example in running summer schools, in developing links to industry, forming links with schools through the Mathematical Association, and with the writing of a wonderful series of books on the subject.
      
    • It contains chapters on: Matrix algebra; Elimination methods of Gauss, Jordan, and Aitken; Compact elimination methods of Doolittle, Crout, Banachiewicz and Cholesky; Orthogonalization methods; Condition, accuracy and precision; Comparison of methods, measure of work; Iterative and gradient methods; Iterative methods for latent roots and vectors; and Notes on error analysis for latent roots and vectors.
      
    • In 1968 he published Chebyshev polynomials in numerical analysis in collaboration with I B Parker.
      
    • The material might also be used in the numerical analysis part of diplomas in computation, and perhaps also by scientists, with a reasonable mathematical training ..
      
    • It considers the success achieved in the production of new techniques, machine-oriented techniques, error analysis, mathematical theorems and the solution of practical problems, and contrasts this with corresponding work in the field of linear algebra.
      
    • One of his last papers was Early numerical analysis in the United Kingdom presented to a conference on the history of scientific computing held at Princeton in 1987.
      
    • He served on its council and as editor of its journal until he became editor of its Journal of Numerical Analysis when it started publication in 1981.
      
    • An indication of the high regard he was held in by his friends and colleagues is the enthusiastic response to support the creation of a Leslie Fox Prize for Numerical Analysis.
      

12. Todd John biography
    
    • He spent ten years in Washington at the National Applied Mathematical Laboratories, developing high-speed computer programming, and becoming a world leader in numerical analysis and numerical algebra.
      
    • Todd was chief of the computation laboratory [from 1949] and later headed the numerical analysis section [from 1954], while Olga served as a consultant.
      
    • Over this period Todd's publications included: The condition of a certain matrix (1950); On the relative extrema of the Laguerre orthogonal functions (1950); Notes on modern numerical analysis.
      
    • Solution of differential equations by recurrence relations (1950); Experiments on the inversion of a 16 × 16 matrix (1953); Experiments in the solution of differential equations by Monte Carlo methods (1954); The condition of the finite segments of the Hilbert matrix (1954); Motivation for working in numerical analysis (1954); and A direct approach to the problem of stability in the numerical solution of partial differential equations (1956).
      
    • The following year, they arrived at the Institute, where Todd developed the first undergraduate courses in numerical analysis and numerical algebra, prerequisites to learning computing.
      
    • To present prospective mathematicians an account of some elegant, but usually overlooked ideas from classical analysis ..
      
    • some mild propaganda for numerical analysis ..
      
    • They made a remarkably generous commitment to the future of Caltech and the mathematics department, and their legacy also includes the inspiring stories of their lives and careers - Olga, as one of the very first women to make a mark in 20th-century mathematics, and Jack as a pioneer in numerical analysis and computing.
      

13. Box biography
    
    • In 1953 Box submitted his thesis Departures from Independence and Homoscedastisity in the Analysis of Variance and Related Statistical Analysis to the University of London and was awarded a Ph.D.
      
    • The main areas to which Box has contributed are: statistical inference, robustness, and modelling strategy; experimental design and response surface methodology; time series analysis and forecasting; distribution theory, transformation of variables, and nonlinear estimation; and applications of statistics.
      
    • His early papers included Non-normality and tests on variances (1953), A note on regions for tests of kurtosis (1953), Some theorems on quadratic forms applied in the study of analysis of variance problems.
      
    • Effect of inequality of variance in the one-way classification (1954), Some theorems on quadratic forms applied in the study of analysis of variance problems.
      
    • Times series analysis.
      
    • Bayesian inference in statistical analysis (1973), written by Box in collaboration with George Tiao, is described in a review by Anthony O'Hagan as:- .
      
    • The emphasis is on design of experiments, data analysis, and model building.
      

14. Jordan biography
    
    • From 1873 he was an examiner at the Ecole Polytechnique where he became professor of analysis on 25 November 1876.
      
    • Topology (called analysis situs at that time) played a major role in some of his first publications which were a combinatorial approach to symmetries.
      
    • In some respects this is a little strange since it is a rigorous analysis text built on top of the attempts to put the topic on a firm foundation begun by Cauchy and given considerable impetus by Weierstrass.
      
    • There had been a tradition of rigorous analysis at the Ecole Polytechnique begun, of course, by Cauchy himself.
      
    • Jordan was aware that his work was at a level that would be somewhat inappropriate for engineering students for he once said to Lebesgue that he called it "Ecole Polytechnique analysis course" since:- .
      
    • However between the editions Jordan had taught more advanced courses on analysis at the College de France and this may have influenced him to put set topology right up front in the second edition.
      
    • In this respect one can see the second edition as setting a tone for analysis textbooks which continues today.
      
    • Among Jordan's many contributions to analysis we should also mention his generalisation of the criteria for the convergence of a Fourier series.
      

15. Frechet biography
    
    • The importance of the thesis is that it develops axiomatic analysis systems providing an abstraction of different objects studied by analysis in a similar way to group theory providing an abstraction of algebraic systems.
      
    • He was both professor of higher analysis at the University of Strasbourg and Director of the Mathematics Institute there from 1919 to 1927.
      
    • It was after going to Strasbourg that he began to become interested in statistics but he only published a small number of articles on probability at this stage, most of his papers being on general analysis and topology.
      
    • From 1929 he was also professor of analysis and mechanics at the Ecole Normale Superieure.
      
    • made a major contribution toward laying the foundations of general topology and abstract analysis.
      
    • contains selections by [Frechet] from his papers on general analysis.
      
    • In the earliest of these letters the young Russian scholars express their gratitude to Frechet for having created the theory of abstract spaces on which their earliest investigations were based and cite as the source of their first published works problems posed by N Luzin in his analysis seminar at Moscow University.
      

16. Orlicz biography
    
    • It should be emphasized that from the functional analysis point of view (that is, as function spaces) Orlicz spaces appeared for the first time in 1932 in Orlicz's paper: Uber eine gewisse Klasse von Raumen vom Typus B in Bull.
      
    • Orlicz continued his seminar Selected Problems of Functional Analysis until 1989.
      
    • He was interested in works of other mathematicians and in branches far removed from functional analysis.
      
    • His book Linear Functional Analysis, (Peking 1963, 138 pp - in Chinese), based on a series of lectures delivered in German on selected topics of functional analysis at the Institute of Mathematics of Academia Sinica in Beijing in 1958, was translated into English and published in 1992 by World Scientific, Singapore.
      
    • In recent decades those spaces have been used in analysis, constructive theory of functions, differential equations, integral equations, probability, mathematical statistics, etc.
      
    • .functional analysis owes its magnificient development to Banach and his students, especially to Mazur, Orlicz and Schauder.
      
    • 23(1981), 222-231 and Achievements of Polish Mathematicians in the Domain of Functional Analysis in the Years 1919 - 1951, and biographies of S Banach, S Kaczmarz, A Lomnicki, S Mazur, J P Schauder).
      

17. Euler biography
    
    • Nowhere else could he have been surrounded by such a group of eminent scientists, including the analyst, geometer Jakob Hermann, a relative; Daniel Bernoulli, with whom Euler was connected not only by personal friendship but also by common interests in the field of applied mathematics; the versatile scholar Christian Goldbach, with whom Euler discussed numerous problems of analysis and the theory of numbers; F Maier, working in trigonometry; and the astronomer and geographer J-N Delisle.
      
    • The core of his research program was now set in place: number theory; infinitary analysis including its emerging branches, differential equations and the calculus of variations; and rational mechanics.
      
    • The publication of many articles and his book Mechanica (1736-37), which extensively presented Newtonian dynamics in the form of mathematical analysis for the first time, started Euler on the way to major mathematical work.
      
    • He wrote books on the calculus of variations; on the calculation of planetary orbits; on artillery and ballistics (extending the book by Robins); on analysis; on shipbuilding and navigation; on the motion of the moon; lectures on the differential calculus; and a popular scientific publication Letters to a Princess of Germany (3 vols., 1768-72).
      
    • He integrated Leibniz's differential calculus and Newton's method of fluxions into mathematical analysis.
      
    • One could claim that mathematical analysis began with Euler.
      
    • In 1748 in Introductio in analysin infinitorum Euler made ideas of Johann Bernoulli more precise in defining a function, and he stated that mathematical analysis was the study of functions.
      
    • The distinguishing feature of Euler's investigations in mechanics as compared to those of his predecessors is the systematic and successful application of analysis.
      

18. Burkill biography
    
    • Burkill is equally well known for his research in analysis and the excellent teaching books which he wrote.
      
    • Among his books are The Lebesgue integral (1951), A first course in mathematical analysis (1962) and A second course in mathematical analysis (1970).
      
    • The groundwork in analysis and calculus with which the reader is assumed to be acquainted is, roughly, what is in Hardy's "A course of pure mathematics "(1908).
      
    • A second course in mathematical analysis is described by T M Apostol in a review as a:- .
      
    • well-written text is designed as an introductory course in real and complex analysis for students familiar with elementary calculus and linear algebra.
      
    • In 1961 Cambridge promoted Burkill to be Reader in Mathematical Analysis.
      
    • It examines problems in Fourier analysis that led to the development of the theory of generalised functions.
      

19. Pappus biography
    
    • In Book VII Pappus writes about the Treasury of Analysis (see for example [Selections illustrating the history of Greek mathematics II (London, 1941).',3)">3]):- .
      
    • The so-called "Treasury of Analysis", my dear Hermodorus, is, in short, a special body of doctrine furnished for the use of those who, after going through the usual elements, wish to obtain power to solve problems set to then involving curves, and for this purpose only is it useful.
      
    • It is the work of three men, Euclid the writer of the "Elements", Apollonius of Perga and Aristaeus the elder, and proceeds by the method of analysis and synthesis.
      
    • Pappus then goes on to explain the different approaches of analysis and synthesis [Selections illustrating the history of Greek mathematics II (London, 1941).',3)">3]:- .
      
    • in analysis we suppose that which is sought to be already done, and inquire what it is from which this comes about, and again what is the antecedent cause of the latter, and so on until, by retracing our steps, we light upon something already known or ranking as a first principle..
      
    • But in synthesis, proceeding in the opposite way, we suppose to be already done that which was last reached in analysis, and arranging in their natural order as consequents what were formerly antecedents and linking them one with another, we finally arrive at the construction of what was sought..
      
    • 19 (3-4) (1982), 350-370.',13)">13] is a wide ranging discussion of analysis and synthesis, taking this work by Pappus as a starting point.
      
    • Pappus on analysis and synthesis in geometry .
      

20. Lions Jacques-Louis biography
    
    • It is a work to be recommended to every serious student of partial differential equations and particularly to those who are fascinated by the manner in which modern functional analysis has aided and influenced their study.
      
    • In Paris he began a weekly numerical analysis seminar series and, later, he set up a numerical analysis laboratory.
      
    • Although at this stage Lions did not publish on the topic, the lecture notes from graduate courses he gave on numerical analysis began to circulate and be used to set up numerical analysis courses in other institutions.
      
    • Analysis meant here everything from the most abstract existence theorems to approximation and numerical issues and computer implementations; control would come later.
      
    • reports on methods of solving nonlinear boundary value problems for partial differential equations, on a theoretical and functional analysis basis.
      
    • Perhaps the most outstanding contribution by Lions was the vast treatise Mathematical analysis and numerical methods for science and technology which he wrote with Robert Dautray.
      

21. Silva biography
    
    • Enriques thought that the proposed thesis would not be understood at that time, and thus Silva produced a second thesis in functional analysis Analytic functions and functional analysis.
      
    • These conclusions not only systematize and clarify many things in all parts of mathematics, but can also be usefully applied to problems in functional analysis.
      
    • He also published papers on functional analysis such as Sull'analisi funzionale lineare nel campo delle funzioni analitiche (1946).
      
    • Silva's functional analysis thesis was submitted to the Faculty of Sciences in Lisbon in 1949 and Silva was awarded his doctorate; the thesis was published as a 130 page paper in Portugaliae Mathematica in 1950.
      
    • This paper appears to be inspired in part by the work of Pincherle and Fantappie, but it is written more in the recent style of functional analysis in which abstract spaces, particularly Banach spaces, play a central role.
      
    • Porto 56 (4) (1973), 339-349.',6)">6] Kothe looks at Sila's contributions to functional analysis appearing in 25 papers between 1947 and 1967.
      

22. Ito biography
    
    • In 1923, against this scientific background, Wiener defined probability measures in path spaces, and used the concept of Lebesgue integrals to lay the mathematical foundations of stochastic analysis.
      
    • Ito began to reconstruct from scratch the concept of stochastic integrals, and its associated theory of analysis.
      
    • He continued to develop his ideas on stochastic analysis with many important papers on the topic.
      
    • Ito is the father of the modern stochastic analysis that has been systematically developing during the twentieth century.
      
    • Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis.
      
    • Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater.
      
    • For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future.
      

23. Collatz biography
    
    • Most of these publications are in numerical analysis but those range through almost every area within the subject.
      
    • An interesting combining of two areas was presented in Functional analysis and numerical mathematics (1966), which was an English translation of a German book published two years earlier.
      
    • It seems strange that this book should be the first of its kind, since it hardly needs to be said that "numerical mathematics" must draw heavily from functional analysis.
      
    • Nevertheless, in an unnecessarily modest preface, the author disclaims any intention of writing a textbook on either functional analysis or numerical mathematics, offering the book instead as illustrating the artificiality of any separation of applied from pure mathematics.
      
    • In spite of the disclaimer, the book could be used as a basis for a rather extensive course on functional analysis for numerical analysts, and the footnotes and the bibliography provide for a considerable amount of collateral reading.
      
    • The book Aufgaben aus der Angewandten Mathematik (1972) (with J Albrecht) provides a collection of problems (with their solutions) on the solution of equations and systems of equations, interpolation, quadrature, approximation, and harmonic analysis.
      
    • [T]he total effect is to provide a stimulating introduction to the subject to people with both pure and applied inclinations, and at the same time, providing a good primary or secondary reference for an advanced undergraduate course, or a beginning research seminar in approximation theory and/or numerical analysis.
      

24. Hua biography
    
    • Hua's lucid analysis caught the eye of a discerning professor at Quing Hua University in Beijing, and in 1931 Hua was invited, despite his lack of formal qualification and not without some reservations on the part of several faculty members, to join the mathematics department there.
      
    • By now he had published widely on questions within the orbit of Waring's problem (also on other topics in diophantine analysis and function theory) and he was well prepared to take advantage of the stimulating environment of the Hardy-Littlewood school, then at the zenith of its fame.
      
    • In 1918 Hardy and Ramanujan returned to the case k = 2 in order to determine the number of representations of an integer as the sum of s squares by means of Fourier analysis, an approach inspired by their famous work on partitions, and they succeeded.
      
    • In the closing years of the Kunming period Hua turned his interests to algebra and to analysis, as much as anything for the benefit of his students in the first instance, and soon began to make original contributions in these subjects too.
      
    • Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains came out in 1958 and was translated into Russian in the same year, followed by an English translation by the American Mathematical Society in 1963.
      
    • Their theory was set out in Applications of Number Theory to Numerical Analysis, which was published much later, in 1978, and by Springer in English translation in 1981.
      
    • There are several joint papers on numerical analysis (with Wang Yuan) and on optimisation (with Ke Xue Tong Bao) in the 1970s, but these are probably based on work done earlier; there are also expository articles and texts derived from the vast teaching and consulting experience he accumulated over the years.
      

25. Householder biography
    
    • Here he changed topic, leaving behind his research interest of mathematical biology and moving into numerical analysis which was increasing in importance due to the advances in computers.
      
    • Even before this first publication in numerical analysis, Householder had been appointed Head of the Mathematics Panel of the Oak Ridge National Laboratory in 1948.
      
    • This role certainly did not prevent him from taking a leading role in research in numerical analysis in general and in numerical linear algebra in particular.
      
    • Of particular importance is his appreciation of the value of elementary hermitian matrices in numerical analysis.
      
    • In 1964 Householder published one of his most important books The theory of matrices in numerical analysis.
      
    • Without question, this book represents one of the real highs in scholarly attainment in numerical analysis, and as such, it belongs on the shelves of students and researchers alike in this field.
      
    • For his impact and influence on computer science in general and particularly for his contributions to the methods and techniques for obtaining numerical solutions to very large problems through the use of digital computers, and for his many publications, including books, which have provided guidance and help to workers in the field of numerical analysis, and for his contributions to professional activities and societies as committee member, paper referee, conference organiser, and society President.
      

26. Carleson biography
    
    • During his career as a mathematician Carleson has been influential in several major areas of analysis and dynamical systems over nearly half a century of mathematical activity.
      
    • His contributions have provided future generations with tools to carry out a systematic study of analysis and dynamical systems.
      
    • As so often in his work, not only did he solve the problem but in doing so he introduced what are today called 'Carleson measures' which went on to become a fundamental tool in complex analysis and harmonic analysis.
      
    • for his profound and seminal contributions to harmonic analysis and the theory of smooth dynamical systems.
      
    • Carleson's work has forever altered our view of analysis.
      
    • His research in analysis is a series of towering and fundamental discoveries.
      

27. Zaanen biography
    
    • As a student, he came into contact with the ideas of modern analysis via Zygmund's book on trigonometric series and Banach's book on linear transformations.
      
    • During three years in Bandoeng he was occupied with writing the functional analysis text Linear analysis.
      
    • The book is a valuable contribution to the growing literature of textbooks on Functional Analysis.
      
    • After three years in Indonesia, Zaanen returned to the Netherlands where he was appointed as Professor of Analysis in the Technical University of Delft in 1950.
      
    • During this period Zaanen made essential contributions to several parts of mathematics, mainly in functional analysis, integration theory and Riesz space theory.
      
    • The first, Linear analysis.
      

28. Rademacher biography
    
    • Since its discovery, Rademacher's orthonormal system has been utilised in many instances in several areas of analysis.
      
    • The second point is that analytic number theory is not merely a device for proving number theoretical results with the aid of analysis, but that it is really a thorough fusion of analysis and arithmetic in which the main interest is often as much on the analytical part as on the arithmetical part.
      
    • In addition to the significant contributions to real analysis and measure theory which we have briefly mentioned above, he contributed to complex analysis, geometry, and numerical analysis.
      
    • serve not only as a fitting memorial to a great mathematician and human being, but also provide excellent examples of how mathematics should be presented, and serve as leisurely but authentic introductions to some fascinating parts of analysis and number theory.
      

29. Calderon biography
    
    • The Calderon-Zygmund theory changed the direction of mathematical analysis, each bringing a distinctive flavour to the theory [The Guardian (May, 1998).',4)">4]:- .
      
    • Calderon's influence on analysis and related areas is due in large part to the many methods that he invented and perfected.
      
    • In modern Fourier analysis, theorems are usually less important than the techniques developed to prove them.
      
    • Calderon's techniques have been absorbed as standard tools of harmonic analysis and are now propagating into nonlinear analysis, partial differential equations, complex analysis, and even signal processing and numerical analysis.
      

30. Fubini biography
    
    • Fubini's interests were exceptionally wide moving from his early work on differential geometry towards analysis.
      
    • He taught courses on these analysis topics at both the Politecnico and the University in Turin.
      
    • In addition to the areas of analysis detailed above, he worked on the calculus of variations where he studied reducing Weierstrass's integral to a Lebesgue integral and also he worked on the expression of surface integrals in terms of two simple integrations.
      
    • Another analysis topic he studied was non-linear integral equations.
      
    • His contributions opened new paths for research in several areas of analysis, geometry, and mathematical physics.
      
    • This last textbook was one of an impressive collection of important textbooks on analysis which included books which described analysis courses which he had given and also books which were collections of problems.
      

31. Ibrahim biography
    
    • I have found that contemporary geometers have neglected the method of Apollonius in analysis and synthesis, as they have in most of the things I have brought forward, and that they have limited themselves to analysis alone in so restrictive a manner that they have led people to believe that this analysis did not correspond to the synthesis effected.
      
    • Another work is On the method of analysis and synthesis, and the other procedures in geometrical problems which contains a systematic exposition of analysis, synthesis and related subjects, with many easy examples.
      
    • This is in contrast to The selected problems in which 41 difficult geometrical problems are solved, usually by analysis only, without a discussion of the number of solutions or conditions which make the solutions possible.
      
    • It also provides a critical analysis of the observations underlying Ptolemy's solar theory, and Ibrahim ibn Sinan provides his own theory of the sun.
      

32. Polya biography
    
    • When several years later Polya decided to write a problem book on analysis he knew that it was not a task he could accomplish without help, so he turned to Szego and over a number of years the two assembled a wonderful collection of problems.
      
    • What was the great novelty which made Polya and Szego's book of analysis problems so different? It was Polya's idea to classify the problems not by their subject, but rather by their method of solution.
      
    • Polya and Szego approached the publisher Springer in 1923 with their idea for a two volume work and in 1925 Aufgaben und Lehrsatze aus der Analysis appeared.
      
    • His basic research contributions span complex analysis, mathematical physics, probability theory, geometry, and combinatorics.
      
    • a remarkable theorem in a remarkable paper, and a landmark in the history of combinatorial analysis.
      
    • Polya's interest in complex analysis led him to investigate singularities of power series, gap theorems, power series with integral coefficients and those taking integral values at the positive integers, the Polya representation for entire functions of exponential type, and the location of zeros.
      
    • Polya and Szego's Problems and Theorems in Analysis .
      

33. Roy biography
    
    • He made important contributions to multivariate analysis, working on his own and also collaborating with other members of the group.
      
    • A sample of the papers Roy published during this period follows: The use and distribution of the Studentized D2-statistic when the variances and covariances are based on k samples (1940), On hierarchical sampling, hierarchical variances and their connexion with other aspects of statistical theory (1940), The distribution of the root-mean-square of the second type of the multiple correlation co-efficient (1940), Analysis of variance for multivariate normal populations: the sampling distribution of the requisite p-statistics on the null and non-null hypotheses (1942), Bernoulli's theorem and Tshebycheff's analogue (1945), On a certain class of multiple integrals (1945), Notes on testing of composite hypotheses (1947), and On the construction of an unbiassed and most powerful critical region out of any given statistic (1948).
      
    • He published Some aspects of multivariate analysis in 1957, a book which brought together many of the ideas Roy had published.
      
    • This monograph does not attempt to cover the entire area of multivariate analysis, the statistical analysis of samples from multivariate normal populations, or even a major part of it.
      
    • In chapter 15, the last of the monograph, some nonparametric generalizations of analysis of variance and multivariate analysis applied to categorized data in contingency tables are considered ..
      

34. Titchmarsh biography
    
    • From [Hardy] I learnt what mathematical analysis is, and at his suggestion I devoted myself to research in pure mathematics.
      
    • Not only did he lecture in London, where he supervised doctoral students, but he also began publishing high quality research papers on mathematical analysis.
      
    • Titchmarsh, from his earliest research days, displayed a power of analysis that marked him out as a mathematician whose reputation would be world wide.
      
    • All Titchmarsh's work was in analysis, in fact he refused to lecture on any other topic.
      
    • in recognition of his distinguished researches on the Riemann zeta-function, analytic theory of numbers, Fourier analysis and eigenfunction expansions.
      
    • He was a scholarly man who sat in his room and wrote beautiful books - impeccable, effectively written textbooks, from which many students have learnt their complex analysis.
      

35. Rado biography
    
    • However unlike Rado, who had only just begun his university studies, Helly was already a research mathematician who had made remarkable progress in his work on functional analysis, proving the Hahn-Banach theorem in 1912.
      
    • At University of Szeged his teachers included Alfred Haar and Frigyes Riesz and, with an interest in analysis coming from his contacts with Helly, he undertook research under Riesz's supervision.
      
    • Thus far mathematical analysis has not been able to envisage any general method which would permit us to begin the study of this beautiful question.
      
    • He was invited to speak at the International Congress of Mathematicians in 1950 in Cambridge, Massachusetts and he chose a similar theme to his American Mathematical Society Colloquium Lectures, lecturing on Applications of area theory in analysis.
      
    • Their theory was fully explained in the important monograph Continuous transformations in analysis : With an introduction to algebraic topology published in 1955.
      
    • Around this time he lectured on The Mathematical Theory of Rigid Surfaces: An Application of Modern Analysis at a conference at the University of North Carolina sponsored by the National Science Foundation.
      

36. Rey Pastor biography
    
    • In 1911, Pastor was appointed secretary of the society and, in the same year, he became Professor of Mathematical Analysis at the University of Oviedo.
      
    • His second course, given in 1921, was a specialised one for engineering students and included the following topics: functions of a complex variable, conformal mapping, advanced geometry (non-euclidean), mathematical analysis and mathematical methodology.
      
    • In 1927, he was given a permanent appointment at the University of Buenos Aires and held two chairs: one of Mathematical Analysis and the other of Higher Geometry.
      
    • In 1931, Rey Pastor published one of his most elegant works on analysis in the Rendiconti del Circolo Matematico di Palermo, an Italian mathematical journal.
      
    • In the introduction to Algabraic Analysis, Rey Pastor comments that rather than follow the general tendency of elevating elemental problems to the point of abstraction, it is his goal to simplify complicated questions whilst maintaining a rigorous approach.
      
    • According to Rey Pastor however, it is a didactic mistake and historically absurd to attempt to approach the concepts of analysis in this contrary manner.
      

37. Daubechies biography
    
    • The use of wavelets as an analytical tool is like Fourier analysis - simple and yet very powerful.
      
    • In fact, wavelets are an extension of Fourier analysis to the case of localization in both frequency and space.
      
    • And like Fourier analysis, it has both a theoretical side and practical importance.
      
    • Ian Stewart has described a number of applications of wavelet analysis.
      
    • Perhaps the best-known application of wavelet analysis to date derived from the U.S.
      
    • her deep and beautiful analysis of wavelets and their applications.
      

38. Littlewood biography
    
    • It was an aspect which he enjoyed, delivering courses on his own wide areas of interest in analysis.
      
    • Almost all of Littlewood's mathematical research was in classical analysis, but in this area he looked at a remarkable range of subjects and he used an even broader range of techniques in proving his results.
      
    • Monthly 103 (10) (1996), 833-845.',16)">16], and in particular the work on van der Pol's equation is discussed in [Harmonic analysis and nonlinear differential equations, Riverside, CA, 1995, Contemp.
      
    • Cartwright and Littlewood's analysis of the van der Pol equation and its generalizations led them to explore some interesting topological methods, including the development of a fixed-point theorem for continua invariant under a homeomorphism of the plane.
      
    • They were among the earliest mathematicians to apply Poincare's transformation theory to the analysis of dissipative systems.
      
    • in recognition of his distinguished contributions to many branches of analysis, including Tauberian theory, the Riemann zeta-function, and non-linear differential equations.
      

39. Julia biography
    
    • At the same time he was appointed repetiteur in analysis at the Ecole Polytechnique, examiner at the Ecole Navale, and professor at the Sorbonne.
      
    • This appointment to a professorship at the Sorbonne came without a specific chair, but in 1925 he was named to the Chair of Applications of Analysis to Geometry at the Sorbonne.
      
    • Volume 3 contains four parts: (i) Functional equations and conformal mapping; (ii) Conformal mapping; (iii) General lectures; and (iv) Isolated works in analysis on Implicit function defined by the vanishing of an active function, and on certain series.
      
    • Volume 4 is again in four parts: (i) Functional calculus and integral equations; (ii) Quasianalyticity; (iii) Various techniques of analysis; and (iv) Works concerning Hilbert space.
      
    • About two-thirds of the first volume is devoted to the applications of analysis to geometry.
      
    • In this first volume the essential difficulties of quantum mechanics (some of which concern the fact that Hubert space is not finite dimensional) are merely foreshadowed, the attention being directed in the main to vector analysis in a space of finite dimensions.
      

40. Krein biography
    
    • Krein completed his doctorate at Odessa in the following year and remained on the staff at the university building up one of the most important centres for functional analysis research in the world.
      
    • Not only was Krein dismissed but the whole of the functional analysis school at Odessa was closed down.
      
    • Also from 1944, he held a part-time post as head of the functional analysis and algebra department at the Mathematical Institute of the Ukranian Academy of Science in Kiev.
      
    • Among other important work, Krein wrote eight papers on harmonic analysis and representation theory in the 1940s.
      
    • He also studied analysis on homogeneous spaces and duality theorems.
      
    • Krein brought the full force of mathematical analysis to bear on problems of function theory, operator theory, probability and mathematical physics.
      

41. Schwartz biography
    
    • In the article on Analysis in Encyclopaedia Britannica Francois Treves describes Schwartz's work as follows:- .
      
    • Schwartz's idea (in 1947) was to give a unified interpretation of all the generalized functions that had infiltrated analysis as (continuous) linear functionals on the space Cc of infinitely differentiable functions vanishing outside compact sets.
      
    • He provided a systematic and rigorous description, entirely based on abstract functional analysis and on duality.
      
    • This has led to extensive studies of topological vector spaces beyond the familiar categories of Hilbert and Banach spaces, studies that, in turn, have provided useful new insights in some areas of analysis proper, such as partial differential equations or functions of several complex variables.
      
    • I think every reader of his cited paper, like myself, will have left a considerable amount of pleasant excitement, on seeing the wonderful harmony of the whole structure of the calculus to which the theory leads and on understanding how essential an advance its application may mean to many parts of higher analysis, such as spectral theory, potential theory, and indeed the whole theory of linear partial differential equations ..
      
    • Later work by Schwartz on stochastic differential calculus is described by him in the survey article [Analyse Mathematique et Applications (1988).',5)">5], see also [Mathematical analysis and applications A (New York-London, 1981), 1-25.',4)">4].
      

42. Christoffel biography
    
    • Elwin Christoffel was noted for his work in mathematical analysis, in which he was a follower of Dirichlet and Riemann.
      
    • These papers, which appeared in 1858, are on numerical analysis, in particular numerical integration.
      
    • Christoffel published papers on function theory including conformal mappings, geometry and tensor analysis, Riemann's o-function, the theory of invariants, orthogonal polynomials and continued fractions, differential equations and potential theory, light, and shock waves.
      
    • The Christoffel symbols [ij,k] which he introduced are fundamental in the study of tensor analysis.
      
    • Indeed this influence is clearly seen since this allowed Ricci-Curbastro and Levi-Civita to develop a coordinate free differential calculus which Einstein, with the help of Grossmann, turned into the tensor analysis mathematical foundation of general relativity.
      
    • Christoffel not only contributed to all these fields, but his interests extended to orthogonal polynomials and continued fractions, and the applications of his work to the foundations of tensor analysis, to geodetical science, to the theory of shock waves, to the dispersion of light.
      

43. Gelfand biography
    
    • His work was in functional analysis and he was fortunate to be in a strong school of functional analysis so he received much support from other mathematicians such as A E Plessner and L A Lyusternik.
      
    • Gelfand presented his thesis Abstract functions and linear operators in 1935 which contains important results, but is perhaps even more important for the methods that he used, studying functions on normed spaces by applying linear functionals to them and using classical analysis to study the resulting functions.
      
    • Gelfand's theory of normed rings revealed close connections between Banach's general functional analysis and classical analysis.
      
    • These ideas, apart from their biological significance, served as a starting point for the creation of new methods of finding an extremum, which were succesfully applied to problems of X-ray structural analysis, problems of recognition, ..
      
    • Through his pioneering and monumental work in mathematical sciences, especially in functional analysis - which has experienced tremendous development this century and not only affected other areas of mathematics but has also provided indispensable mathematical tools for the physics of elementary particles and quantum mechanics - he has brought up and inspired many prominent mathematicians in the course of his creative career.
      

44. Turan biography
    
    • The book mentioned here is On a new method of analysis and its applications which was published in 1984.
      
    • In 1953 the author published a book, A new method of analysis and its applications ..
      
    • giving a systematic account of his methods for estimating "power sums", which he had developed (1941-53) into a versatile and powerful technique with numerous applications to Diophantine approximations, zero-free regions for the Riemann zeta function and the error term in the prime number theorem, and to problems in other parts of classical analysis.
      
    • In the opinion of the reviewer this book renders a great service to mathematicians working in a wide area of classical analysis, particularly analytic number theorists; Turan's methods are still of great relevance in current research, and it is particularly gratifying to have all this material within the confines of a single volume.
      
    • The book is a fitting tribute to Turan's remarkable achievements in analysis, and the editors of the manuscript deserve high praise for their efforts in bringing it to publication.
      
    • But this is only a part of the editorial work Turan undertook, being on the editorial boards of Acta Arithmetica, Archiv fur Mathematik, Analysis Mathematica, Compositio Mathematica, Journal of Number Theory, and essentially all Hungarian mathematical journals.
      

45. Lebesgue biography
    
    • Up to the end of the 19th century, mathematical analysis was limited to continuous functions, based largely on the Riemann method of integration.
      
    • His contribution is one of the achievements of modern analysis which greatly expands the scope of Fourier analysis.
      
    • He was appointed maitre de conferences in mathematical analysis at the Sorbonne in 1910.
      
    • Lebesgue held his post at the Sorbonne until 1918 when he was promoted to Professor of the Application of Geometry to Analysis.
      
    • This ninety-two page work also provides an analysis of the contents of Lebesgue's papers.
      

46. Copson biography
    
    • Copson studied classical analysis, asymptotic expansions, differential and integral equations, and applications to problems in theoretical physics.
      
    • There are many books on functional analysis; and some of them seem to go over the preliminaries to the subject far too quickly.
      
    • The aim here is to provide a more leisurely approach to the theory of the topology of metric spaces, a subject which is not only the basis of functional analysis but also unifies many branches of classical analysis.
      
    • to problems in classical algebra and analysis show how much can be done without ever defining a normed vector space, a Banach space or a Hilbert space.
      
    • It was typical of his work, very much on the borderline between mathematics and physical science, and exhibiting technical skill in classical analysis that is rare nowadays.
      

47. Goursat biography
    
    • His teachers included Jean Darboux and Charles Hermite who influenced him to work on analysis and its applications.
      
    • The next 12 years were spent back at Ecole Normale Superieure where his lectures would form the basis of his famous three volume analysis text.
      
    • Then he taught analysis at the University of Paris until his retirement.
      
    • He then produced an impressive series of papers which contributed to almost every area of analysis which was being studied at that time.
      
    • However, his best known work is Cours d'analyse mathematique (1902-13) which introduced many new analysis concepts.
      
    • Edouard Goursat's three-volume 'A Course in Mathematical Analysis' remains a classic study and a thorough treatment of the fundamentals of calculus.
      

48. Briot biography
    
    • From this time on the two school friends began a collaboration on analysis which was to last throughout their careers and result in many joint publications.
      
    • Briot undertook research on analysis, heat, light and electricity.
      
    • His first major work on analysis was Recherches sur la theorie des fonctions which he published in the Journal of the Ecole Polytechnique in 1859, and he also published this work as a treatise in the same year.
      
    • Briot, however, developed a sophisticated mathematical theory to study these properties, and although his work has no great importance to physics, the analysis he had to develop during his working out of the theory led to significant results in the integral calculus and also in the theory of elliptic and abelian functions.
      
    • The physical motivation for the mathematical theories which gave rise to this work in analysis was published by Briot in 1864 when he published his work on light, Essai sur la theorie mathematique de la lumiere and five years later when he published his work on heat, Theorie mecanique de la chaleur.
      

49. Granville biography
    
    • Entering Yale in the autumn of 1945, she began research in functional analysis under Hille's supervision.
      
    • In the final analysis, however, Granville - who wanted to become a teacher since she was a little girl - was unable to accept the highly restrictive terms under which black women could hold academic posts in the early 1950s.
      
    • The work entailed consulting with ordinance engineers and scientists on the mathematical analysis of problems related to the development of missile fuses.
      
    • At first she worked in Washington writing programs for the IBM 650 computer, then in 1957 she moved to New York City to take up a post as a consultant on numerical analysis at the New York City Data Processing Center of the Service Bureau Corporation, which was part of IBM.
      
    • Her job involved undergraduate teaching and she taught both numerical analysis and computer programming.
      

50. Cech biography
    
    • There he lectured on analysis and algebra, becoming a full professor in 1928.
      
    • Cech was interested in geometry but he was appointed to the chair of analysis at Masaryk University since this had been Lerch's chair.
      
    • although geometry was Cech's field of research, Cech had to take over courses in analysis and algebra.
      
    • Cech's interpretation became a very important tool of general topology and also of some branches of functional analysis.
      
    • The conference took place in 1961 under the name Symposium on general topology and its relations to Modern Analysis and Algebra.
      

51. Bremermann biography
    
    • This was an extraordinary period for the famous Munster school in complex analysis, centred round Heinrich Behnke since the 1920s.
      
    • Naturally Bremermann too learned complex analysis and went on to make significant contributions to the field ..
      
    • During this time he continued to produce high quality results in complex analysis continuing to push the results of his doctoral dissertation towards a general solution to the Levi problem.
      
    • The year 1957 saw Bremermann move into a new area of research when he collaborated with the physicists R Oehme and J G Taylor applying his expertise in complex analysis to work on quantum field theory.
      
    • The author has succeeded in writing a book understandable to readers with very little knowledge of functional analysis and topological vector spaces.
      

52. Levy Paul biography
    
    • Finishing his studies at the Ecole des Mines in 1910 he began research in functional analysis.
      
    • Levy became professor Ecole des Mines in Paris in 1913, then professor of analysis at the Ecole Polytechnique in Paris in 1920 where he remained until he retired in 1959.
      
    • As we indicated above Levy first worked on functional analysis [Bull.
      
    • Now it is a fully-fledged branch of mathematics using techniques from all branches of modern analysis and making its own contribution of ideas, problems, results and useful machinery to be applied elsewhere.
      
    • Not only did Levy contribute to probability and functional analysis but he also worked on partial differential equations and series.
      

53. Ahlfors biography
    
    • Among them are Complex analysis (1953), Riemann surfaces (with L Sario) (1960).
      
    • Allow me [EFR] a personal note on Ahlfors' Complex analysis.
      
    • This was the text recommended to me by Copson who taught me complex analysis and it is indeed a tribute to Ahlfors that Copson, who had himself written a superb book on complex analysis, should recommend Ahlfors' book rather than his own.
      
    • I found Ahlfors' Complex analysis beautifully written, an example of the very highest quality in mathematical texts, combining clarity with an excitement for the topic.
      

54. Carlson biography
    
    • From 1927 he became a professor of higher mathematical analysis at the Stockholm University College.
      
    • Such names as Carlson inequality, Carlson - Levin constants, Carlson theorem in complex analysis, Polya - Carlson theorem on rational functions and Carlson theorem on Dirichlet series are well-known in mathematics (see [Inequalities (Cambridge, 1934).
      
    • Different proofs, further generalizations together with some historical remarks and applications in interpolation theory and functional analysis are discussed in [Inequalities (Cambridge, 1934).
      
    • Carlson's theorem in complex analysis, says that if f (z) is an analytic function satisfying |f (z)| ≤ Cek|z|, where k < π for Re z ≥ 0, and if f (z) = 0 for z = 0, 1, 2, ..
      
    • Analysis of operators (New York, 1978).',6)">6]).
      

55. Bourgain biography
    
    • Bourgain has made outstanding contributions across a whole range of topics in analysis.
      
    • Bourgain's work touches on several central topics of mathematical analysis: the geometry of Banach spaces, convexity in high dimensions, harmonic analysis, ergodic theory, and finally, nonlinear partial differential equations from mathematical physics.
      
    • He has an extremely strong analytic power which he often combined with ideas and methods of "soft" analysis to solve a very long list of well-known hard problems from many different areas.
      
    • In 1989 he proved some remarkable results, using analytic and probabilistic methods, which solved the L(p) problem which had been a longstanding one in Banach space theory and harmonic analysis.
      
    • He has been on the editorial boards of many journals including: the Annals of Mathematics, the Journal de l'Institut de Mathematiques de Jussieu, the Publications Mathematiques de l'IHES, the International Mathematical Research Notices, the Journal of Geometrical and Functional Analysis, the Journal d'Analyse de Jerusalem, the Journal of Discrete and Continuous Dynamical Systems, the Journal of Functional Analysis, the Duke Mathematical Journal, the Journal of the European Mathematical Society, and Comptes Rendus of the Academy of Sciences in Paris.
      

56. Pillai biography
    
    • In [Advances in multivariate statistical analysis (Dordrecht-Boston, MA, 1987), xv-xvi.',2)">2] his contributions to Purdue as described as follows:- .
      
    • Pillai's research was in statistics, in particular in multivariate statistical analysis.
      
    • In [Advances in multivariate statistical analysis (Dordrecht-Boston, MA, 1987), xv-xvi.',2)">2] his work is described:- .
      
    • Perhaps his best known contribution is the widely used multivariate analysis of variance test which bears his name.
      
    • This is described in [Advances in multivariate statistical analysis (Dordrecht-Boston, MA, 1987), xv-xvi.',2)">2]:- .
      

57. Beckenbach biography
    
    • First, he almost single-handedly brought to bear the influence that caused the creation in 1948 of the Institute for Numerical Analysis on the UCLA campus.
      
    • The book begins with a study of axiomatics, then examines several classical inequalities of analysis such as the relationship between the arithmetic mean and geometric mean, the Cauchy, Holder, and Minkowski inequalities, and the triangle inequality.
      
    • We have mentioned one such text above, but let us give an incomplete list: College Algebra (1964), Modern Introduction to Analysis (1964), Applied Combinatorial Analysis (1964), Essential os College Algebra (1965), Integrated College Algebra and Trigonometry (1966), Modern School Mathematics (1967), Algebra (1968), Pre-algebra (1970), Modern College Algebra and Trigonometry (1969), Analysis of Elementary functions (1970), Intermediate Algebra for College Students (1971), Modern Analytic Geometry (1972), Concepts of Communications: Interpersonal, Intrapersonal and Mathematical (1972), and College Mathematics for Students of Business and the Social Sciences (1987).
      

58. Haselgrove biography
    
    • Haselgrove spent four months at the California Institute of Technology in Pasadena in 1956-57, continuing work on computers with Fred Hoyle to model stellar evolution, and returned to take up a post as a Senior Lecturer in computing in Manchester University [Manchester Centre for Computational Mathematics, Annual Report: January-December 2003, Numerical Analysis Report No.
      
    • Haselgrove's work in Manchester is described in [Manchester Centre for Computational Mathematics, Annual Report: January-December 2003, Numerical Analysis Report No.
      
    • He also studied numerical analysis.
      
    • Haselgrove's teaching at Manchester is described in [Manchester Centre for Computational Mathematics, Annual Report: January-December 2003, Numerical Analysis Report No.
      
    • Student numbers were relatively small at first, but the course provided a source of research students in Numerical Analysis.
      

59. Riesz biography
    
    • Riesz was a founder of functional analysis and his work has many important applications in physics.
      
    • Many of Riesz's fundamental findings in functional analysis were incorporated with those of Banach.
      
    • His theorem, now called the Riesz-Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space.
      
    • His book Lecon's d'analyse fonctionnelle is one of the most readable accounts of functional analysis ever written.
      
    • Here, in the first half written by himself, we find the old master picturing to us Real Analysis as he saw it, lovingly, leisurely, and with the discerning eye of an artist.
      

60. Koenigs biography
    
    • In 1883 he was appointed as a lecturer in mechanics at the Faculty of Sciences at Bresancon then, two years later, as a lecturer in mathematical analysis at Toulouse.
      
    • He looked at iteration theory in analysis and, following Darboux's plea for a more rigorous approach to analysis, he published papers in 1884 and 1885 on iteration of complex functions using rigorous arguments based on uniform convergence.
      
    • Koenigs contributions to complex analysis are described in [A history of complex dynamics.
      
    • Further, the method should have the necessary breadth and unity, and be possessed of the clearness and directness of geometry and the power and generality of analysis.
      

61. Loyd biography
    
    • He began to develop more unusual puzzles such as the following retrograde analysis problem which he submitted to Musical World in 1859.
      
    • (It is a retrograde analysis problem since you can deduce from the fact that there is a mate in 2 that Black cannot castle - the mate is then easy.) .
      
    • Click HERE for this first retrograde analysis problem.
      
    • Scientists tried it without success, and indeed no single absolutely correct analysis was ever submitted.
      
    • Yet his powers for rapid analysis were almost unrivalled.
      

62. Hammersley biography
    
    • as a graduate assistant at Oxford in the Lectureship in the Design and Analysis of Scientific Experiment.
      
    • No detailed analysis of its content is here made because it would be irrelevant.
      
    • Let us note the title of a few of these papers to indicate the breadth of his interests: Electronic computers and the analysis of stochastic processes (1950); The absorption of radioactive radiation in rods (1951); Capture-recapture analysis (1953); Tables of complete elliptic integrals (1953); Percolation in crystals: gravity crystals (1956); The zeros of a random polynomial (1956); On the statistical loss of long-period comets from the solar system (1961); The mathematical analysis of traffic congestion (1962); Long-chain polymers and self-avoiding random walks (1963); Contribution to discussion on subadditive ergodic theory (1973); The design of future computing machinery for functional integration (1985); and Biological growth and spread (1980).
      

63. Fowler David biography
    
    • He graduated with a first, and then stayed on to do research in analysis for two years ..
      
    • This style extended to writing textbooks such as Introducing Real Analysis which he published in 1973.
      
    • Steve Abbott writes (in a review of another analysis book):- .
      
    • In 1977, when I began my first analysis course, it consisted essentially of a monologue by the lecturer, most of which was simultaneously written on the blackboard for us to copy down.
      
    • On the subject of differentiability he started with chords tending to tangents and the wrote "For what perverse reasons then, shall I shortly be giving a completely different, non-intuitive, non-geometrical definition? This, I know requires some explanation." I still have the book, its spine broken and with most of the pages loose, because it helped me understand analysis.
      

64. Lanczos biography
    
    • His mathematics teacher was Fejer and Lax writes in [Studies in numerical analysis (papers in honour of Cornelius Lanczos on the occasion of his 80th birthday) (London, 1974), ix-xi.',2)">2]:- .
      
    • During his time at Purdue, Lanczos published mathematical physics papers at first but in 1938 he published his first work in numerical analysis.
      
    • In 1949 he moved to the Institute for Numerical Analysis of the National Bureau of Standards in Los Angeles.
      
    • At the Institute for Numerical Analysis he had Otto Szasz, Taussky-Todd and her husband John Todd as colleagues.
      
    • At the Institute for Numerical Analysis, as in many other institutions, there were investigations and suspicions and the atmosphere became unpleasant.
      

65. Hadamard biography
    
    • This theorem was conjectured in the 18th century, but it was not proved until 1896, when Hadamard and (independently) Charles de la Vallee Poussin, used complex analysis.
      
    • This problem was one of the major motivations for the development of complex analysis from 1851 to 1896 when Riemann's outlined proof was finally completed.
      
    • In the following year he published Lecons sur le calcul des variations which helped lay the foundations of functional analysis (he introduced the word functional).
      
    • Then in 1912 he was appointed as professor of analysis at the Ecole Polytechnique where he succeed Jordan.
      
    • He was appointed to Appell's chair of analysis at the Ecole Centrale in 1920 but retained his positions in the Ecole Polytechnique and the College de France.
      

66. Karlin biography
    
    • He was appointed to the California Institute of Technology in 1948 and began publishing papers on functional analysis such as Unconditional convergence in Banach spaces (1948), Bases in Banach spaces (1948), Orthogonal properties of independent functions (1949), and (with L S Shapley) Geometry of reduced moment spaces (1949).
      
    • applied game theory to the analysis of games of pursuit and evasion like a dogfight between warplanes.
      
    • In addition to those already mentioned, he wrote: (with William Studden) Tchebycheff systems: With applications in analysis and statistics (1966); A first course in stochastic processes (1966); and Total positivity.
      
    • In particular he concentrated on the development of mathematical and computational techniques and tools for the analysis of DNA and protein sequences.
      
    • He worked on descriptive and statistical analysis of protein structure properties, including methods for characterizing and comparing protein structures and sequences.
      

67. Hahn biography
    
    • As Menger explains, Hahn was a pioneer in set theory and functional analysis.
      
    • He was interested in real analysis, writing on a variety of different topics in that area.
      
    • Hahn wrote four papers on functional analysis.
      
    • Fourier analysis also interested Hahn, and he looked at singular integrals and orthogonal expansions investigating the validity of the Parseval relation in various circumstances.
      
    • In some papers he looked at generalised harmonic analysis (independently of Norbert Wiener), and he also wrote a short note on Fejer summability.
      

68. Vallee Poussin biography
    
    • Gilbert was an excellent mathematician and the author of a fine analysis textbook.
      
    • Vallee Poussin's first mathematical research was on analysis, in particular concentrating on integrals and solutions of differential equations.
      
    • The clue to two independent proofs being produced at the same time is that the necessary tools in complex analysis had not been developed until that time.
      
    • In fact the solution of this major open problem was one of the major motivations for the development of complex analysis during the period from 1851 to 1896.
      
    • It was [Jordan's Cours d'Analyse] which, as is recorded by Hardy and other mathematicians of his generation, opened their eyes to what analysis really was.
      

69. Magiros biography
    
    • The book [Selected papers of Demetrios G Magiros: Applied mathematics, nonlinear mechanics, and dynamical systems analysis (D.
      
    • Dynamical systems analysis.
      
    • This part includes papers on stability analysis, precessional phenomena and separatrices of dynamical systems.
      
    • The dominant subject in the analysis of dynamical systems is the stability of the ensuing motion.
      
    • Tzafestas, in [S G Tzafestas (ed.), Selected papers of Demetrios G Magiros: Applied mathematics, nonlinear mechanics, and dynamical systems analysis (D.
      

70. Cohen Wim biography
    
    • a thorough survey of applications of the theory of regenerative processes to the analysis of queueing systems.
      
    • The monograph Boundary value problems in queueing system analysis, coauthored with Onno J Boxma, is:- .
      
    • The monograph referred to in this quote is Analysis of random walks (1992):- .
      
    • This monograph deals with the analysis of random walks that live in the nonnegative orthants of Rnand get absorbed or reflected at the boundary.
      
    • The motivation for the analysis arises from queueing models stemming from computer systems and telecommunication engineering.
      

71. Singer biography
    
    • Singer is justifiably famous among mathematicians for his deep and spectacular work in geometry, analysis, and topology, culminating in the Atiyah-Singer Index theorem and its many ramifications in modern mathematics and quantum physics.
      
    • Singer's series of five papers with Michael F Atiyah on the Index Theorem for elliptic operators (which appeared in 1968 - 71) and his three papers with Atiyah and V K Patodi on the Index Theorem for manifolds with boundary (which appeared in 1975 - 76) are among the great classics of global analysis.
      
    • They have spawned many developments in differential geometry, differential topology, and analysis ..
      
    • However, [the Index Theorem] represents only a small part of his contributions to geometry and analysis.
      
    • for their discovery and proof of the index theorem, bringing together topology, geometry and analysis, and their outstanding role in building new bridges between mathematics and theoretical physics.
      

72. Weatherburn biography
    
    • He took me through the topics in his two books on vector analysis, and perhaps also some differential geometry..
      
    • He was neat and clear and interesting, and for me it was a very easy and efficient way of mastering vector analysis.
      
    • Certainly vector analysis was not universally accepted at this time and Weatherburn fought the battle for its acceptance against opposition from people such as Harold Jeffreys.
      
    • When Weatherburn published the first of his two volumes on vector analysis in 1921 he wrote in the introduction:- .
      
    • At about this time his research interests changed from vector analysis to differential geometry.
      

73. Pompeiu biography
    
    • 26 (1978), 309-329.',9)">9] and traces their influence on the development of analysis.
      
    • There is no doubt that Pompeiu's preferred area was analysis, especially complex analysis, but he achieved remarkable results in other areas such as mechanics.
      
    • This simple remark has led to many interesting problems in analysis known as the problem of Pompeiu.
      
    • In [\'Gheorghe Titeica and Dimitrie Pompeiu\' Symposium on Geometry and Global Analysis, Bucharest, 1973 (Editura Acad.
      

74. Robinson biography
    
    • Robinson's most famous invention was non-standard analysis which he introduced in 1961.
      
    • I want to emphasise that non-standard analysis was not a sudden tangential direction in which Robinson moved.
      
    • Rather, it was the systematic application of the same viewpoint which he earlier applied to algebra to the study of analysis.
      
    • In 1966 Robinson published his famous text Non-standard analysis.
      

75. Rogers James biography
    
    • [Ramanujan (New York, 1940).',2)">2], [q-series: their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra, (Providence, 1986).',4)">4], [Math.
      
    • They are therefore stated without proof in the second volume of MacMahon's "Combinatory Analysis".
      
    • [Real Analysis.
      
    • Wiley, New York 1984).',3)">3], [Real Analysis and Probability (Wadsworth, 1989).',5)">5], [Math.
      

76. Stiefel biography
    
    • Stiefel's declared goal was to advance numerical analysis.
      
    • Within a few years Zurich rose to be one of the foremost centres in numerical analysis.
      
    • These topics include possible number systems, the questions of "fixed" vs "floating" point and complementation, the arithmetic processes, the grouping of numbers to achieve higher than normal precisions, conversion between number systems, the structure of finite approximation methods, error analysis, programming and coding as well as the physical organs of a machine.
      
    • Unlike the majority of introductory texts on numerical analysis, the present one reflects this interest in a small number of algorithms of broad applicability.
      

77. Cauchy biography
    
    • At the Ecole Polytechnique he attended courses by Lacroix, de Prony and Hachette while his analysis tutor was Ampere.
      
    • In 1815 Cauchy lost out to Binet for a mechanics chair at the Ecole Polytechnique, but then was appointed assistant professor of analysis there.
      
    • Cauchy's creative genius found broad expression not only in his work on the foundations of real and complex analysis, areas to which his name is inextricably linked, but also in many other fields.
      
    • Cauchy's theorem in Complex analysis .
      

78. Whiteside biography
    
    • It is still widely parroted in secondary histories of mathematics that in his Philosophiae Naturalis Principia Mathematica (first edition, London, 1687) Newton recast into a superficially classical form dynamical results which he had derived by an equivalent prior fluxional analysis, but which he opted not to put to the public in their original dress.
      
    • The well known preliminary fluxional analysis of the solid of revolution of least resistance is unique, and Newton made no attempt to do other than state its result in the book as published (Book 2, Prop.
      
    • 1 - 14, especially 10 where he uses a proto-Lagrangian analysis to deduce a third-order defining differential equation).
      
    • No whiff of any fluxional analysis is found here.
      

79. Steinhaus biography
    
    • by Steinhaus and Banach, concentrated mainly on functional analysis and its diverse applications, the general theory of orthogonal series, and probability theory.
      
    • to focus on research in functional analysis and related topics.
      
    • It was a very big class, and the analysis lecture was attended by over 220 students squeezed into a smallish and poorly ventilated lecture room, standing in the aisles, and sitting on the window sills.
      
    • He did important work on functional analysis, but he himself described his greatest discovery in this area as Stefan Banach.
      

80. Fourier biography
    
    • In 1797 he succeeded Lagrange in being appointed to the chair of analysis and mechanics.
      
    • Fourier returned to France in 1801 with the remains of the expeditionary force and resumed his post as Professor of Analysis at the Ecole Polytechnique.
      
    • the manner in which the author arrives at these equations is not exempt of difficulties and that his analysis to integrate them still leaves something to be desired on the score of generality and even rigour.
      
    • If they had illuminated this branch of physics by important and general views and had greatly perfected the analysis of partial differential equations, if they had established a principal element of the theory of heat by fine experiments ..
      

81. Weierstrass biography
    
    • In his lectures of 1859/60 Weierstrass gave Introduction to analysis where he tackled the foundations of the subject for the first time.
      
    • Weierstrass's approach still dominates teaching analysis today and this is clearly seen from the contents and style of these lectures, particularly the Introduction course.
      
    • Known as the father of modern analysis, Weierstrass devised tests for the convergence of series and contributed to the theory of periodic functions, functions of real variables, elliptic functions, Abelian functions, converging infinite products, and the calculus of variations.
      
    • because his critical sense invariably compelled him to base any analysis on a firm foundation, starting from a fresh approach and continually revising and expanding.
      

82. Al-Haytham biography
    
    • Rashed examines ibn al-Haytham's attempt to prove it in Analysis and synthesis which, as Rashed points out, is not entirely successful [The development of Arabic mathematics : between arithmetic and algebra (London, 1994).',7)">7]:- .
      
    • Ibn al-Haytham's main purpose in Analysis and synthesis is to study the methods mathematicians use to solve problems.
      
    • The ancient Greeks used analysis to solve geometric problems but ibn al-Haytham sees it as a more general mathematical method which can be applied to other problems such as those in algebra.
      
    • In this work ibn al-Haytham realises that analysis was not an algorithm which could automatically be applied using given rules but he realises that the method requires intuition.
      

83. Bauer biography
    
    • Lectures Bauer gave in the summer semester of 1965 at Hamburg were published as Harmonische Raume und ihre Potentialtheorie (1966) and further lectures, inspired by Dieudonne's book Foundations of modern analysis appeared as two separate texts Differential- und Integralrechnung.
      
    • These latter two texts give an excellent account of the basic concepts of analysis.
      
    • the theory of multidimensional Lebesgue integration as a tool for handling integrals involved in problems of analysis and mathematical statistics (the gamma function, the Gauss distribution function, potential theory, the volume of the n-dimensional sphere, etc.).
      
    • Professor Bauer is involved in research in integration theory, functional analysis (convexity and approximation theory), potential theory, and Markov processes.
      

84. Specker biography
    
    • He attended Bernays' seminar on Axiomatics and Logistics and one of the topics studied led to Specker's paper Nicht konstruktiv beweisbare Satze der Analysis (1949).
      
    • He also attended Deane Montgomery's seminar and discussed problems on recursive analysis with Godel.
      
    • Geneve, Geneva, 1982), 11-24.',5)">5] where his 32 publications up to 1979 are divided into 10 categories: topology, recursive analysis, combinatorial set theory, type theory, axiomatic set theory, Ramsey's theorem, arithmetic, logic of quantum mechanics, algorithms, and miscellaneous.
      
    • Examples of his later papers are The fundamental theorem of algebra in recursive analysis (1969), Die Entwicklung der axiomatischen Mengenlehre (1978), (with H Kull) Direct construction of mutually orthogonal Latin squares (1987), Application of logic and combinatorics to enumeration problems (1988).
      

85. Gronwall biography
    
    • Only a mathematician with Gronwall's gift for analysis and most uncommon grasp of the literature of chemistry and physics could have contributed the elegant solution which he gave.
      
    • Gronwall's work contains classical analysis (Fourier series, Gibbs phenomenon, summability theory, Laplace and Legendre series), differential and integral equations, analytic number theory (transcendental numbers, divisor function, L-function of Dirichlet), complex function theory (Dirichlet L-series, conformal mappings, univalent functions), differential geometry, mathematical physics (problems of elasticity, ballistics, induction, potential theory, kinetic theory of gases, optics), nomography, atomic physics (wave mechanics of hydrogen and helium atom, lattice theory of crystals) and physical chemistry where he is especially known as a very important contributor.
      
    • His command of the classical tools of analysis was superb; he worked in practically all the main fields of analysis and left a mark for himself in several.
      

86. Banach biography
    
    • is sometimes said to mark the birth of functional analysis.
      
    • to focus on research in functional analysis and related topics.
      
    • Banach founded modern functional analysis and made major contributions to the theory of topological vector spaces.
      
    • The importance of Banach's contribution is that he developed a systematic theory of functional analysis, where before there had only been isolated results which were later seen to fit into the new theory.
      

87. Stolz biography
    
    • He was charmed by Weierstrass's approach to analysis and began to investigate problems in that area; these have proved to be his most significant contributions.
      
    • He later dedicated an increasing part of his research to real analysis, in particular to convergence problems in the theory of series, including double series; to the discussion of the limits of indeterminate ratios; and to integration.
      
    • In the 1870s Weierstrass's ε, δ approach to analysis became to standard approach and, in B Bolzano's Bedeutung in der Geschichte der Infinitesimalrechnung (1881), Stolz pointed out that Bolzano had suggested a similar approach even before Cauchy had attempted his own way of making analysis more rigorous.
      

88. Delsarte biography
    
    • It was during his regular visits to Paris during 1934-35 that Delsarte became heavily involved in the Bourbaki project to write a new analysis textbook which expanded into the remarkable Elements de Mathematique.
      
    • In October 1936 he was appointed professor of higher analysis at Nancy.
      
    • Delsarte worked in analysis extending work on series expansions due to Whittaker and Watson.
      
    • He was greatly influenced by their text A Course of Modern Analysis and by Watson's Treatise on the Theory of Bessel Functions.
      

89. Szego biography
    
    • He cooperated with Polya in bringing out a joint Problem Book: Aufgaben und Lehrsatze aus der Analysis, vols I and II (Problems and Theorems in Analysis ) (1925) which has since gone through many editions and which has had an enormous impact on later generations of mathematicians.
      
    • The book Aufgaben und Lehrsatze aus der Analysis, the result of our cooperation, is my best work and also the best work of Gabor Szego.
      
    • Polya and Szego's Problems and Theorems in Analysis .
      

90. Casorati biography
    
    • On this and later journeys, for example he discussed the foundations of analysis with Kronecker and Weierstrass.
      
    • He taught geodesy and analysis at Pavia from 1865 to 1868 when he moved to Milan where he taught until 1875, although he continued to hold the chair at Pavia.
      
    • Leaving Milan he returned to Pavia in 1875 where he taught analysis until his death.
      
    • The paper [Historia Mathematica 5 (2) (1978), 139-166.',9)">9] contains a careful analysis which shows convincingly that, although Weierstrass and Casorati were in correspondence, it was Casorati who gave the first proof.
      

91. Wilkinson biography
    
    • In [Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002.',9)">9] Wilkinson makes the interesting comment that if the war had only lasted for three years he would almost certainly have returned to Cambridge and resumed his research on classical analysis.
      
    • He continued work becoming more involved in writing many high quality papers on numerical analysis, particularly numerical linear algebra.
      
    • In numerical linear algebra he developed backward error analysis methods.
      
    • As well as the large numbers of papers on his theoretical work on numerical analysis, Wilkinson developed computer software, working on the production of libraries of numerical routines.
      

92. Moore Eliakim biography
    
    • Moore was a fiery enthusiast, brilliant, and keenly interested in the popular mathematical research movements of the day; Bolza, a product of the meticulous German school of analysis led by Weierstrass, was an able, and widely read research scholar; Maschke was more deliberate than the other two, sagacious, brilliant in research, and a most delightful lecturer in geometry.
      
    • The third interest that Moore took up after 1906 was on the foundations of analysis [Dictionary of Scientific Biography (New York 1970-1990).',1)">1]:- .
      
    • He diligently advanced general analysis, which for him meant the development of a theory of classes of functions on a general range.
      
    • Throughout his work in general analysis, Moore stressed fundamentals, as he sought to strengthen the foundations of mathematics.
      

93. Golub biography
    
    • Mr Golub has been studying the problems associated with factor analysis and is also working on other problems associated particularly with matrix operations.
      
    • He has programmed Rao's Maximum Likelihood Factor Analysis Method, and has obtained new results, which he will publish.
      
    • This summer, he presented a paper on tests of significance in factor analysis at the International Psychological Congress in Montreal, and in September will present another at the meeting of the American Psychological Association in New York.
      
    • So I was no longer doing statistics, although I was getting my degree in statistics, I was doing numerical analysis.
      

94. Lopatynsky biography
    
    • Lopatynsky's first papers were on analysis: On uniform convergence (1929); Embedding of a Riemannian space in a Euclidean space (1934); (with L P Fridolina) The justification of mathematics, a critical situation (1934); and Limiting values of an analytic function on a set of singular points of measure greater than zero on a rectified curve (1935).
      
    • This book makes the reader familiar with the basic notions and facts of algebra, topology, and functional analysis, and gives a general idea how to apply these notions to the theory of differential equations.
      
    • More detailed presentations can be found in many monographs on topology and functional analysis which will be cited systematically in this text.
      
    • We illustrate the theoretical material with an analysis of the solution of many examples.
      

95. Menshov biography
    
    • In 1933 a new chair of Analysis and Theory of Functions was created at Moscow University and Lavrentev appointed.
      
    • In 1938 the Faculty of Mechanics and Mathematics at Moscow University founded two chairs, the chair of the Theory of Functions and the chair of Functional Analysis.
      
    • Lusternik held the chair of Functional Analysis from 1938.
      
    • In 1943 these two chairs were combined and the Department of Theory of Functions and Functional Analysis was created with Menshov as its head.
      

96. Monge biography
    
    • (a) the analogy or correspondence of operations in analysis with geometric transformations; .
      
    • (b) the genetic classification and parametrisation of surfaces through analysis of the movement of generating lines.
      
    • Monge regarded analysis as being [Stud.
      
    • new approach addressed itself to the most profound, intimate and universal relations in space and their transformations, putting him in a position to interconnect geometry and analysis in a fertile, previously unheard-of fashion.
      

97. Whittaker biography
    
    • He taught a course based on his famous book A Course of Modern Analysis (1902).
      
    • Soon after he arrived in Edinburgh, Whittaker set up the Edinburgh Mathematical Laboratory to give a practical side to his interest in numerical analysis.
      
    • Whittaker's best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics.
      

98. Pitt biography
    
    • Experienced staff were qualified to teach the major areas of analysis, algebra, geometry, statistics, and the mechanics of rigid and deformable bodies, fluids and electromagnetism.
      
    • The first part is devoted to the theory of integration in a sufficiently general context to make it applicable in other branches of analysis.
      
    • This compact account develops the theory as it applies to abstract spaces, describes its importance to differential and integral calculus, and shows how the theory can be applied to geometry, harmonic analysis, and probability.
      
    • The second part also has three chapters: Each one of them considers an area of application: geometry, harmonic analysis and probability.
      

99. Smullyan biography
    
    • This struck me as a fascinating idea, and I straightway set to work and composed a problem in retrograde analysis.
      
    • Although Smullyan had not heard of retrograde analysis at this time, such a field of chess problems did exist.
      
    • During this spell in New York, Smullyan composed many chess problems in retrograde analysis and they later were used in his two books on the topic [The Chess Mysteries of the Sherlock Holmes (New York, 1979).',2)">2] and [The Chess Mysteries of the Arabian Knights (New York, 1981).',3)">3].
      
    • Smullyan's publications have been quite remarkable with the two outstanding books on retrograde analysis chess problems [The Chess Mysteries of the Sherlock Holmes (New York, 1979).',2)">2] and [The Chess Mysteries of the Arabian Knights (New York, 1981).',3)">3], a whole series of marvellous popular puzzle books such as [What is the name of this book? (New York, 1978).',1)">1] and [Satan, Cantor, and Infinity and other mind-boggling puzzles (New York, 1992).',4)">4], and some books on the foundations of mathematics and mathematical logic which are in many ways in a class of their own.
      

100. Fisher biography
     
     • He accepted the post at Rothamsted where he made many contributions both to statistics, in particular the design and analysis of experiments, and to genetics.
       
     • There he studied the design of experiments by introducing the concept of randomisation and the analysis of variance, procedures now used throughout the world.
       
     • The sub-experiments were designed in such a way as to permit differences in their outcome to be attributed to the different factors or combinations of factors by means of statistical analysis.
       
     • It was a handbook for the methods for the design and analysis of experiments which he had developed at Rothamsted.
       

101. Luke biography
     
     • His first appointment was as Head of the Mathematical Analysis Section, a position he held until he was made Senior Advisor for Mathematics in 1961.
       
     • He was one of the first mathematicians to realise the potential of the Tau Method for the analysis and praxis of numerical approximation problems.
       
     • Luke used this method at a time when most of the interest in numerical analysis was still centred around finite difference techniques.
       
     • He gave a wonderful series of lectures on special functions, asymptotic analysis, and approximation theory.
       

102. Bellman biography
     
     • It was clear to me that there was a good deal of good analysis there.
       
     • These include, in addition to those already mentioned: A Survey of the Theory of the Boundedness, Stability, and Asymptotic Behavior of Solutions of Linear and Nonlinear Differential and Difference Equations (1949); A survey of the mathematical theory of time-lag, retarded control, and hereditary processes (1954); Dynamic programming of continuous processes (1954); Dynamic programming (1957); Some aspects of the mathematical theory of control processes (1958); Introduction to matrix analysis (1960); A brief introduction to theta functions (1961); An introduction to inequalities (1961); Adaptive control processes: A guided tour (1961); Inequalities (1961); Applied dynamic programming (1962); Differential-difference equations (1963); Perturbation techniques in mathematics, physics, and engineering (1964); and Dynamic programming and modern control theory (1965).
       
     • Richard Bellman is a towering figure among the contributors to modern control theory and systems analysis.
       
     • His invention of dynamic programming marked the beginning of a new era in the analysis and optimization of large-scale systems and opened a way for the application of sophisticated computer-oriented techniques in a wide variety of problem-areas ranging from the design of guidance systems for space vehicles to pest control and network optimization.
       

103. John biography
     
     • In 1950-51 the National Bureau of Standards appointed him as Director of research for the Institute of Numerical Analysis while at New York University he became involved with the Courant Group, an applied mathematics research team which Richard Courant was building based on the Gottingen model.
       
     • He wrote an important series of papers on numerical analysis, studying ill-posed problems.
       
     • It was in this period that John introduced the space of functions of bounded mean oscillations which plays a fundamental role in harmonic analysis and nonlinear elliptic equations.
       
     • For anyone interested in the analysis of partial differential equations, the work of Fritz John is especially rewarding.
       

104. Eells biography
     
     • Eells was keen to find a permanent appointment at Warwick and in 1969 he was appointed as the first Professor of Analysis.
       
     • It was an appointment which fitted perfectly with the philosophy of the department at that time, which was to feature research in global, rather than traditional, analysis; and it was already becoming known as a centre for the global approach to dynamical systems theory.
       
     • It is tempting to describe global analysis as a holistic approach to mathematics.
       
     • This he did with "Global Analysis" in 1971-72, "Geometry of the Laplace Operator" in 1976-77, and "Partial Differential Equations in Differential Geometry", in 1989-90.
       

105. Bochner biography
     
     • He developed major results in harmonic analysis [Dictionary of Scientific Biography (New York 1970-1990).',1)">1]:- .
       
     • He says he is interested in the whole field of analysis.
       
     • Bochner's years at Princeton continued to break new ground in startling new directions, including functional analysis and group theory.
       
     • His major book on this topic is Harmonic Analysis and the Theory of Probability (1955).
       

106. Puri biography
     
     • Non-parametric methods in univariate analysis.
       
     • Non-parametric methods in multivariate analysis.
       
     • Non-parametric methods in design and analysis of experiments.
       
     • The methodology that he developed in the statistical design and analysis of experiments has paved the way for the development of clinical designs, epidemiological investigations and environmental studies.
       

107. Dini biography
     
     • Dini progressed quickly in his career at the University of Pisa, being appointed to Betti's chair of analysis and higher geometry in 1871.
       
     • In 1877 he was appointed to a second chair in the University of Pisa, from then on holding the chair of infinitesimal analysis in addition to his earlier professorial appointment.
       
     • XII (Wiesbaden, 1985), 591-605.',4)">4], puts Dini's work in context showing that it was carried out at a time when those studying real analysis were seeking to determine precisely when the theorems which had earlier been stated and proved in an imprecise way were valid.
       
     • He published Foundations of the theory of functions of a real variable in 1878; a treatise on Fourier series in 1880; and a two volume work Lessons on infinitesimal analysis with the first volume appearing in 1907 and the second in 1915.
       

108. Alling biography
     
     • The third book 'Foundations of analysis over surreal number fields' appeared in 1987, and includes an account of Conway's theory of surreal numbers.
       
     • Foundations of analysis over surreal number fields is described by L Marki:- .
       
     • As indicated by the title, the book aims at laying the foundations of analysis over these fields.
       
     • On the other hand, the book contains many new results - in fact, analysis over surreal number fields seems to make its first appearance here.
       

109. Baire biography
     
     • The examiners were hard on Baire and he was extremely disappointed with the outcome, but he then determined to examine again his analysis course while researching into the concept of continuity of a general function.
       
     • In 1907 he was promoted to Professor of Analysis at Dijon.
       
     • Despite being unable to work for long periods, Baire wrote a number of important analysis books including Theorie des nombres irrationels, des limites et de la continuite (1905) and Lecons sur les theories generales de l'analyse, 2 Vols.
       
     • Baire made a decisive step in moving away from the intuitive idea of functions and continuity and he saw clearly that a theory of infinite sets was fundamental for rigorous real analysis.
       

110. Wald biography
     
     • Wald also developed generalizations of the problem of gambler's ruin which play an important role in statistical sequential analysis.
       
     • He invented the topic of sequential analysis in response to the demand for more efficient methods of industrial quality control during World War II.
       
     • His main results on sequential analysis and the theory of decision functions, another topic which was founded by him, were gathered together in his monograph Sequential Analysis (1947).
       

111. Fomin biography
     
     • In 1964 Fomin became professor in the Department of the Theory of Functions and Functional Analysis and two years later he was appointed as a professor in the Department of General Control Problems.
       
     • While he was carrying out his work in mathematical biology, Fomin was also studying global analysis which he did from 1966 until his death.
       
     • He wrote Elements of the theory of functions and functional analysis in two volumes.
       
     • This excellent work is used and will be used for the study of functional analysis by many generations of students.
       

112. Trudinger biography
     
     • With the exception of the prerequisites of basic real analysis and linear algebra the material of this book is almost entirely self-contained.
       
     • In 1982 he became Director of the Centre for Mathematical Analysis at ANU, holding this position until 1990.
       
     • In the nonlinear analysis section, the prize goes to N S Trudinger of the Australian National University for the paper "Isoperimetric inequalities for quermassintegrals".
       
     • Today Trudinger coordinates the Applied and Nonlinear Analysis programme at the Australian National University.
       

113. Beurling biography
     
     • It is known that he based his analysis on only 24 hours of traffic intercepted on 25 may 1940.
       
     • A quick analysis showed that the first assumptions probably were correct.
       
     • Beurling worked on the theory of generalized functions, differential equations, harmonic analysis, Dirichlet series and potential theory.
       
     • I presented mimeographed notes of their proofs at the summer school in Harmonic Analysis, organized by Peter Lax at Stanford University in August 1961.
       

114. Goodstein biography
     
     • He entered Magdalene College Cambridge in 1931 and his special subject in his undergraduate course was analysis.
       
     • During the war years he had to cover teaching in a wide range of pure and applied mathematical topics, among them engineering, applied mathematics, analysis and group theory.
       
     • Goodstein worked on mathematical logic, in particular ordinal numbers, recursive arithmetic, analysis, and the philosophy of mathematics.
       
     • He was disappointed that his mathematical analysis text ..
       

115. Koopmans biography
     
     • His doctoral thesis Linear regression analysis of economics was presented to the University of Leiden and he was awarded his doctorate in 1936.
       
     • In this 1944 work he initiated the topic of operational research called 'activity analysis' for which he received (jointly with Kantorovich) the Nobel Prize in Economics for 1975.
       
     • is a masterful introduction to the welfare properties of competitive allocation mechanisms in terms of activity analysis.
       
     • The emphasis lies heavily on applications of the theory of convex sets, and in particular of convex polyhedra, to problems relating to efficient allocation of economic resources, as the following outline indicates: Existence and optimality of competitive equilibrium; equilibrium in international trade; equilibrium over time and capital theory; von Neumann's linear growth model; linear activity analysis and some applications; macroeconomic dynamics; econometrics.
       

116. Smithies biography
     
     • There he took courses by G H Hardy on Fourier analysis, John Whittaker on integral equations, and Ebenezer Cunningham on mechanics.
       
     • He was influenced, by reading books by Banach and Stone, and attending lectures by Courant and von Neumann, to become interested in functional analysis despite Hardy's dislike of abstract mathematics.
       
     • Although he published little in the way of original research in functional analysis after 1940, Smithies was the greatest influence on the development of the subject in Britain.
       
     • In 1982 Smithies published the paper The background to Cauchy's definition of the integral then Cauchy's conception of rigour in analysis in 1986 and he work culminated in the wonderful book Cauchy and the creation of complex function theory in 1997.
       

117. Cramer Harald biography
     
     • The first phase, beginning at the start of World War II, is devoted to extending the 1934 results of Khinchin on univariate stationary stochastic processes to multivariate stationary stochastic processes, and to studying the connections between Khinchin's work and the earlier cognate work on generalised harmonic analysis by Norbert Wiener [in] 1930.
       
     • [It] is devoted to the analysis of non-stationary processes, specifically to determining the extent to which the representations available for stationary process survive for non-stationary ones.
       
     • One finds treated such fields as number theory, function theory, mathematical statistics, probability and stochastic processes, demography, insurance risk theory, functional analysis and the history of mathematics.
       
     • Such highlights as the probabilistic method in the study of asymptotic properties of prime numbers, the spectral analysis of stationary processes, the mathematical foundation of inference and the fundamental work on risk theory all add up to a brilliant career as a scientist.
       

118. Hilbert biography
     
     • Hilbert's work in integral equations in about 1909 led directly to 20th-century research in functional analysis (the branch of mathematics in which functions are studied collectively).
       
     • This work also established the basis for his work on infinite-dimensional space, later called Hilbert space, a concept that is useful in mathematical analysis and quantum mechanics.
       
     • Hilbert contributed to many branches of mathematics, including invariants, algebraic number fields, functional analysis, integral equations, mathematical physics, and the calculus of variations.
       
     • In the analysis of mathematical talent one has to differentiate between the ability to create new concepts that generate new types of thought structures and the gift for sensing deeper connections and underlying unity.
       

119. Mises biography
     
     • Professor Dr Richard von Mises [gave] excellent, very clear and stimulating lectures on applied analysis ..
       
     • He classified his own work, not long before his death, into eight areas: practical analysis, integral and differential equations, mechanics, hydrodynamics and aerodynamics, constructive geometry, probability calculus, statistics and philosophy.
       
     • Much of his work involved numerical methods and this led him to develop new techniques in numerical analysis.
       
     • He made considerable progress in the area of frequency analysis which was started by Venn.
       

120. Duarte biography
     
     • He was professor of geometry, algebra, analysis and mechanics at UCV (1909-1911 and 1936-1939).
       
     • Duarte's most important work in mathematics was done in algebra, number theory and mathematical analysis.
       
     • 11(1948)), with 27 chapters on 250 pages, which contains more information on π and e than has ever before been collected in one place; Lessons on Infinitesimal Analysis (Caracas 1943, 606 pp.) (Spanish) containing material from courses in analysis at UCV during his first three or four years there; and Bibliography of Euclid, Archimedes, Newton (Acad.
       

121. Lagrange biography
     
     • With this work Lagrange transformed mechanics into a branch of mathematical analysis.
       
     • Lagrange was its first professor of analysis, appointed for the opening in 1794.
       
     • the principles of the differential calculus, freed from all consideration of the infinitely small or vanishing quantities, of limits or fluxions, and reduced to the algebraic analysis of finite quantities.
       
     • Lagrange's foundations of the calculus is assuredly a very interesting part of what one might call purely philosophical study: but when it is a case of making transcendental analysis an instrument of exploration for questions presented by astronomy, marine engineering, geodesy, and the different branches of science of the engineer, the consideration of the infinitely small leads to the aim in a manner which is more felicitous, more prompt, and more immediately adapted to the nature of the questions, and that is why the Leibnizian method has, in general, prevailed in French schools.
       

122. Bendixson biography
     
     • He then worked as an assistant to the professor of mathematical analysis from 5 March 1891 until 31 May 1892.
       
     • On 16 June 1905 he became professor of higher mathematical analysis at Stockholm University and from 1911 until 1927 he was rector of the University.
       
     • This came about because of his work in real analysis.
       
     • The analysis problem which intrigued Bendixson more than all others was the investigation of integral curves to first order differential equations, in particular he was intrigued by the complicated behaviour of the integral curves in the neighbourhood of singular points.
       

123. Pearson biography
     
     • These papers contain contributions to regression analysis, the correlation coefficient and includes the chi-square test of statistical significance (1900).
       
     • The paper looked at heredity and argued using a mathematical analysis of large amounts of collected data.
       
     • Biologists in the Royal Society were not, however, prepared to accept biological conclusions based on mathematical analysis.
       
     • if the analysis is correct which seems highly probable, I should be delighted to publish the paper in Biometrika.
       

124. Scheffe biography
     
     • After 1950 Scheffe's research was concerned with aspects of linear models, particularly the analysis of variance.
       
     • He also studied other aspects of analysis of variance such as paired comparisons which he studied in 1952, then mixed models studied two years later.
       
     • His most important work was a comprehensive review of nonparametric statistics in 1943 and his book The Analysis of Variance (1959).
       
     • Lehmann, who worked jointly with Scheffe on a general theory of similar tests, describes the book The Analysis of Variance in [Dictionary of Scientific Biography (New York 1970-1990).',1)">1]:- .
       

125. Aitken biography
     
     • Familiarity with numbers acquired by innate faculty sharpened by assiduous practice does give insight into the profounder theorems of algebra and analysis.
       
     • Aitken's mathematical work was in statistics, numerical analysis, and algebra.
       
     • In numerical analysis he introduced the idea of accelerating the convergence of a numerical method.
       
     • the papers on numerical analysis, statistical mathematics and the theory of the symmetric group continued to write themselves in steady succession, with other small notes on odds and ends.
       

126. Peres biography
     
     • Peres' work on analysis and mechanics was always influenced by Volterra, extending results of Volterra's on integral equations.
       
     • By the time the work was published the ideas it contained were no longer in the mainstream of development of functional analysis since topological and algebraic concepts introduced by Banach, von Neumann, Stone and others were determining the direction of the subject.
       
     • However, the analysis which Peres and Volterra studied proved important in developing ideas of mathematical physics rather than analysis and Peres made good use of them in his applications.
       

127. Yang Hui biography
     
     • In 1261 Yang wrote the Xiangjie jiuzhang suanfa (Detailed analysis of the mathematical rules in the Nine Chapters and their reclassifications).
       
     • Yang's Detailed analysis contained twelve chapters.
       
     • There is other work in Yang's Detailed analysis that we should single out for a mention.
       
     • A year after producing Detailed analysis Yang wrote Riyong suanfa (Mathematics for everyday use).
       

128. Ampere biography
     
     • By this time Ampere had a fair reputation as both a teacher of mathematics and as a research mathematician and on the strength of this reputation he was appointed repetiteur (basically a tutor) in analysis at the Ecole Polytechnique in 1804.
       
     • Ampere and Cauchy shared the teaching of analysis and mechanics and there was a great contrast between the two with Cauchy's rigorous analysis teaching leading to great mathematical progress but found extremely difficult by students who greatly preferred Ampere's more conventional approach to analysis and mechanics.
       

129. Stoilow biography
     
     • Later in his career he wrote articles on some of these outstanding French mathematicians (for example Mathematical work of Henri Lebesgue (Romanian) (1942) and Emile Borel and modern mathematical analysis (Romanian) (1956)).
       
     • In 1919 Stoilow was appointed as a lecturer in the Department of Mathematical Analysis at the University of Iasi.
       
     • He left Iasi in 1921 when he was appointed as a lecturer in the Department of Analysis at Bucharest University.
       
     • Stoilow was known as a Romanian mathematician with influential work in the field of complex analysis.
       

130. Lang biography
     
     • Other books by Lang include Introduction to algebraic geometry (1958), Abelian varieties (1959), Diophantine geometry (1962), Introduction to differentiable manifolds (1962), Algebraic numbers (1964), Linear algebra (1966), Introduction to diophantine approximations (1966), Introduction to transcendental numbers (1966), Algebraic structures (1967), Algebraic number theory (1970), Introduction to algebraic and abelian functions (1972), Differential manifolds (1972), Elliptic functions (1973), SL(R) (1975), Introduction to modular forms (1976), Complex analysis (1977), Cyclotomic fields (1978), Elliptic curves: Diophantine analysis (1978), Undergraduate analysis (1983), Complex multiplication (1983), Riemann-Roch algebra (1985), The beauty of doing mathematics.
       
     • Three public dialogues (1985), Introduction to complex hyperbolic spaces (1987), Introduction to Arakelov theory (1988), Topics in Nevanlinna theory (1990), Basic analysis of regularized series and products (1993), Fundamentals of differential geometry (1999), and Math talks for undergraduates (1999).
       

131. Pasch biography
     
     • His main interests were the foundations of projective geometry and of analysis.
       
     • The results of his efforts have been expressed in his books Vorlesungen uber neuere Geometrie [Teubner, Leipzig, 1882], Einleitung in die Differential- und Integralrechnung [Teubner, Leipzig, 1882], and Grundlagen der Analysis [Teubner, Leipzig, 1908].
       
     • Pasch's analysis relating to the order of points on a line and in the plane is both striking and pertinent to its understanding.
       

132. MacMahon biography
     
     • He gave a Presidential Address to the London Mathematical Society on combinatorial analysis in 1894.
       
     • MacMahon wrote a two volume treatise Combinatory analysis (volume one in 1915 and the second volume in the following year) which has become a classic.
       
     • He wrote An introduction to combinatory analysis in 1920.
       

133. Hardy biography
     
     • My eyes were first opened by Professor Love, who first taught me a few terms and gave me my first serious conception of analysis.
       
     • Hardy's interests covered many topics of pure mathematics - Diophantine analysis, summation of divergent series, Fourier series, the Riemann zeta function, and the distribution of primes.
       
     • for his distinguished part in the development of mathematical analysis in England during the last thirty years.
       

134. Mackenzie Gladys biography
     
     • At Honours level: Natural Philosophy, Mathematics, Final Natural Philosophy, Final Mathematics, Calculus, General Analysis, Heat, Electricity I and II, General Physics, Higher Algebra and Geometry.
       
     • (i) analysis of crystal structure, .
       
     • (iii) spectroscopic analysis of composite radiations; and .
       

135. Fefferman biography
     
     • Fefferman contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalisations of classical low-dimensional results.
       
     • Fefferman's work on partial differential equations, Fourier analysis, in particular convergence, multipliers, divergence, singular integrals and Hardy spaces earned him a Fields Medal at the International Congress of Mathematicians at Helsinki in 1978.
       
     • They continue to provide deep, important problems for analysis.
       
     • for his many fundamental contributions to different areas of analysis..
       
     • Professor Charles Fefferman's contributions and ideas have had an impact on the development of modern analysis, differential equations, mathematical physics and geometry, with his most recent work including his sharp (computable) solution of the Whitney extension problem.
       

136. Fenyo biography
     
     • The material should therefore be regarded as supplementing the methods of classical analysis, algebra and geometry which are now the bread and butter of research workers.
       
     • Their thesis is that the classical theory of linear integral equations produced many ideas for the later development of the theory of linear operators, and in turn functional analysis has helped the further development of integral equations.
       
     • Therefore it is not surprising to find, in addition to his scientific works in Mathematical Analysis, also works on the History of Mathematics, on the Philosophy of Science, and countless others on the applications of mathematics to Medicine, Engineering and Computer Science.
       

137. Kakutani biography
     
     • He read various classic texts including those of Stone and Banach and by the time of his graduation at the end of the three year course he had a good foundation in modern analysis.
       
     • During his years at Osaka University Shizuo Kakutani had already established himself as a research mathematician by publishing a number of papers in functional analysis and ergodic theory, and the 1937 paper in the Japanese Journal on Mathematics on Riemann surfaces.
       
     • Among the areas on which he has written papers we must mention: complex analysis, topological groups, fixed point theorems, Banach spaces and Hilbert spaces, Markov processes, measure theory, flows, Brownian motion, and ergodic theory.
       

138. Picard Emile biography
     
     • He requested exchanging his chair for that of analysis and higher algebra in 1897 so that he was able to train research students.
       
     • Picard made his most important contributions in the fields of analysis, function theory, differential equations, and analytic geometry.
       
     • Picard also applied analysis to the study of elasticity, heat and electricity.
       

139. Sargent biography
     
     • The main emphasis there was on analysis and it was certainly a topic which attracted her.
       
     • After graduating Sargent began to undertake research in analysis but after working for a while she felt that she was not producing results of the exceptionally high standard which she had set herself.
       
     • In 1939 Sargent registered as a doctoral student of Bosanquet who was at that time a Reader in the University of London having interests in analysis which were close to those of Sargent.
       

140. Boutroux biography
     
     • Boutroux's topics range from rational numbers to an analysis of the notion of a function.
       
     • In light of the historical method used by the author, he might better have entitled this book "An Analysis of the Progress of Mathematical Thought".
       
     • Other work included a study of dynamics before Newton where he improved on Duhem's work, and an analysis of the work of Paul Tannery which was not published until 1938, sixteen years after Boutroux's death.
       

141. Levi-Civita biography
     
     • In 1918 he was appointed to the Chair of Higher Analysis at Rome, and two years later he was appointed to the Chair of Mechanics there.
       
     • In [Italian mathematics between the two world wars (Pitagora, Bologna, 1987), 125-141.',18)">18] the authors argue that Levi-Civita was interested in the theory of stability and qualitative analysis of ordinary differential equations for three reasons: his interest in geometry and geometric models; his interest in classical mechanics and celestial mechanics, in particular, the three-body problem; and his interest in stability of movement in the domain of analytic mechanics.
       
     • Their results include the conception of the localized induction approximation for the induced velocity of thin vortex filaments, the derivation of the intrinsic equations of motion, the asymptotic potential theory applied to vortex tubes, the derivation of stationary solutions in the shape of helical vortices and loop-generated vortex configurations, and the stability analysis of circular vortex filaments.
       

142. Kerekjarto biography
     
     • Solomon Lefschetz was at that time writing his own famous monograph on topology in 1924 entitled L'analysis situs et la geometrie algebrique and he wrote a review (published in 1925) of Kerekjarto's book for the Bulletin of the American Mathematical Society [Bull.
       
     • This production, from the pen of a young Hungarian mathematician, who is beginning to be known for his contributions to analysis situs, is welcome for several reasons.
       
     • (b) Combinatorial analysis situs of two-dimensional manifolds.
       

143. Borok biography
     
     • She became a full professor there after an award of her habilitation in 1970, and from 1983 to 1994 she was the Chair of the analysis department.
       
     • Valentina Mikhailovna was considered THE teacher of rigorous analysis in Kharkov State University.
       
     • She also developed and published original lecture notes on a number of other core, as well as more specialized courses, in analysis and partial differential equations.
       

144. Kantorovich biography
     
     • The mathematical formulation of production problems of optimal planning was presented here for the first time and the effective methods of their solution and economic analysis were proposed.
       
     • These other areas include functional analysis and numerical analysis and within these topics he published papers on the theory of functions, the theory of complex variables, approximation theory in which he was particularly interested in using Bernstein polynomials, the calculus of variations, methods of finding approximate solutions to partial differential equations, and descriptive set theory.
       

145. Wolfowitz biography
     
     • This research group was working on problems related to war work and one of the statistical methods it was working on was sequential analysis.
       
     • Wald and Wolfowitz were both attached to the Statistical Research Group at Columbia and they led the research project to develop a theory for sequential analysis.
       
     • We have mentioned Wolfowitz's work on nonparametric inference and his work on sequential analysis.
       

146. Kendall Maurice biography
     
     • One of his first papers came about because of his work at the Ministry of Agriculture and was on factor analysis applied to crop productivity.
       
     • He also published A course in multivariate analysis and Cluster analysis as well a whole series of articles Studies in the history of probability and statistics.
       

147. Madhava biography
     
     • [Madhava] took the decisive step onwards from the finite procedures of ancient mathematics to treat their limit-passage to infinity, which is the kernel of modern classical analysis.
       
     • Rajagopal's claim that Madhava took the decisive step towards modern classical analysis seems very fair given his remarkable achievements.
       
     • We may consider Madhava to have been the founder of mathematical analysis.
       

148. Naimark biography
     
     • Mark Naimark studied mathematics on his own for four years from the age of fifteen completing a university course on analysis.
       
     • Once he had established himself in Moscow he worked on functional analysis and group representations.
       
     • He made a detailed analysis of the infinite-dimensional representations of the semisimple Lie groups.
       

149. Kleene biography
     
     • It had been Oswald Veblen who had proposed that the development of logic required careful analysis by mathematicians.
       
     • He served two terms as the Chair of the Department of Mathematics and one term as the Chair of the Department of Numerical Analysis (later renamed the Department of Computer Science).
       
     • chapter one of this book provides the first systematic exposition of the foundations of intuitionist analysis set out as an axiomatic system treating Brouwer's fan theorem, the bar theorem, and the continuity principle (called Brouwer's principle).
       

150. Young Alfred biography
     
     • He wrote a series of papers On quantitative substitutional analysis which arose out of the classical theory of invariants and contained his results in this area.
       
     • His ninth (and final) paper On quantitative substitutional analysis was published in 1952, eleven years after his death.
       
     • He worked on different aspects of what he called 'Substitutional analysis' and filled numerous folders designated A - Z, A2, AB, ..
       

151. Janovskaja biography
     
     • He used the axiomatic method to lay the logical foundations of geometry, algebraic fields, Galois theory and analysis and his areas of interest had a large influence on his student Neimark.
       
     • The history of mathematics was another topic which attracted Janovskaja and she published work on Egyptian mathematics On the theory of Egyptian fractions (1947), Zeno of Elea's paradoxes, Rolle's criticisms of the calculus in Michel Rolle as a critic of the infinitesimal analysis (1947), Descartes's geometry (see below), and Lobachevsky's work on non-euclidean geometry in papers such as The leading ideas of N I Lobachevsky - a combat weapon against idealism in mathematics (1950), On the philosophy of N I Lobachevsky (1950), and On the Weltanschauung of N I Lobachevsky (1951).
       
     • An analysis is given for the problem of finding geometric solutions for algebraic equations of degree higher than two by locating points of intersection of conic sections with other curves.
       

152. Allan Graham biography
     
     • The material was, to me, a lovely blend of algebraic foundations with a substantial super-structure of real, complex, and functional analysis.
       
     • Allan was appointed to lead and build up a group in modern mathematical analysis; he was very successful in leading the development of a new undergraduate syllabus, and in building up a strong research team.
       
     • The author assumes no previous knowledge of Banach algebra theory, but some acquaintance with the beginnings of functional analysis is assumed as is the general notion of a holomorphic function of several complex variables.
       

153. Mazya biography
     
     • Maz'ya lists his mathematical interests as: linear and non-linear PDEs; asymptotic and numerical methods for PDEs, including homogenization and boundary elements; spectral theory; harmonic analysis; approximation theory; wavelets; elasticity theory; function spaces; ill-posed problems; non-linear potential theory; fluid mechanics; and the history of mathematics.
       
     • All the proofs are complete and rely on undergraduate university courses on real and complex analysis and some basic facts of functional analysis and of the theory of partial differential equations.
       
     • From 30 June to 3 July 2008 the Conference 'Analysis, PDEs and Applications' was held in Rome, and on 25 -27 August 2008 the Nordic-Russian Symposium was held in Stockholm in his honour.
       
     • In addition the American Mathematical Society published Perspectives in Partial Differential Equations, Harmonic Analysis and Applications: A Volume in Honor of Vladimir G Maz'ya's 70th Birthday in their Proceedings of Symposia in Pure Mathematics series.
       

154. Bugaev biography
     
     • His research was mainly on analysis and number theory.
       
     • Bugaev's most important work in number theory was based on an analogy between some operations in number theory and the operations such as differentiation and integration in analysis.
       
     • XII (Wiesbaden, 1985), 651-673.',5)">5] Demidov sees Bugaev's work on the philosophy of mathematics as contributing to the foundation of the school of real analysis.
       

155. Plessner biography
     
     • His interests at this time moved to functional analysis and particularly spectral theory.
       
     • It seems that his interest in functional analysis arose when he read Banach's book of 1932.
       
     • His role in mathematics is however a major one and must be considered as a founder of the Moscow school of functional analysis.
       

156. Lupas biography
     
     • Alexandru and Luciana Lupas, together with Heiner, were editors of the Proceedings of the conference Mathematical analysis and approximation theory which consisted of papers presented to the 5th Romanian-German Seminar on Approximation Theory held in Sibiu from 12 to 15 June 2002.
       
     • Professor at the Department of Mathematics of the University "Lucian Blaga" in Sibiu, Romania, he was a specialist in Approximation Theory, Classical Analysis, Inequalities, Convexity, Numerical Analysis, Special Functions, Finite Operatorial Calculus (Umbral Calculus) and q-Calculus.
       

157. Rolle biography
     
     • He worked on Diophantine analysis, algebra (using methods of Claude Gaspar Bachet de Meziriac involving the use of the Euclidean algorithm) and, to a lesser extent, on geometry.
       
     • This is a cleverly constructed example, but Varignon was able to see the subtle error in Rolle's analysis.
       
     • Rolle was a skillful algebraist who broke with Cartesian techniques; and his opposition to infinitesimal methods, in the final analysis, was beneficial.
       

158. Cunningham Leslie biography
     
     • During World War II he was Superintendent of the Air Warfare Analysis Section, Ministry of Aircraft Production.
       
     • In normal practice the errors are smoothed, but an analysis shows that smoothing may introduce large new errors and that only high frequency components of the tracking errors can be practically eliminated.
       
     • In the analysis the predictor is considered as a linear device and is characterized by its response to the so-called Heaviside impulse function.
       

159. Wilson Edwin biography
     
     • in 1901 and, in the same year, a textbook which he had written on vector analysis was published.
       
     • Vector analysis (1901) was based on Gibbs' lectures and [Dictionary of Scientific Biography (New York 1970-1990).',1)">1]:- .
       
     • This beautiful work, published when Wilson was only twenty-two years old, had a profound and lasting influence on the notation for and the use of vector analysis.
       

160. Caccioppoli biography
     
     • In 1931 he was appointed to the Chair of Algebraic Analysis in Padua and eventually returned to Naples in 1934.
       
     • From then, he taught group theory until 1943 and Mathematical Analysis until his death in 1959.
       
     • Coming back to his main interest in functional analysis he deduced (in Sui teoremi di esistenza di Riemann.
       

161. Kruskal Martin biography
     
     • Kruskal's later work studied soliton equations, asymptotic analysis, and surreal numbers.
       
     • He was led to asymptotic analysis in his plasma physics studies and from there to solutions of Hamiltonian equations as in Asymptotic theory of Hamiltonian and other systems with all solutions nearly periodic (1962).
       
     • In 1986 he received the Potts Gold Medal of the Franklin Institute and then the National Academy of Sciences Award in Applied Mathematics and Numerical Analysis in 1989.
       

162. Kuiper biography
     
     • For example in his paper Analysis of variance (1952) he shows how terms used in factorial design can be conceptionally simplified in the language of linear vector spaces.
       
     • In particular, his technique of the analysis of topsets became an essential tool in almost all work in the area of tight immersions and maps.
       
     • a masterly introduction to the subject and a good exposition of some more advanced topics, concentrating on topological aspects, in particular the analysis of topsets.
       

163. Birkhoff biography
     
     • Also in 1904 he submitted a paper on analysis to the American Mathematical Society.
       
     • During these two years at Harvard the teacher who influenced him most was Bocher who taught him algebra and classical analysis.
       
     • This theory, which resolved in principle one of the fundamental problems arising in the theory of gases and statistical mechanics, has been influential not only in dynamics itself but also in probability theory, group theory, and functional analysis.
       

164. Hormander biography
     
     • There he was taught by Marcel Riesz who lectured to him on classical function theory and harmonic analysis.
       
     • In particular he describes how the main areas developed which are covered by his four volume text The analysis of linear partial differential operators the volumes of which appeared between 1983 and 1985.
       
     • Hormander's text, An Introduction to Complex Analysis in Several Variables, has become a classic dealing with the theory of functions of several complex variables.
       

165. Wiener Norbert biography
     
     • Moreover, it led me very directly to the periodogram, and to the study of forms of harmonic analysis more general than the classical Fourier series and Fourier integral.
       
     • This in turn led him to study harmonic analysis in 1930.
       
     • His work on generalised harmonic analysis led him to study Tauberian theorems in 1932 and his contributions on this topic won him the Bocher Prize in 1933.
       

166. Kober biography
     
     • He became interested in functional analysis and linear operators and, from 1937 to 1939 he published numerous papers in German but in British mathematical journals.
       
     • Kober was a highly productive mathematician working on special functions, functional analysis (in this area Kober's Theorem which appeared A theorem on Banach spaces (1939) is named after him), approximation theory and the theory of functions of a real variable.
       
     • He had a great love of music, and wrote a play "Dance of the Devils", an analysis of Hitler and the Third Reich.
       

167. Mackenzie biography
     
     • At Honours level: Natural Philosophy, Mathematics, Final Natural Philosophy, Final Mathematics, Calculus, General Analysis, Heat, Electricity I and II, General Physics, Higher Algebra and Geometry.
       
     • (i) analysis of crystal structure, .
       
     • (iii) spectroscopic analysis of composite radiations; and .
       

168. De Bruijn biography
     
     • He held this position until September 1960, and it is during this period that he published the remarkable text Asymptotic methods in analysis published by the North-Holland Publishing Company in 1958.
       
     • He lists his interests (on his website) as: Geometry, Number Theory, Classical and Functional Analysis, Applied Mathematics, Combinatorics, Computer Science, Logic, Mathematical Language, Brain Models.
       
     • De Bruijn's famous contributions to mathematics include his work on generalized function theory, analytic number theory, optimal control, quasicrystals, the mathematical analysis of games and much more.
       

169. Hindenburg biography
     
     • Hindenburg hoped for combinatorial operations to have the same importance as those of arithmetic, algebra and analysis but his expectations were not realised.
       
     • ',4)">4], it was Hindenburg's combinatorial analysis which was the main influence on this work.
       
     • It was not only for his school of combinatorial analysis that Hindenburg is famous.
       

170. Haar biography
     
     • Most of Haar's work was in analysis.
       
     • Haar is best remembered, however, for his work on analysis on groups.
       
     • The concept of Haar was used by von Neumann, by Pontryagin in 1934, and Weil in 1940, to set up an abstract theory of commutative harmonic analysis.
       

171. Karman biography
     
     • In 1911, using results from the wind tunnel, he made an analysis of the alternating double row of vortices behind a flat body in a fluid flow which is now known as Karman's Vortex Street.
       
     • They used three dimensional Fourier analysis and periodic boundary conditions in this important study.
       
     • His viewpoint was that of an engineer of an earlier era who may be considered to have discharged his debt to society once he has contrived to "provide an analysis of what would happen if certain things were done"; he thought that "scientists as a group should not try to force or even persuade the government to follow their decisions".
       

172. Taussky-Todd biography
     
     • Hardy helped her obtain a teaching post in a London college in 1937 where she soon met an Irishman Jack (John Todd) who was teaching analysis at a different London College.
       
     • She continued to write papers on matrix theory, group theory, algebraic number theory but she also wrote on numerical analysis.
       
     • In 1955 Taussky-Todd and her husband spent a year's leave at the Courant Institute in New York where she taught a matrix theory course and her husband taught a numerical analysis course.
       

173. Gram biography
     
     • He began working on probability and numerical analysis, two topics whose practical applications in his day to day work in calculating insurance made their study important to him.
       
     • We have already mentioned the very practical applications to forestry which he continued to study at this time, and his work on probability and numerical analysis involved both the theory and its application to very practical situations.
       
     • Gram's work on probability and numerical analysis led him in a natural way to study abstract problems in number theory.
       

174. Shields biography
     
     • Shields' first post was as a Research Instructor in Mathematics at Tulane where he learnt a lot of functional analysis and wrote papers on topological semigroups.
       
     • Shields worked on a wide range of mathematical topics including measure theory, complex functions, functional analysis and operator theory.
       
     • He was one of the world's most versatile practitioners in the art of applying functional analysis to gain insight on and solve problems of classical function theory.
       

175. Black biography
     
     • Two years earlier he had published a work Vagueness: An exercise in logical analysis in the Philosophical Society.
       
     • Black was famed for his contributions to the philosophy of language, the philosophy of mathematics and science, the philosophy of art, conceptual analysis, and his studies of the work of philosophers such as Frege (publishing a major work in 1952) and Wittgenstein (publishing A companion to Wittgenstein's Tractatus in 1964).
       
     • In 1954 Black published Problems of Analysis which examined the problems associated with induction, namely making generalisations and predictions based on a few cases.
       

176. Mazur biography
     
     • Mazur was a close collaborator with Banach at Lvov and became a member of the Lvov School of Mathematics, a group of about a dozen mathematicians working in functional analysis, real functions and probability theory.
       
     • Mazur made important contributions to geometrical methods in linear and non-linear functional analysis and to the study of Banach algebras.
       
     • The award was made in recognition that he was a leading Polish mathematician and a cofounder with Banach of the Polish School of Functional Analysis.
       

177. Post biography
     
     • He reason he did not publish was because he felt that a 'complete analysis' was necessary to gain acceptance.
       
     • The correctness of this result is clearly entirely dependent on the trustworthiness of the analysis leading to the above generalisation..
       
     • for full generality a complete analysis would have to be given of all possible ways in which the human mind could set up finite processes for generating sequences.
       

178. Bishop biography
     
     • He wrote a famous text Foundations of constructive analysis (1967) which aimed to show that a constructive treatment of analysis is feasible.
       
     • Bishop was working on a revision of this text at the time of his death and this was completed and published as Constructive analysis in 1985 by Douglas Bridges:- .
       

179. Leslie biography
     
     • Leslie was a successful professor of mathematics, attracting large classes of students and publishing his lectures in popular textbooks such as the three part work Elements of Geometry, Geometrical Analysis, and Plane Trigonometry (1809).
       
     • He mixed classical mathematical teaching with some new continental approaches to analysis and algebra particularly in his advanced classes.
       
     • John Leslie's versatile but undisciplined intellect was more suited to invention and speculation than to logical analysis.
       

180. Anderson biography
     
     • Thus his emphasis on casual analysis of non-experimental data is a reminder that this important sector of applied statistics is far less developed than descriptive statistics and experimental analysis..
       
     • This led him to nonparametric methods and to the necessity of casual analysis in economics.
       

181. Pincherle biography
     
     • Pincherle worked on functional equations and functional analysis.
       
     • Together with Volterra, he can claim to be one of the founders of functional analysis.
       
     • This work is important both in the development of analysis and in particular the progress of mathematics in Italy.
       

182. Harish-Chandra biography
     
     • His primary interests revolved about the representation theory of reductive groups and harmonic analysis on these groups and their related homogeneous spaces.
       
     • He has built a fundamental theory of representations of Lie groups and Lie algebras, respectively of harmonic analysis on these groups and their homogeneous spaces.
       
     • His scientific work, being a synthesis of analysis, algebra and geometry, is still of lasting influence.
       

183. Benjamin biography
     
     • His particular aim was to show how more abstract mathematical analysis could, as the pioneering Russian school had already begun to demonstrate, really contribute a deeper understanding of different types of flow ..
       
     • his deep analysis of particular problems, such as the similarities in movements of sea breezes, avalanches and air pockets in tubes; why thin vortices on aircraft wings can behave like shock waves and suddenly become thicker and change the whole flow; how tiny bubbles collapse, and hence cause damaging erosion found on propellers; or how the flexible skins of dolphins and, nowadays, 'smart' submarines can damp out fluctuations in the turbulent flow over their skins to increase their speed and reduce the noise heard by nearby prey or predators.
       
     • a careful and thorough analysis of the flows over a simple harmonic wavy boundary which is either (a) rigid (b) a flexible solid or (c) completely mobile, as if it were the interface with a second fluid.
       

184. Ruffini biography
     
     • Cassiani's course at Modena on the foundations of analysis was taken over by Ruffini in 1787-88 although he was still a student at this time.
       
     • Ruffini must have made a good job of the foundations of analysis course he took over from Cassiani for, on 15 October 1788, he was appointed professor of the foundations of analysis.
       

185. Livsic biography
     
     • Livsic took part in the functional analysis seminar and studied analytic functions.
       
     • Krein was dismissed from his post and the school of functional analysis closed.
       
     • He remained there until 1957, publishing results on applications of his functional analysis results to quantum theory.
       

186. Peano biography
     
     • In his third year Francesco Faa di Bruno taught him analysis and D'Ovidio taught geometry.
       
     • We understood that such a subtle analysis of concepts, such a minute criticism of the definitions used by other authors, was not adapted for beginners, and especially was not useful for engineering students.
       
     • It became clear to me that his notation afforded an instrument of logical analysis such as I had been seeking for years ..
       

187. G‰teaux biography
     
     • The name of R Gateaux, killed at the beginning of the war (September 1914), is well known to all those who are interested in functional analysis.
       
     • The memoir on the theory of integrals and potentials in functional analysis is, though last in date (June 1914), that which we publish first.
       
     • It opens a new and important chapter in functional analysis and reading it makes it possible to realise what an immense loss the person of Gateaux is to science.
       

188. Betti biography
     
     • Back in Pisa he moved in 1859 to the chair of analysis and higher geometry.
       
     • His final move was to substitute the chair of celestial mechanics for his chair of analysis and geometry in 1870.
       
     • Dini, who Betti had taught earlier, was appointed to fill his chair of analysis and higher geometry.
       

189. Riesz Marcel biography
     
     • Marcel Riesz's interests ranged from functional analysis to partial differential equations, mathematical physics, number theory and algebra.
       
     • To the consummate skill in handling formulas which is typical of the classical Hungarian school he now added a more abstract, functional analytic view, long before functional analysis had become a commonplace tool.
       
     • His work covered a wide area of analysis and just an enumeration would be too long for a review.
       

190. Rutishauser biography
     
     • Within a few years Zurich rose to be one of the foremost centres in numerical analysis.
       
     • These topics include possible number systems, the questions of "fixed" vs "floating" point and complementation, the arithmetic processes, the grouping of numbers to achieve higher than normal precisions, conversion between number systems, the structure of finite approximation methods, error analysis, programming and coding as well as the physical organs of a machine.
       
     • The present booklet devotes some attention to the problems of doing QD on automatic computers, and belongs in every numerical analysis library.
       

191. Hamming biography
     
     • Hamming also worked on numerical analysis, integrating differential equations, and the Hamming spectral window which is much used in computation for smoothing data before Fourier analysing it.
       
     • His major works include Numerical Methods for Scientists and Engineers (1962), Introduction to applied numerical analysis (1971), Digital filters (1977), Coding and information theory (1980), Methods of mathematics applied to calculus, probability, and statistics (1985), Introduction to applied numerical analysis (1989), The Art of Probability for Scientists and Engineers (1991) and The Art of Doing Science and Engineering : Learning to Learn (1997).
       

192. Besicovitch biography
     
     • He was taught by Markov at the University of St Petersburg where he originally intended to work in mathematical logic but he changed topics to study analysis since the library was not good enough in the logic area.
       
     • At Cambridge Besicovitch lectured on analysis in most years but he also gave an advanced course on a topic which was directly connected with his research interests such as almost periodic functions, Hausdorff measure, or the geometry of plane sets.
       
     • This work was more congenial to him than the abstract developments of, for example, functional analysis.
       

193. Motzkin biography
     
     • We spoke of many different themes running through Motzkin's research and one of these was combinatorial analysis.
       
     • In 1950 he was appointed to the Institute of Numerical Analysis at the University of California, Los Angeles and ten years later he became Professor of Mathematics there.
       
     • Exceptionally broad, the range of his work included beautiful and important contributions to the theory of linear inequalities and programming, approximation theory, convexity, combinatorics, algebraic geometry, number theory, algebra, function theory, and numerical analysis.
       

194. Tikhonov biography
     
     • His first-class achievements in topology and functional analysis, in the theory of ordinary and partial differential equations, in the mathematical problems of geophysics and electrodynamics, in computational mathematics and in mathematical physics are all widely known.
       
     • In fact Tikhonov's work led from topology to functional analysis with his famous fixed point theorem for continuous maps from convex compact subsets of locally convex topological spaces in 1935.
       
     • These results are of importance in both topology and functional analysis and were applied by Tikhonov to solve problems in mathematical physics.
       

195. Kuttner biography
     
     • He was to spend the rest of his career at Birmingham being promoted to lecturer in 1936, Senior Lecturer in 1952, Reader in 1955 and then to the chair of Mathematical Analysis in 1969.
       
     • Mathematical Reviews lists over 120 of his papers, and the continuation of joint papers appearing after his death show clearly that even into his 80s his love for his favourite topics of analysis remained as strong as ever.
       
     • He regularly attended the annual British Mathematical Colloquium and I [EFR] remember him as someone held in great respect by my colleagues who were working in analysis when I began attending these Colloquia in the second half of the 1960s.
       

196. Renyi biography
     
     • As well as undertaking research in analysis she was very successful in encouraging young university students in their research in all branches of mathematics.
       
     • Renyi worked on probability theory which was to be his main research topic throughout his life, but his interests were broad and also covered statistics, information theory, combinatorics, graph theory, number theory and analysis.
       
     • a pure mathematician of massive achievements and towering stature in the classical fields of number theory and analysis.
       

197. Szasz biography
     
     • He did make a research visit spending a year at the Institute of Numerical Analysis at the University of California in Los Angeles but he seemed content to devote the rest of his life to teaching, research, and his students in Cincinnati [Bull.
       
     • Szasz's main work was in real analysis, particularly Fourier series.
       
     • His life and energy were dedicated to the promotion of simple and beautiful problems of mathematics, in particular of the classical analysis.
       

198. Gergonne biography
     
     • In 1813 Gergonne wrote a prize winning essay for the Bordeaux Academy Methods of synthesis and analysis in mathematics.
       
     • Despite the title of the essay, he suggests that the terms "analysis" and "synthesis" should not be used since everyone uses them with a different meaning.
       
     • He noticed the fact that certain forms of geometry yielded theorems which appeared in related pairs, and this led him to a more detailed analysis of why this was so.
       

199. Landen biography
     
     • Landen's work appeared as A Short Discourse Concerning the Residual Analysis published in 1758 and, in a more complete form, in Residual analysis which was published in 1764.
       
     • The problem of rectification of conics was a central question of analysis in the 18th century.
       

200. Remez biography
     
     • He gave courses at these institutions on analysis, differential equations and differential geometry while undertaking research for his doctorate.
       
     • He continued to undertake research in approximation theory, particularly in the constructive theory of functions, and in numerical analysis for the rest of his career.
       
     • Little is presupposed on the part of the reader except the most basic concepts of algebra and analysis.
       

201. Behnke biography
     
     • The first is to give a rigorous detailed account of the classical theory of functions of a complex variable for beginning students who have had prior training in classical real analysis.
       
     • With Hans Grauert, Behnke wrote the paper Analysis in non-compact complex spaces (1960) which was based on a lecture Behnke gave at a conference on analytic functions at Princeton in 1957.
       
     • In addition to his work on complex analysis, Behnke wrote many articles on mathematicians.
       

202. Lax Peter biography
     
     • embodying, as few others do, the unity of abstract mathematical analysis with the most concrete power in solving individual problems.
       
     • Another important cornerstone of modern numerical analysis is the 'Lax Equivalence Theorem'.
       
     • A fairly recent book by Lax is Functional analysis (2002) which, like the linear algebra text, grew out of graduate lectures that Lax gave at the Courant Institute over many years.
       

203. Veblen biography
     
     • Already at this time he had begun to undertake research in topology (or analysis situs as it was then called) and he published Theory on plane curves in non-metrical analysis situs in 1905.
       
     • Analysis Situs (1922) provided the first systematic coverage of the basic ideas of topology and contributed to the development of modern topology.
       

204. Askey biography
     
     • Already attracted towards analysis by the strong analysis school at Washington University, he then went to Harvard University to study for his Master's degree and in 1956 he received his M.A.
       
     • It is impossible in an article like this to give much in the way of details of the impressive publications by Askey on the harmonic analysis of special functions, orthogonal polynomials and special functions, and special functions related to group theory.
       

205. Khinchin biography
     
     • The book Eight lectures on mathematical analysis by Khinchin ran to several editions.
       
     • The book was designed to be used to supplement a standard course on the calculus and gives a careful treatment of some of the basic notions of mathematical analysis.
       
     • The book was written in such a way as to be useful both to mathematicians who wanted to become better acquainted with some applications of analysis to physics, and also to physicists who wanted to understand more about the mathematical foundations for their subject.
       

206. Speiser biography
     
     • Within a few years Zurich rose to be one of the foremost centres in numerical analysis.
       
     • These topics include possible number systems, the questions of "fixed" vs "floating" point and complementation, the arithmetic processes, the grouping of numbers to achieve higher than normal precisions, conversion between number systems, the structure of finite approximation methods, error analysis, programming and coding as well as the physical organs of a machine.
       

207. Hermite biography
     
     • The year 1869 saw him become a professor when he succeeded Duhamel as professor of analysis both at the Ecole Polytechnique and at the Sorbonne.
       
     • Hermite's great love was for analysis and, not surprisingly, he had a great respect for Weierstrass.
       

208. Monte biography
     
     • For example Guidobaldo shows that systems of pulleys can be reduced to problems with levers with some excellent analysis.
       
     • His "Perspectivae libri sex" provided a definitive and often original analysis of the mathematics of perspective projection, in a far more extended way than either Commandino or Benedetti had aimed to do.
       

209. Mahler biography
     
     • This set of notes contains an elementary introduction to the theory of p-adic numbers and their analysis.
       
     • Nevertheless, while many recent books on algebra have short chapters or paragraphs on the subject, a really good introduction to p-adic numbers from the standpoint of elementary analysis does not seem to exist.
       

210. Potts biography
     
     • In addition to research on Ising-type models in mathematical physics and on road traffic analysis, Potts contributed to three other areas of research: operations research, especially networks; difference equations; and robotics.
       
     • The last chapter is devoted to an analysis of several trip distribution models (Hitchcock model, entropy models, and Stouffer's opportunity models).
       

211. Plancherel biography
     
     • Michel Plancherel's main research fields were analysis, mathematical physics and algebra.
       
     • In his work he achieved fundamental results, one of them is the famous Plancherel theorem in harmonic analysis and which is now known in many generalizations (Plancherel measures).
       

212. Vinogradov biography
     
     • These were: fundamental questions of analysis and mathematical physics; special areas of function theory of real variables; number theory and Galois theory; probability theory; theoretical mechanics; applied methods of analysis.
       

213. Weber Heinrich biography
     
     • Weber's main work was in algebra, number theory, analysis and applications of analysis to mathematical physics.
       

214. Atiyah biography
     
     • Michael Atiyah has contributed to a wide range of topics in mathematics centring around the interaction between geometry and analysis.
       
     • This 'index theorem' had antecedents in algebraic geometry and led to important new links between differential geometry, topology and analysis.
       

215. Weldon biography
     
     • Why is this zoologist in our History of Mathematics Archive? His work soon began to involve statistical analysis.
       
     • He extended the statistical analysis that Galton and Quetelet had applied to humans to other zoological species.
       

216. Lame biography
     
     • He lectured on analysis, physics, mechanics, chemistry, and engineering topics.
       
     • It concerns Lame's attempt to spread Cauchy's new ideas of rigorous analysis.
       

217. Uhlenbeck biography
     
     • Of the lectures he attended those on the foundations of analysis he found greatly to his liking, finding that the rigour of analysis was particularly pleasing to him.
       

218. Mittag-Leffler biography
     
     • Mittag-Leffler made numerous contributions to mathematical analysis particularly in areas concerned with limits and including calculus, analytic geometry and probability theory.
       
     • He was a mathematician of the front rank, whose contributions to analysis had become classical, and had played a great part in the inspiration of later research; he was a man of strong personality, fired by an intense devotion to his chosen study; and he had the persistence, the position, and the means to make his enthusiasm count.
       

219. Cartwright biography
     
     • He told her to read Whittaker and Watson's Modern analysis and to attend Hardy's evening sessions.
       
     • in recognition of her distinguished contributions to analysis and the theory of functions of a real and complex variable.
       

220. De Giorgi biography
     
     • In 1958 De Giorgi was appointed to the Chair of Mathematical Analysis at the University of Messina and he took up the appointment in December of that year.
       
     • In the autumn of 1959 De Giorgi moved to Pisa to take up the Chair of Mathematical Analysis [Notices Amer.
       

221. Chernoff biography
     
     • Wald was at North Carolina and Chernoff prepared by reading papers by Wald on sequential analysis.
       
     • This monograph was entitled Sequential analysis and optimal design and is described by P Whittle:- .
       

222. Fejer biography
     
     • During his period in the chair at Budapest Fejer led a highly successful Hungarian school of analysis.
       
     • Fejer's main work was in harmonic analysis.
       

223. Herschel biography
     
     • In 1812 the three undergraduates founded the Analytical Society which had as its aim the introduction of Continental methods of mathematical analysis into English universities.
       
     • Herschel's great versatility is shown by the fact that in 1821, having recently become involved in astronomy and chemistry, he was awarded the Copley Medal of the Royal Society of London for his work on mathematical analysis.
       

224. Raphson biography
     
     • His election to that Society was on the strength of his book Analysis aequationum universalis which was published in 1690 contained the Newton method for approximating the roots of an equation.
       
     • Raphson published a second edition of his analysis book and, at the same time, De spatio reali which is an application of mathematical reasoning to theological issues.
       

225. Thurston biography
     
     • Thurston has fantastic geometric insight and vision: his ideas have completely revolutionised the study of topology in 2 and 3 dimensions, and brought about a new and fruitful interplay between analysis, topology and geometry.
       
     • The method is a new level of geometrical analysis - in the sense of powerful geometrical estimation on the one hand, and spatial visualisation and imagination on the other, which are truly remarkable.
       

226. Hunyadi biography
     
     • considering that analytic geometry is principally a geometrical discipline, it is the author's modest view that we have to make every effort not to delegate the main role to algebra and analysis, confusing the means with the end, but to give the main aim 'geometry' its due importance.
       
     • This position is further supported by the argument that if we do approach analytic geometry from the opposite end, we might commit the error of reducing the analytic teaching of geometry to a collection of exercises in algebra and analysis which would certainly go against the spirit of the science.
       

227. Frege biography
     
     • For the first time, a deep analysis was possible of deductive inferences involving sentences containing multiply embedded expressions of generality.
       
     • However, we should note that he only applied the thesis to number theory and real analysis.
       

228. Poincare biography
     
     • Immediately after receiving his doctorate, Poincare was appointed to teach mathematical analysis at the University of Caen.
       
     • Poincare's Analysis situs , published in 1895, is an early systematic treatment of topology.
       

229. Lovelace biography
     
     • These two memoirs taken together furnish, to those who are capable of understanding the reasoning, a complete demonstration - That the whole of the developments and operations of analysis are now capable of being executed by machinery.
       
     • her power of generalisation was indeed most remarkable, coupled as it was with that of minute and intricate analysis.
       

230. Stone biography
     
     • From 1929 he worked on self-adjoint operators in Hilbert space and included his results in the major publication of his 662 page book Linear transformations in Hilbert space and their applications to analysis (1932).
       
     • In the language of the 1990's the book belongs to functional analysis (a subject we used to call topological algebra - didn't we?).
       

231. Fermat biography
     
     • I have also found many sorts of analyses for diverse problems, numerical as well as geometrical, for the solution of which Viete's analysis could not have sufficed.
       
     • Recognition of the significance of Fermat's work in analysis was tardy, in part because he adhered to the system of mathematical symbols devised by Francois Viete, notations that Descartes' "Geometrie" had rendered largely obsolete.
       

232. Reynaud biography
     
     • Between 1808 and 1811 he assisted de Prony with the mechanics course and, from 1812 to 1814 he replaced Poinsot on the analysis course.
       
     • Certainly Reynaud, although his results in this area were rather trivial, must get the credit for being one of the first people to give an explicit analysis of an algorithm, an area of mathematics which is of major importance today.
       

233. Landau biography
     
     • Edmund Landau's Foundations of Analysis Prefaces .
       
     • Edmund Landau's Foundations of Analysis Contents .
       

234. Goldstine biography
     
     • These include The computer from Pascal to von Neumann (1972), and A history of numerical analysis from the 16th through the 19th century (1977), described as:- .
       
     • fundamental contributions to development of the digital computer, computer programming and numerical analysis.
       

235. Watson biography
     
     • He is best known as a joint author with Whittaker of A Course of Modern Analysis published in 1915.
       
     • in recognition of his distinguished contributions to pure mathematics in the field of mathematical analysis and in particular for his work on asymptotic expansion and on general transforms.
       

236. Bortolotti biography
     
     • His teaching at Modena at this time included analysis and rational mechanics.
       
     • Bortolotti studied topology at first but later went in the direction of analysis considering the calculus of finite differences, continued fractions, convergence of infinite algorithms, summation of series, the asymptotic behaviour of series and improper integrals.
       

237. Ricci Giovanni biography
     
     • In 1936 Ricci moved to Milan where he was appointed as Professor of Mathematical Analysis at the University.
       
     • Ricci held the chair of Mathematical Analysis in Milan for over 36 years.
       

238. Appell biography
     
     • He then wrote on algebraic functions, differential equations and complex analysis.
       
     • The article [Acta Mathematica 45 (1925), 161-285.',2)">2], written by Appell himself, lists 140 works in analysis, 30 works in geometry, 87 works in mechanics as well as many textbooks, addresses, lectures on the history of mathematics and lectures on mathematical education.
       

239. Seidel biography
     
     • It is worth noting that these two theses, submitted only six months apart, were on two completely different topics - the first was on astronomy while the second was on mathematical analysis.
       
     • Like these two theses, Seidel worked on dioptics and mathematical analysis throughout his career.
       

240. Boersma biography
     
     • The results of the airfoil analysis are infinite systems of linear equations, from which numerical results can be obtained by truncation.
       
     • Complex Function Theory, Applied Analysis and Partial Differential Equations which provided the interesting combination of mathematical theory applied to physics problems.
       

241. Grassmann biography
     
     • His essay Theorie der Ebbe und Flut was 200 pages long and introduced for the first time an analysis based on vectors, including vector addition and subtraction, vector differentiation, and vector function theory.
       
     • Grassmann's mathematical methods were slow to be adopted but eventually they inspired the work of Elie Cartan and have since been used in studying differential forms and their application to analysis and geometry.
       

242. Germain biography
     
     • At the end of Lagrange's lecture course on analysis, using the pseudonym M.
       
     • She had not derived her hypothesis from principles of physics, nor could she have done so at the time because she had not had training in analysis and the calculus of variations.
       

243. Lacroix biography
     
     • He was appointed to a chair at the Ecole Centrale des Quatres Nations, then was appointed professor of mathematics at the Ecole Polytechnique from 1799 where he held the chair of analysis.
       
     • monumental work consisted a clear picture of mathematical analysis, documented and completely up to date.
       

244. Levinson biography
     
     • subsumes much of Levinson's brilliant early research in harmonic and complex analysis.
       
     • The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential and integral equations, harmonic, complex and stochastic analysis, and analytic number theory during more than half a century.
       

245. Klein biography
     
     • The journal specialised in complex analysis, algebraic geometry and invariant theory.
       
     • It also provided an important outlet for real analysis and the new area of group theory.
       

246. Blackwell biography
     
     • It was a course on real analysis, based on Hardy's Pure Mathematics, rather than the calculus which really turned him on to a career in mathematics [Mathematical People (Boston, 1985), 18-32.',2)">2]:- .
       
     • It was a lecture in 1945 by Abe Girshick of the Department of Agriculture on sequential analysis which sparked Blackwell's interest in statistics.
       

247. Robinson Raphael biography
     
     • He undertook research in complex analysis supervised by John McDonald and he was awarded a Ph.D.
       
     • His doctoral dissertation was on complex analysis, but he also worked on logic, set theory, geometry, number theory, and combinatorics.
       

248. Navier biography
     
     • During this first year at the Ecole Polytechnique, Navier was taught analysis by Fourier who had a remarkable influence on the young man.
       
     • He did not just carry on the traditional teaching in the school, but rather he changed the syllabus to put much more emphasis on physics and on mathematical analysis.
       

249. Berwick biography
     
     • Following this he moved to the University of Leeds as a lecturer but, in 1921, he was promoted to Reader in Mathematical Analysis there.
       
     • a great deal of courage and patience must have been needed for such a complex and laborious analysis.
       

250. Laplace biography
     
     • Imparting geometry, trigonometry, elementary analysis, and statics to adolescent cadets of good family, average attainment, and no commitment to the subjects afforded little stimulus, but the post did permit Laplace to stay in Paris.
       
     • I have sought to establish that the phenomena of nature can be reduced in the last analysis to actions at a distance between molecule and molecule, and that the consideration of these actions must serve as the basis of the mathematical theory of these phenomena.
       

251. Grinbergs biography
     
     • In particular he developed a theory for analysis and synthesis of linear electrical circuits, using the theory of approximation of functions to make electrical circuits easy to describe mathematically.
       
     • By 1954 he was allowed to lecture at the University of Latvia and in 1956 he defended a second thesis (to replace the one declared void by the authorities) Problems of analysis and synthesis of simple linear circuits.
       

252. Eisenhart biography
     
     • Important contributions to it were made by Bianchi, Beltrami, Christoffel, Schur, Voss, and others, and Ricci-Curbastro coordinated and extended the theory with the use of tensor analysis and his absolute calculus.
       
     • The new chapter began about 1920 with the extended studies of tensor analysis, Riemannian geometry and its generalizations, and the application of the theory of continuous groups to the new physical theories.
       

253. Hankel biography
     
     • His work on complex analysis, however, is not considered of the first rank and in [Opuscula Math.
       
     • influence on the foundations of complex analysis was not as essential as that of those mathematicians discussed in more detail [Riemann, Weierstrass, Hurwitz, Bieberbach ..
       

254. Schlafli biography
     
     • Although he was only fifteen years old when he entered the Gymnasium, Schlafli was already studying the differential calculus using Kastner's famous book Mathematische Anfangsgrunde der Analysis des Unendlichen.
       
     • This treatise, which I have the honour of presenting to the Imperial Academy of Science, is an attempt to found and to develop a new branch of analysis that would, as it were, be a geometry of n dimensions, containing the geometry of the plane and space as special cases for n = 2, 3.
       

255. Young Lai-Sang biography
     
     • Today it stands at the crossroads of several areas of mathematics, including analysis, geometry, topology, probability, and mathematical physics.
       
     • analysis of strange attractors; .
       

256. Ostrowski biography
     
     • His association with the United States was not restricted to the many universities he visited, for he in the 1950s had a close association with the National Bureau of Standards, first at the Institute for Numerical Analysis at Los Angeles and later in Washington, and this fitted in well with his increasing interest in numerical methods.
       
     • These are determinants, linear algebra, algebraic equations, multivariate algebra, formal algebra, number theory, geometry, topology, convergence, theory of real functions, differential equations, differential transformations, theory of complex functions, conformal mappings, numerical analysis and miscellany.
       

257. Schubert biography
     
     • He wrote the first in the series Arithmetik und Algebra and a later book in the series on analysis Niedere Analysis.
       

258. Doob biography
     
     • Through the fortunate accident of having a tedious instructor I had gained a year! The analytic function course, taken in my junior year with Osgood as teacher, was my first course in rigorous analysis and I took to it right away in spite of his mannerisms.
       
     • Graduate students and researchers in probability or classical analysis will find much to learn from this fine book by a master of both areas.
       

259. Mackey biography
     
     • Mackey has written many beautiful survey articles and in 1992 the American Mathematical Society and the London Mathematical Society in their wonderful series 'History of Mathematics' published The scope and history of commutative and noncommutative harmonic analysis by Mackey.
       
     • But the author's theory is surprisingly versatile, with applications in number theory, harmonic analysis, ergodic theory, quantum mechanics, and statistical mechanics, and these applications are worked out in detail..
       

260. Meray biography
     
     • Meray is remembered for having anticipated, clearly and with only minor differences of style, Cantor's theory of irrational numbers, one of the main steps in the arithmetisation of analysis.
       
     • Meray's work consistently follows Lagrange in basing the whole of analysis on the concept of functions written as Taylor series.
       

261. Bolzano biography
     
     • a sample of a new way of developing analysis.
       
     • But he was reading and recording his ideas on a host of other subjects as well, including the problem of how best to approach the proper mathematical understanding of zero; Legendre's work on surfaces, convexity, concavity, and conditions for congruity; analysis of other geometric concepts, including lengths, areas, volumes, and spheres; trigonometric formulas and spherical trigonometry; imaginary and exponential numbers; definition of the differential and discussion of the infinite and various opinions about it, as well as aspects of maxima and minima.
       

262. Lighthill biography
     
     • it allows an analysis in depth of four important and representative types of waves in fluids (sound waves, one-dimensional waves in fluids, water waves, internal waves)..
       
     • He did considerable work developing new mathematical tools particularly in the area of Fourier analysis and generalised functions.
       

263. Lesniewski biography
     
     • Lesniewski, whose doctoral supervisor was Kazimierz Twardowski, published the two papers A contribution to the analysis of existential propositions and An attempt at a proof of the ontological principle of contradiction while still undertaking his doctoral research.
       
     • Lesniewski's views developed from his analysis of Russell's paradox which he concluded confused two different notions of class.
       

264. Lakatos biography
     
     • This article, Cauchy and the Continuum : The Significance of Non-Standard Analysis for the History and Philosophy of Mathematics is one of the most enjoyable that I have read.
       
     • The point is not merely to rethink the reasoning of Cauchy, not merely to use the mathematical insight available from Robinson's non-standard analysis to re-evaluate our attitude towards the whole history of the calculus and the notion of the infinitesimal.
       

265. Knopp biography
     
     • Friedrich Losch added a fourth volume in 1980 to cover more modern material: set theory, Lebesgue measure and integral, topological spaces, vector spaces, functional analysis, integral equations.
       
     • This famous and comprehensive introduction to analysis by von Mangoldt and Knopp has been popular for generations of German-speaking students, in mathematics, physics and other natural sciences, and engineering.
       

266. Floer biography
     
     • Combining this observation with detailed, careful analysis, and using work of many other mathematicians as well as his own, Andreas developed a theory that led to the solution of a number of outstanding problems.
       
     • While teaching a course in real analysis, he had taken the material apart from top to bottom, reanalysing standard concepts and theorems in order to prepare his students for mathematics as it is done today.
       

267. Hammer biography
     
     • More than anyone else, Peter Hammer has used and extended Boole's machina universalis to handle questions relating to decision making, analysis and synthesis as they arise in natural, economic and social sciences.
       
     • Over the span of his scientific career, he has conducted eclectic forays into the interactions between Boolean methods, optimization, and combinatorial analysis, while adapting his investigations to the most recent advances of mathematical knowledge and of various fields of application.
       

268. Duhamel biography
     
     • Appointed as entrance examiner at the Ecole Polytechnique in 1835, Duhamel was named professor of analysis and mechanics in 1836.
       
     • However, from 1851, he again filled the analysis chair at the Ecole Polytechnique after Liouville was appointed to the vacant chair at the College de France.
       

269. Hurwitz biography
     
     • The lectures contained Weierstrass's version of the arithmetisation of analysis including his "construction" of the real numbers, the ε, δ approach to analysis and his theory of complex functions based on power series.
       

270. Kovalevskaya biography
     
     • When Sofia was 11 years old, the walls of her nursery were papered with pages of Ostrogradski's lecture notes on differential and integral analysis.
       
     • During Kovalevskaya's years at Stockholm, she carried out what many consider her most important research She taught courses on the latest topics in analysis and became an editor of the new journal Acta Mathematica.
       

271. Courant biography
     
     • During the four semesters that Courant served as Hilbert's assistant, Hilbert was devoting himself almost exclusively to subjects in analysis ..
       
     • Courant took to analysis as if it were his natural element.
       

272. Grave biography
     
     • Among the many books that Grave wrote were Theory of Finite Groups (1910) and A Course in Algebraic Analysis (1932).
       
     • He also studied the history of algebraic analysis.
       

273. Stewartson biography
     
     • The methods used are a combination of experimental observation, computation often on a very large scale, and analysis of the structure of the asymptotic form of the solution as the friction tends to zero.
       
     • Alternatively they could reveal unexpected phenomena which would then be subjected to analysis.
       

274. Gohberg biography
     
     • Gohberg was appointed to the Academy of Sciences in Kishinyov where, in 1964, he became the Head of Functional Analysis.
       
     • In addition to Gohberg's outstanding work in analysis and in particular in operator theory and matrix methods, he founded the major international journal Integral equations and operator theory in the late 1980s.
       

275. Littlewood Dudley biography
     
     • He remained at Cambridge, where he began research in analysis, but it appears that he was neither sufficiently good or interested in analysis and, lacking financial support, decided to give up research and look for a job.
       

276. Kirchhoff biography
     
     • In a period of expanding scientific horizons, the need soon arises for ordering and logical analysis of new knowledge.
       
     • His mode of thinking is as conspicuous in his contributions of immediate practical value (the laws of electrical networks) as in those with wide implications (the method of spectral analysis).
       

277. Kiefer biography
     
     • However he also wrote papers on a whole variety of topics in mathematical statistics including decision theory, inventory theory, stochastic approximation, queuing theory, nonparametric inference, estimation, sequential analysis, and conditional inference.
       
     • He gave eight lectures at Beijing University covering topics such as multivariate analysis, sequential methods, nonparametric estimation, robustness and efficiency of nonparametric methods, fundamentals of experimental design, complete class and regression design, factorial experiment, and nonlinear models, sequential design, and robust design.
       

278. Radon biography
     
     • Radon gave a course on complex analysis completely from memory having no materials available to help him.
       
     • It assumed a fundamental importance for functional analysis and has become of equal importance for the application to the logarithmic potential.
       

279. Kagan biography
     
     • In 1927, Kagan organised a seminar on vector and tensor analysis.
       
     • He founded a publication associated with this seminar Transactions of the seminar on Vector and Tensor Analysis with its applications to Geometry, Mechanics and Physics in 1933.
       

280. Billy biography
     
     • Billy had collected many problems from Fermat's letters and, after the death of his father, Fermat's son appended de Billy's collection under the title Doctrinae analyticae inventum novum (New discovery in the art of analysis) as an annex to his edition of the Arithmetica of Diophantus (1670).
       
     • It is an elaborate study of the techniques of indeterminate analysis used by Fermat and, on the whole, it explains them correctly.
       

281. Kolmogorov biography
     
     • Almost simultaneously [Kolmogorov] exhibited his interest in a number of other areas of classical analysis: in problems of differentiation and integration, in measures of sets etc.
       
     • his ideas in set-theoretic topology, approximation theory, the theory of turbulent flow, functional analysis, the foundations of geometry, and the history and methodology of mathematics.
       

282. Erdos biography
     
     • The theorem was conjectured in the 18th century, Chebyshev himself came close to a proof, but it was not proved until 1896, when Hadamard and de la Vallee Poussin independently proved it using complex analysis.
       
     • He had been a true child prodigy, publishing his first results at the age of eighteen in number theory and in combinatorial analysis.
       

283. Montroll biography
     
     • This is a review of some developments in the analysis of the vibration spectrum of crystal lattices with particular emphasis on the observation that the frequency distribution function is expected to have singularities.
       
     • In 1963 he took up the position of Vice President for Research at the Institute for Defense Analysis in Washington, D.C.
       

284. Lefschetz biography
     
     • His most important results from this period are contained in On certain numerical invariants of algebraic varieties with application to abelian varieties, which he had published in the Transactions of the American Mathematical Society in 1921, and in his famous monograph of 1924 L'analysis situs et la geometrie algebrique.
       
     • In the end the ideas he developed became the foundation of a new branch of mathematics, namely global analysis.
       

285. De Finetti biography
     
     • Meanwhile, against the will of his mother, who was worried about his future, he moved to the recently founded (1925) University of Milan and there, in 1927, he graduated in Applied Mathematics with a dissertation on affine geometry supervised by Giulio Vivanti, a mathematician who made some noteworthy contributions to complex analysis.
       
     • Here, leaving aside his contributions to mathematical analysis, as well as those to financial and actuarial mathematics, it is worth considering his vital interest in economics and social justice, together with his enthusiastic involvement in the teaching of mathematics.
       

286. Wilks biography
     
     • His early papers on multivariate analysis were his most important, one of most influential being Certain generalizations in the analysis of variance.
       

287. Meissel biography
     
     • He also wrote on Bessel functions, asymptotic analysis, refraction of light in the earth's atmosphere, and the three body problem.
       
     • His work is based entirely on things that he learnt during his student days (before 1850), whereas he seems to have been ignorant of newer developments in analysis such as the theory of functions of one complex variable.
       

288. Szekeres biography
     
     • He embraced the computer age with enthusiasm, making early contributions to techniques of numerical analysis, especially in the theory of computing high dimensional integrals.
       
     • In 1965 he wrote a numerical analysis paper Some estimates of the coefficients in the Chebyshev series expansion of a function and a paper dealing with a combinatorial problem On a problem of Schutte and Erdos written jointly with his wife Esther.
       

289. Possel biography
     
     • In 1951 he was appointed to the specially created chair of higher analysis at the Faculty of Science at Algiers.
       
     • From 1959 he was professor of numerical analysis at the Faculty of Science in Paris.
       

290. Wishart biography
     
     • This distribution is described in [An Introduction to Multivariate Statistical Analysis (1958).',1)">1] as:- .
       
     • fundamental to multivariate statistical analysis ..
       

291. Morse biography
     
     • Morse theory is important in the field of global analysis which is the study of ordinary and partial differential equations from a global or topological point of view.
       
     • Morse's major works include Calculus of variations in the large (1934), Functional topology and abstract variational theory (1938), Topological methods in the theory of functions of a complex variable (1947) and Lectures on analysis in the large (1947).
       

292. Frenkel biography
     
     • He had already published a number of major books: The structure of matter I (1922), The theory of relativity (1923), The structure of matter II (1924), Vector and tensor analysis (1925), Electricity and matter (1925), and Electrodynamics (1926).
       
     • Other major books included Analytical mechanics (1935) and Theoretical mechanics based on vector and tensor analysis (1940).
       

293. Andrews biography
     
     • The combinatorial and formal power series aspects of the subject have usually been treated in books on elementary number theory or combinatorial analysis.
       
     • Currently I am reviving MacMahon's "Partition Analysis", collaborating on further applications of partitions to statistical mechanics and computer science, and completing my study of the relationship between Ramanujan's enigmatic identities and quadratic forms.
       

294. Kendall biography
     
     • Kendall is a leading world authority on applied probability and data analysis.
       
     • Kendall has been joint editor of a number of important works, including Mathematics in the Archaeological and Historical Sciences (1971), Stochastic Analysis (1973), Stochastic Geometry (1974), Analytic and Geometric Stochastics (1986).
       

295. Humbert Georges biography
     
     • In 1893 he was elected to the role of president of the French Mathematical Society and, two years later, he was appointed professor of analysis at the Ecole Polytechnique.
       
     • He thus enriched analysis and gave the complete solution of the two great questions of the transformation of hyperelliptic functions and of their complex multiplication.
       

296. Hsu biography
     
     • Many of his publications on multivariate analysis from this period show that he had been strongly influenced by R A Fisher while at University College.
       
     • the forefront of the development of the mathematical theory of multivariate analysis.
       

297. Gateaux biography
     
     • Meanwhile, he had begun to prepare a thesis in mathematics, on themes closely related to functional analysis a la Hadamard and its application to potential theory.
       
     • Volterra himself, invited by Borel and Hadamard, came to Paris to give a series of lectures on functional analysis, published in 1913 ([Lecons sur les fonctions de lignes (Gauthier-Villars, Paris, 1913).',23)">23]) and whose redaction was precisely made by Peres.
       

298. Rutherford biography
     
     • I have looked out for one who is competent to teach particularly in Analysis and Applied Mathematics.
       
     • His most important work was Substitutional Analysis (1948) in which explicit representations of the symmetric group are given.
       

299. Calugareanu biography
     
     • His investigations on Picard's fundamental theorem, on theorems of Borel and Nevanlinna in connection with the study of exceptional values of meromorphic functions of finite genus, made him already in the third and fourth decades of this century one of the first important Romanian mathematicians as well as a mathematician of European stature and distinguished member of the Romanian school of complex analysis founded by David Emmanuel and Dimitrie Pompeiu.
       
     • Through their work in the theory of polygenic functions, both Pompeiu and Calugareanu established themselves as genuine founders of the theory of generalized analytic functions, a branch of complex analysis that developed considerably in the period 1930-1970.
       

300. Binet biography
     
     • He became a teacher at Ecole Polytechnique in 1807 and, one year later, he was appointed to assist the professor of applied analysis and descriptive geometry.
       
     • Binet's analysis [of the algorithm] is surprisingly modern in presentation.
       

301. Konig Julius biography
     
     • Konig worked on a wide range of topics in algebra, number theory, geometry, set theory, and analysis.
       
     • He published many research papers in analysis, but his greatest significance in this area comes from the excellent textbooks which he wrote on the topic.
       

302. Dedekind biography
     
     • There he was to receive a good understanding of basic mathematics studying differential and integral calculus, analytic geometry and the foundations of analysis.
       
     • As well as his analysis of the nature of number, his work on mathematical induction, including the definition of finite and infinite sets, and his work in number theory, particularly in algebraic number fields, is of major importance.
       

303. Pringsheim biography
     
     • He also suggested that the paradoxes of the infinitary calculus arose from transferring properties of real numbers to infinite-dimensional domains where they fail, and agreed with Cantor that any use of infinitesimals in analysis would necessarily lead to inconsistencies.
       
     • An interesting comment concerning Pringsheim appears in [Algebraic number theory and Diophantine analysis, Graz, 1998 (de Gruyter, Berlin, 2000,) 521-530.
       

304. Roch biography
     
     • He was a fine mathematician who wrote an excellent analysis textbook which helped the development of rigorous analysis in Germany.
       

305. Grothendieck biography
     
     • In 1949 Grothendieck moved to the University of Nancy where he worked on functional analysis with Dieudonne.
       
     • During this period Grothendieck's work provided unifying themes in geometry, number theory, topology and complex analysis.
       

306. Greenhill biography
     
     • Hence he valued applications of analysis above the analysis itself, and was led to work out minutely the details of multitudes of special cases.
       

307. Leray biography
     
     • He then returned to work on analysis, in particular studying differential equations arising from hydrodynamics.
       
     • In producing this theory Leray introduced many ideas of functional analysis which have today become standard tools.
       

308. FitzGerald biography
     
     • London (1901).',9)">9] gives a similar, but fairer, analysis of FitzGerald's work:- .
       
     • the leisure of long patient analysis was not his, nor did his genius altogether lie in this direction: he was at his best when, under the stimulus of discussion, his mind teemed with brilliant suggestions, some of which he at once proceeded to test by rough quantitative calculation, for which he was an adept in discerning the necessary data.
       

309. Hartree biography
     
     • Hartree was basically a theoretical physicist, and he developed powerful methods in numerical analysis.
       
     • He wrote a number of important books including Numerical analysis in 1952 which became a classic of the subject.
       

310. Kolchin biography
     
     • Although the articles in this volume are in the main devoted to commutative algebra, linear algebraic group theory, and differential algebra, the diversity of subjects covered - complex analysis, algebraic K-theory, logic, stochastic matrices, differential geometry, ..
       
     • Following the tradition set by Joseph Fels Ritt (1893 - 1951), the founding father of differential algebra, his desire has been to remove the algebraic aspects of differential equations from analysis.
       

311. Montgomery biography
     
     • So we began with Oswald Veblen's Analysis Situs.
       
     • He undertook other war work at that time working with von Neumann on numerical analysis:- .
       

312. Schouten biography
     
     • Schouten's doctoral thesis, presented in 1914, was on tensor analysis, a topic he worked on all his life.
       
     • Schouten produced 180 papers and 6 books on tensor analysis.
       

313. Richardson biography
     
     • Another application of mathematics by Richardson was in his study of the causes of war and he published the results of his analysis in a number of major books: Generalized Foreign Politics (1939), Arms and Insecurity (1949), and Statistics of Deadly Quarrels (1950).
       
     • hardly anything in the way of new knowledge as to the "causes" of wars has emerged from this monumental analysis, unless one views as new the refutation of established notions by negative results.
       

314. Kuczma biography
     
     • He also worked at the Mathematical Analysis Section of the Mathematical Institute of the Polish Academy of Sciences from 1966.
       
     • Fundamental notions such as existence and uniqueness of solutions of equations under consideration are treated throughout the book as well as a surprisingly wide scale of examples showing applications of the theory in dynamical systems, ergodic theory, functional analysis, functional equations in several variables, functional inequalities, geometry, iteration theory, ordinary differential equations, partial differential equations, probability theory and stochastic processes.
       

315. Weaver biography
     
     • They will make it possible to deal with problems which previously were too complicated, and, more importantly, they will justify and inspire the development of new methods of analysis applicable to these new problems of organized complexity.
       
     • The second of the wartime advances is the "mixed-team" approach of operations analysis.
       

316. Van Kampen biography
     
     • Schouten worked all his life on tensor analysis and although this seems quite far removed from the topics that van Kampen had been undertaking research on, nevertheless he collaborated with Schouten on three papers on tensor analysis, published in 1930, 1931 and 1933.
       

317. Prager biography
     
     • The Lectures were published as The extremum principles of the mathematical theory of elasticity and their use in stress analysis in 1950.
       
     • The main topics covered in the text are: basic concepts of stress, strain, and stress-strain relations; trusses and beams; torsion of cylindrical or prismatic bars; plane strain including problems with axial symmetry, general theory, specific problems, contained plastic deformations, limit analysis; and finally, general extremum principles.
       

318. Lerch biography
     
     • 3 (78), (1953), 111-122.',7)">7], mostly on analysis (about 150 papers) and number theory (about 40 papers).
       
     • He is also well known, however, for his work in analysis.
       

319. Pontryagin biography
     
     • Of the advanced courses he took, Pontryagin felt less happy with Khinchin's analysis course but he took a special liking to Aleksandrov's courses.
       
     • In 1934 he became a member of the Steklov Institute and in 1935 he became head of the Department of Topology and Functional Analysis at the Institute.
       

320. Eddington biography
     
     • He had introduced his method of analysis of two star-drifts, and his prevailing interest in statistical stellar astronomy was concentrated on the systematic motions and distribution of the stars throughout his Greenwich years.
       
     • He was a gifted astronomer whose original theories and powers of mathematical analysis took his science a long way forward; he was a brilliant expositor of physics and astronomy, able to communicate the most difficult conceptions in the simplest and most fascinating language; and he was an able interpreter to philosophers of the significance of the latest scientific discoveries.
       

321. Shatunovsky biography
     
     • Shatunovsky's research was on several topics from analysis and algebra.
       
     • He used the axiomatic method to lay the logical foundations of geometry, algebraic fields, Galois theory and analysis.
       

322. Uhlenbeck Karen biography
     
     • In fact the papers of Uhlenbeck which appeared about that time [1982] contained essentially all the analysis required to put this picture on a firm footing.
       
     • She has also served on the editorial boards of many journals; a complete list to date is Journal of Differential Geometry (1979-81), Illinois Journal of Mathematics (1980-86), Communications in Partial Differential Equations (1983- ), Journal of the American Mathematical Society (1986-91), Ergebnisse der Mathematik (1987-90), Journal of Differential Geometry (1988-91), Journal of Mathematical Physics (1989- ), Houston Journal of Mathematics (1991- ), Journal of Knot Theory (1991- ), Calculus of Variations and Partial Differential Equations (1991- ), Communications in Analysis and Geometry (1992- ).
       

323. Gregory biography
     
     • It is remarkable that some decades later, at the time when analysis was in a state of revolutionary development, exactness was at a much lower standard than with Gregory, and generally with the authors writing before the discoveries of Newton and Leibniz (e.g.
       
     • For his reluctance to publish his "several universal methods in geometry and analysis" when he heard through Collins of Newton's own advances in calculus and infinite series, he postumously paid a heavy price ..
       

324. Scott Elizabeth biography
     
     • The resulting analysis showed that for most categories of binaries the distribution is not uniform.
       
     • The majority of Scott's work was in statistical analysis of the data from well-known studies in meteorology such as the Santa Barbara experiment from 1957 to 1959, the 1957-1963 Grossversuch III experiment, and the 1960 - 1964 Whitetop experiment.
       

325. Markov biography
     
     • Markov's early work was mainly in number theory and analysis, algebraic continued fractions, limits of integrals, approximation theory and the convergence of series.
       
     • His profound analysis in the spirit of Chebyshev of the dependencies among observed random phenomena allowed Markov to extend probability theory in an essential way through the introduction and investigation of dependent random quantities.
       

326. Nikodym biography
     
     • the Radon-Nikodym theorem and derivative, the Nikodym convergence theorem, the Nikodym-Grothendieck boundedness theorem), in functional analysis (the Radon-Nikodym property of a Banach space, the Frechet-Nikodym metric space, a Nikodym set), projections onto convex sets with applications to Dirichlet problem, generalized solutions of differential equations, descriptive set theory and the foundations of quantum mechanics.
       
     • The Radon-Nikodym theorem (Radon proved it in 1913 for Rn and Nikodym in 1930 for the general case) is now a fundamental theorem in analysis: .
       

327. Schafer biography
     
     • One of the men who taught the more advanced material, like analysis, openly declared that he would like to fail all women who took his course.
       
     • She had performed exceptionally well and in her third year had won the Crump prize for real analysis.
       

328. McDuff biography
     
     • At Cambridge McDuff was supervised by G A Reid and she worked on problems in functional analysis.
       
     • Her work in symplectic geometry, functional analysis and diffeomorphism groups has provided understanding and unexpected results in a whole range of areas of great importance.
       

329. Lamb biography
     
     • He took delight in the comparison of a well-ordered piece of algebraic analysis with a musical composition, and bemoaned the passing of the scientific memoir, which in the hands of a Lagrange or a Poisson had a completeness and austerity of a great work of art.
       
     • His writings call up before one the picture of an extremely acute and wonderful alert mind, endowed with a profound knowledge of the facts of physics, especially on its dynamical side, keenly interested in the work of others, particularly when it had a bearing on any matter of mechanics or wave transmission, equipped with an exceptionally varied and powerful mathematical technique, and ever on the look-out for topics on which his analysis could be employed for the promotion of natural knowledge.
       

330. Dilworth biography
     
     • In July 1944 he became a member of an analysis unit at the 8th Air Force headquarters at Brampton Park in England.
       
     • This unit was to serve as a liaison between the main operational analysis unit located at the headquarters of the 8th Air Force near London and the command of the 1st Air Division.
       

331. Dantzig George biography
     
     • From 1941 to 1946 he was Head of the Combat Analysis Branch, U.S.A.F.
       
     • Dantzig has received many honours including the Von Neumann Theory Prize in Operational Research in 1975; The National Medal of Science presented by the president of the United States in 1976; the National Academy of Sciences Award in Applied Mathematics and Numerical Analysis in 1977; the Harvey Prize in Science and Technology from Technion, Israel, in 1985; the Silver Medal from the Operational Research Society of Britain in 1986; the Adolph Coors American Ingenuity Award Certificate of Recognition from the State of Virginia in 1989; and the Special Recognition Award from the Mathematical Programming Society in 1994.
       

332. Zorn biography
     
     • Let us now take a brief look at his contributions to analysis.
       
     • In recent years Max became fascinated by the Riemann Hypothesis and possible proofs using techniques from functional analysis.
       

333. Sobolev biography
     
     • The study of Sobolev function spaces, which he introduced in the 1930s, immediately became a whole area of functional analysis.
       
     • In 1950 he published his famous text Applications of functional analysis in mathematical physics (in Russian).
       

334. Iacob biography
     
     • At Cluj he worked in the departments of Analytic Geometry, descriptive Geometry, Analysis, and Complex Functions.
       
     • At this time D V Ionescu was Dean of the Faculty but Ionescu, who was professor in the Department of Mechanics, moved to the Department of Analysis in 1943.
       

335. Halmos biography
     
     • After thinking that algebra was the right subject for him, he quickly changed to analysis and studied for his Ph.D.
       
     • Halmos is known for both his outstanding contributions to operator theory, ergodic theory, functional analysis, in particular Hilbert spaces, and for his series of exceptionally well written textbooks.
       

336. Al-Biruni biography
     
     • Within the sciences themselves he was attracted by those fields then susceptible of mathematical analysis.
       
     • These include: theoretical and practical arithmetic, summation of series, combinatorial analysis, the rule of three, irrational numbers, ratio theory, algebraic definitions, method of solving algebraic equations, geometry, Archimedes' theorems, trisection of the angle and other problems which cannot be solved with ruler and compass alone, conic sections, stereometry, stereographic projection, trigonometry, the sine theorem in the plane, and solving spherical triangles.
       

337. Stieltjes biography
     
     • I have been offered, some days ago, a professorship in analysis (differential and integral calculus) at the University of Groningen.
       
     • Stieltjes worked on almost all branches of analysis, continued fractions and number theory.
       

338. Dirichlet biography
     
     • He turned to Laplace's problem of proving the stability of the solar system and produced an analysis which avoided the problem of using series expansion with quadratic and higher terms disregarded.
       
     • His proofs characteristically started with surprisingly simple observations, followed by extremely sharp analysis of the remaining problem.
       

339. Murnaghan biography
     
     • Perhaps it is easiest to understand how he saw the study of mathematics and its applications by quoting from the Preface to his first book Vector analysis and the theory of relativity (1922).
       
     • Over the period up to 1936, in addition to the major texts we have already mentioned, Murnaghan undertook research and published papers on a wide variety of topics such as electrodynamics, relativity, tensor analysis, elasticity, dynamics, aerodynamics, quantum mechanics, and celestial mechanics.
       

340. Jones biography
     
     • With assistance from Newton himself, Jones produced Analysis per quantitatum series, fluxiones, ac differentia in 1711 although it should be noted that this first edition of 1711 did not record either Newton's name nor that of Jones.
       
     • The second edition of Analysis per quantitatum published in 1723 did contain a preface written by Jones.
       

341. Abel biography
     
     • whose development would have the greatest consequences for analysis and mechanics.
       
     • Crelle's Journal continued to be a source for Abel's papers and Abel began to work to establish mathematical analysis on a rigorous basis.
       

342. Malfatti biography
     
     • These include: Problems and methods of mathematical analysis in the work of Gianfrancesco Malfatti, Contributions of Gianfrancesco Malfatti to combinatorial analysis and to the theory of finite difference equations, The work of Malfatti in the realm of mechanics, The geometrical research of Gianfrancesco Malfatti, Gianfrancesco Malfatti and the theory of algebraic equations, and Gianfrancesco Malfatti and the support problem.
       

343. Rota biography
     
     • The topics were wide-ranging: differential equations, ergodic theory, nonstandard analysis, probability, and of course, combinatorics.
       
     • As we have indicated above, Rota worked on functional analysis for his doctorate and, up to about 1960, he wrote a series of papers on operator theory.
       

344. Lexell biography
     
     • Lexell's work in mathematics is mainly in the area of analysis and geometry.
       
     • Lexell did work in analysis on topics other than differential equations, for example he suggested a classification of elliptic integrals and he worked on the Lagrange series.
       

345. Gelfond biography
     
     • After his return to Russia, Gelfond taught mathematics from 1931 at Moscow State University where he held chairs of analysis, theory of numbers and the history of mathematics.
       
     • In broad terms this means that problems are attacked by direct methods within the framework of the problems themselves, without the use of extraneous disciplines such as the theory of functions of a complex variable, Fourier analysis, trigonometric sums.
       

346. Gentzen biography
     
     • The idea of levels, probably first introduced by Weyl, considers number theory as the first level since it deals with the natural numbers, analysis as the second level since it deals with the real numbers, and set theory as the third level where the full extent of Cantor's cardinal and ordinal numbers would be studied.
       
     • He once confided in me that he was really quite content since now he had at last time to think about a consistency proof for analysis..
       

347. Moore Robert biography
     
     • The importance of the regularly and perfectly separable, therefore metric, spaces in the analysis of continua is indicated by the fact that nine years before the publication of the discoveries of Urysohn, R L Moore assumed these properties in the first of a system of axioms for the foundations of plane analysis situs.
       

348. Mathisson biography
     
     • The subject was of particular interest at that time, as it had become clear that quantum mechanics cannot solve the difficulties that had arisen in connection with the interaction of point particles with fields, and a deeper classical analysis of the problem was needed.
       
     • The transition from the characteristic tensor to the dynamical variables is conveyed by an analysis of the physical meaning of the constituents.
       

349. Schwarz biography
     
     • His interest in geometry was soon combined with Weierstrass's ideas of analysis.
       
     • ideas coming from geometrical considerations were translated [by Schwarz] into the language of analysis.
       

350. Sturm biography
     
     • He worked at the Ecole Polytechnique in Paris from 1838 where he became a professor of analysis and mechanics in 1840.
       

351. Wintner biography
     
     • Wintner published on analysis, number theory, differential equations and probability (with several joint papers with Norbert Wiener).
       

352. Ledermann biography
     
     • It will involve from 8 to 10 lectures or tutorials a week in mathematics pure and applied; and the Court understand that I have looked out for one who is competent to teach particularly in Analysis and Applied Mathematics.
       

353. Urbanik biography
     
     • ',3)">3] divides Urbanik's research into five different major areas: topology, measure theory and analysis; probability theory; stochastic processes; information theory and theoretical physics; and general algebras.
       

354. Genocchi biography
     
     • From 1859 Genocchi held the Chair of Algebra and Complementary Geometry at Turin, then the following year he moved to the Chair of Higher Analysis.
       

355. Meders biography
     
     • Meders worked on differential geometry and mathematical analysis.
       

356. Spitzer biography
     
     • He worked first at the Special Studies Group at Columbia, then did underwater sound research with the Sonar Analysis Group that led the development of sonar.
       

357. Al-Nasawi biography
     
     • ',3)">3] give an analysis of this mid-12th century manuscript which once contained 80 tracts, but of these only 43 survive.
       

358. Bass biography
     
     • This was a rigorous course in analysis, with everything proved.
       

359. Browne biography
     
     • Brown was also a National Science Foundation Faculty Fellow studying computing and numerical analysis at the University of California at Los Angeles.
       

360. Hatvani biography
     
     • He was fortunate to make it through the first few years of life and it is interesting to remark at this point that he would later become the first Hungarian to undertake a statistical analysis of infant mortality and to make medical deductions from the data.
       

361. Voronoy biography
     
     • Today they have wide applications to the analysis of spatially distributed data, so have become important in topics such as geophysics and meteorology.
       

362. Golab biography
     
     • Professor Golab dealt with different fields of mathematics such as geometry, topology, algebra, analysis, logic, functional and differential equations, the theory of numerical methods and various applications of mathematics.
       

363. Krawtchouk biography
     
     • Other areas he wrote on included algebra (where among other topics he studied the theory of permutation matrices), geometry, mathematical and numerical analysis, probability theory and mathematical statistics.
       

364. Pfaff biography
     
     • Pfaff did important work in analysis working on partial differential equations, special functions and the theory of series.
       

365. Lowenheim biography
     
     • The result implies that no uncountable mathematical system, such as those involved in analysis, geometry, and set theory, can be characterised up to isomorphism using only first-order sentences.
       

366. Hamill biography
     
     • Starting with an analysis of the geometrical configuration formed by the centres and the invariant primes of the homologies, she was able, by a very thorough and careful investigation, to obtain, for each of the groups, the distribution of the operations in conjugate sets, and to make the nature of these operations clear.
       

367. Somov biography
     
     • not only deep knowledge but also extraordinary skill in presenting the newest achievements of algebraic analysis.
       

368. Mandelbrot biography
     
     • The first of Hilbert's problems concerned a thicket of issues about the nature of the continuum or the real line, a major concern of 19th and indeed of 20th century analysis.
       

369. Bertrand biography
     
     • In 1862, he became professor of analysis at the College de France, succeeding Biot who died in February of that year.
       

370. Yule biography
     
     • The second half of the book deals with sampling theory: large and small samples, chi-square, analysis of variance.
       

371. Macintyre biography
     
     • In her chosen area of analysis, she introduced powerful refinements of techniques, and what is much harder, new and original problems for investigation.
       

372. Luzin biography
     
     • up to 1938, when Luzin, by means of a subtle analysis of these equations, established that the existence of a principal base is rather rare.
       

373. Faber biography
     
     • In addition to his research areas, Faber lectured on complex analysis, probability theory, the theory of relativity and analytical mechanics.
       

374. Stackel biography
     
     • Stackel thrived during his time at Halle, publishing numerous papers, mainly on topics in analysis, mechanics and differential geometry.
       

375. Erdelyi biography
     
     • He also worked on asymptotic analysis, fractional integration and singular partial differential equations.
       

376. Bortkiewicz biography
     
     • By far [Bortkiewicz's] most important achievement is his analysis of the theoretical framework of the Marxian system, much the best thing ever written on it and, incidentally, on its other critics.
       

377. Eckmann biography
     
     • As an assistant to Plancherel I had the opportunity to work, and even lecture, in different fields, including analysis.
       

378. Einstein biography
     
     • I never realised that so many Americans were interested in tensor analysis.
       

379. Feldman biography
     
     • He then went to Moscow State University where he was appointed as a Reader in the Department of Mathematical Analysis.
       

380. Salem biography
     
     • We should also note that Salem introduced the idea of a random measure into harmonic analysis.
       

381. Condorcet biography
     
     • His most important treatise was Essay on the Application of Analysis to the Probability of Majority Decisions (1785).
       

382. Pauli biography
     
     • Pauli based his investigation on a profound analysis of the experimental and theoretical knowledge in atomic physics at the time.
       

383. Rasiowa biography
     
     • Rasiowa remained active right up to her death, having completed eight chapters of a new monograph Algebraic analysis of non-classical first order logics before entering hospital with her final illness.
       

384. Deans biography
     
     • Her translation of Richard Gans' Vector analysis and applications to physics was published in 1931 and, in the following year, her translation of Pohl Robert Wichard's Physical Principles of Mechanics and Acoustics.
       

385. Bjerknes Vilhelm biography
     
     • He published a book on vector analysis in 1929 which was designed as the first of a larger textbook on theoretical physics.
       

386. Bergman biography
     
     • The authors of [Applicable analysis 8 (1979), 195-199.',6)">6] write:- .
       
     • To escape from the anti-Semitic Nazi regime, Bergman went to Russia in 1934 working at Tomsk in Siberia until 1936, then at Tbilisi in Georgia during 1936-37 [Applicable analysis 8 (1979), 195-199.',6)">6]:- .
       
     • He went to the Institut Henri Poincare in Paris where he wrote an important two-volume monograph on complex analysis.
       
     • Awards are made every year or two in: 1) the theory of the kernel function and its applications in real and complex analysis; or 2) function-theoretic methods in the theory of partial differential equations of elliptic type with attention to Bergman's operator method.
       

387. Tait biography
     
     • not only quaternion analysis profited from acquiring a new.
       

388. Weil biography
     
     • It was not just to these areas that he contributed but, even more importantly, his work brought out fundamental relationships between the areas when he studied harmonic analysis on topological groups and characteristic classes.
       

389. Springer biography
     
     • The general theory is illustrated by a detailed analysis of SL(2, K) and finite groups.
       

390. Lyapunov biography
     
     • (4) (1993), 3-47.',8)">8] include: stability, particularly the stability of critical points; the construction and the application of the Lyapunov function; stability of functional- differential equations; the second Lyapunov method; and the method of the Lyapunov vector function in stability theory and nonlinear analysis.
       

391. Albanese biography
     
     • Albanese left Padua in the year 1920 to take up a professorship in analysis and algebra at the Naval Academy in Livorno which, as happened with Italian chairs, he had won after a competition.
       

392. Montel biography
     
     • The idea of compactness had emerged as a fundamental concept in analysis during the nineteenth century; provided a set is bounded in Rn, it is possible to define for and sequence of points, a subsequence which converges to a point of Rn (the Bolzano-Weierstrass theorem).
       

393. Razmadze biography
     
     • Razmadze wrote the first textbooks in Georgian on analysis and integral calculus.
       

394. Herglotz biography
     
     • The author does show his usual clarity and elegance and the richness of his analysis appears in the many areas of application sketched in a paragraph or two, as one does in lectures.
       

395. Patodi biography
     
     • Patodi's first paper Curvature and the eigenforms of the Laplace operator was part of his thesis and the contents of this paper are described in [Geometry and analysis : papers dedicated to the memory of V K Patodi (Bangalore, 1980), i-iii.',2)">2]:- .
       

396. Krylov Nikolai biography
     
     • Krylov published over 200 papers on analysis and mathematical physics.
       

397. Schlomilch biography
     
     • He began publishing books early in his career with textbooks such as Handbuch der mathematischen Analysis (1845), Handbuch der Differential- und Integralrechnung (1846-48), Theorie der Differenzen und Summen Ein Lehrbuch (1848), Analytische Studien Theorie der Gammafunktionen (1848), Die allgemeine Umkehrung gegebener Funktionen (1849), and Grundzuge einer wissenschaftlichen Geometrie des Masses (1849).
       
     • His textbooks presented Cauchy's techniques in analysis and through them these important methods became well known in Germany.
       
     • After moving to Dresden in 1849, amazingly his output of textbooks became even greater with books such as Mathematische Abhandlungen (1850), Die Reihenentwickelungen der Differenzial- und Integralrechnung (1851), Handbuch der algebraischen Analysis (1851), Der Attractionscalcu (1851), and the two volumes of Compendium der hoheren Analysis (1853).
       
     • Also the first volume of Compendium der hoheren Analysis, published in 1853, had reached its fifth edition by 1881.
       
     • Other highly successful works included the two-volume text Compendium der hoheren Analysis (1862) and the two-volume text †bungsbuch zum Studium der hoheren Analysis (1867, 1868).
       

398. Hobson biography
     
     • He was introduced to modern analysis by Young and after this he began to make a real contribution to research.
       

399. Samoilenko biography
     
     • A monograph on the method of accelerated convergence, written jointly by Samoilenko, N Bogoliubov, and Yu Mytropolsky in 1969, gives an exhaustive analysis of the speed of convergence, error estimates, stability, and applications.
       

400. Listing biography
     
     • The subject was known as analysis situs for many years and only in the late 1920s was the English word topology used by Lefschetz.
       

401. Wang Yuan biography
     
     • However he did write a number of books such as: (with Hua Loo Keng) Applications of number theory to numerical analysis (1978); Goldbach Conjecture (1984); (with Hua Loo Keng) Popularising mathematical methods in the People's Republic of China (1989); Diophantine equations and inequalities in algebraic number fields (1991); (with Fang Kai-Tai) Number theoretic methods in statistics (1994); Hua Loo Keng (1995); and (with Fong Yuen) Calculus (1997).
       

402. Lehmer Derrick biography
     
     • For Lehmer, however, the problem was not so acute for he was able to take up the post of Director of the National Bureau of Standards' Institute for Numerical Analysis for the time that he was unable to hold his faculty position in Berkeley.
       

403. Chrystal biography
     
     • There is nothing like it in English, and it forms an excellent introduction to the various applications of Algebra to the higher analysis.
       

404. Schur biography
     
     • Schur is mainly known for his fundamental work on the representation theory of groups but he also worked in number theory, analysis and other topics described below.
       

405. Cholesky biography
     
     • The method received little attention after its publication in 1924 but Jack Todd included it in his analysis courses in King's College, London, during World War II.
       

406. Kac biography
     
     • He published a classic text Statistical Independence in Probability, Analysis and Number Theory in 1959.
       

407. Wexler-Kreindler biography
     
     • For her work on functional analysis, carried out with G C Moisil as her supervisor, she was awarded a doctorate having submitted her thesis Theory of Pseudolinear operators.
       

408. Wessel biography
     
     • In [A History of Vector Analysis (Notre Dame, 1967).',3)">3] Crowe credits Wessel with being the first person to add vectors.
       

409. Friedrichs biography
     
     • He received many honorary degrees (Aachen, Uppsala, Braunschweig, Columbia, and New York University), and received many awards, in particular the Applied Mathematics and Numerical Analysis Award of the National Academy, and the National Medal of Science in 1976:- .
       

410. Simon biography
     
     • Despite the depth of the results, the book is completely self-contained (assuming only a rudimentary knowledge of real analysis, such as one would find in a first year graduate course), and gets rapidly to the heart of the subject, providing detailed, concise proofs of the theorems.
       

411. Aleksandrov biography
     
     • at grammar school he studied celestial mechanics and mathematical analysis.
       

412. Schrodinger biography
     
     • Schrodinger was so entranced by his new theory that he threw caution to the winds, abandoned any pretence of critical analysis, and even though his new theory was scarcely hatched, he presented it to the Academy and to the Irish press as an epoch-making advance.
       

413. Koch biography
     
     • Yet this work can be said to be the first step on the long road which eventually led to functional analysis, since it provided Fredholm with the key for the solution of his integral equation.
       

414. Shannon biography
     
     • Shannon wrote a Master's thesis A Symbolic Analysis of Relay and Switching Circuits on the use of Boole's algebra to analyse and optimise relay switching circuits.
       

415. Chernikov biography
     
     • Polyhedrally closed systems of linear inequalities are an effective means in the analysis of problems of the theory of approximation of functions, in linear programming (in particular in questions of duality), and in control theory.
       

416. Johnson Barry biography
     
     • In order to undertake research in pure mathematics Johnson returned to England but he first taught at a grammar school in Tamworth before he began research in functional analysis at Gonville and Caius College of the University of Cambridge in October 1958.
       

417. West biography
     
     • These show West to have been familiar with the works of Lagrange, Laplace and Arbogast and, had they been published promptly, would have established him as a leading British exponent of Continental analysis and its applications.
       

418. Temple biography
     
     • Relativity theory, aerodynamics and quantum mechanics have been mentioned above but he also worked on analysis contributing to the study of the Lebesgue integral.
       

419. Lambert biography
     
     • In [Algebraic number theory and Diophantine analysis, Graz, 1998 (Berlin, 2000), 521-530.',34)">34] there is discussion of the claim that Lambert's proof is incomplete and requires a result by Legendre to complete it.
       

420. Chebyshev biography
     
     • [I] found an occasion each day to talk with this geometer concerning [applications of calculus to number theory] as well as other questions on pure and applied analysis.
       

421. Finck biography
     
     • His texts include books on algebra, mechanics, geometry and analysis.
       

422. Blum biography
     
     • Especially striking is the interplay of various mathematical disciplines such as algebraic number theory, algebraic geometry, logic, and numerical analysis, to mention a few.
       

423. Diophantus biography
     
     • The method for solving the latter is now known as Diophantine analysis.
       

424. Ptolemy biography
     
     • However, Ptolemy was not without his supporters by any means and further analysis led to a belief that the accusations made against Ptolemy by Delambre were false.
       

425. Preston biography
     
     • It is interesting to reflect that although we, the students, knew that this syllabus had stood still, neglecting most of modern mathematics - analysis was more up to date - we did not complain about it.
       

426. Minding biography
     
     • At Dorpat Minding taught algebra, analysis, geometry, probability, mechanics and physics.
       

427. Selberg biography
     
     • The necessary analytic tools were known by 1896 when Hadamard and de la Vallee Poussin independently proved the theorem using complex analysis.
       

428. Mandelbrojt biography
     
     • Mandelbrojt and Hadamard jointly published La serie de Taylor et son prolongement analytique, a monograph which covered the topics in classical analysis which Mandelbrojt had studied for his doctorate.
       

429. Hollerith biography
     
     • It saved the United States 5 million dollars for the 1890 census by completing the analysis of the data in a fraction of the time it would have taken without it and with a smaller amount of manpower than would have been necessary otherwise.
       

430. Fine Nathan biography
     
     • As a mathematician Fine had wide interests publishing on many different topics including number theory, logic, combinatorics, group theory, linear algebra, partitions and functional and classical analysis.
       

431. Gregory Duncan biography
     
     • Two other important works by Duncan Gregory are Examples of the Processes of the Differential and Integral Calculus and A Treatise on the Application of Analysis to Solid Geometry.
       

432. Lexis biography
     
     • Many scientists attempted to adapt probability-based methods to social science problems, including Quetelet and Lexis, but in the end they were frustrated, Quetelet because his methods were too insensitive to segregate his data into categories amenable to statistical analysis, Lexis because his binomial models were insufficiently rich for interesting applications.
       

433. De Moivre biography
     
     • which took trigonometry into analysis, and was important in the early development of the theory of complex numbers.
       

434. Mendelsohn biography
     
     • He wrote papers on a wide variety of combinatorial problems, for example: Symbolic solution of card matching problems (1946), Applications of combinatorial formulae to generalizations of Wilson's theorem (1949), Representations of positive real numbers by infinite sequences of integers (1952), A problem in combinatorial analysis (1953), The asymptotic series for a certain class of permutation problems (1956), and Some elementary properties of ill conditioned matrices and linear equations (1956).
       

435. Du Bois-Reymond biography
     
     • Du Bois-Reymond's work was directed at the basic questions of mathematical analysis of the time and is marked by both the personality of the author and the state of mathematics of the period.
       

436. Griffiths biography
     
     • Though the papers selected cover a broad range of topics in complex analysis, algebraic geometry and differential equations ..
       

437. Kochina biography
     
     • In 1979 Kochina was awarded the Order of the Friendship of Nations, then in 1994 an international conference was held in St Petersburg on complex analysis and free boundary layer problems to celebrate her 95th birthday.
       

438. Martin biography
     
     • In his writings and problem-solving, Martin dealt mostly with Diophantine analysis, probability, elliptic integrals, logarithms, and properties of numbers and triangles.
       

439. Pick biography
     
     • His mathematical work was extremely broad and his 67 papers range across many topics such as linear algebra, invariant theory, integral calculus, potential theory, functional analysis, and geometry.
       

440. Ackermann biography
     
     • It was intended to be a consistency proof for elementary analysis although this proof contained significant errors.
       
     • Ackermann presents intuitionism, which constructs a mathematics with a minimum of logic, and the Frege-Russell analysis of the number concept.
       
     • He defends this analysis against certain objections (circularity, necessity of an axiom of infinity).
       

441. Loewy biography
     
     • The first of these was one of the first works to introduce into Germany the methodology, the terminology and the achievements of postulational analysis as it was being developed in the United States.
       

442. Kramer biography
     
     • One cannot easily think of a topic within layman's comprehension which is not presented in considerable detail, including analysis, algebra, logic and foundations.
       

443. Bolza biography
     
     • Moore was a fiery enthusiast, brilliant, and keenly interested in the popular mathematical research movements of the day; Bolza, a product of the meticulous German school of analysis led by Weierstrass, was an able, and widely read research scholar; Maschke was more deliberate than the other two, sagacious, brilliant in research, and a most delightful lecturer in geometry.
       

444. Macdonald William biography
     
     • He was also awarded the Gray Prize in 1872 for his essay on Spectrum Analysis and in the same year he was awarded the Arnott prize.
       

445. Seki biography
     
     • The work is remarkable for the careful analysis of the problems which Seki made and this certainly was one of the reasons for his great success as a teacher.
       

446. Feller biography
     
     • Later he put his results in a functional analysis framework.
       

447. Kurepa biography
     
     • Chapter 4 is on topological and metric spaces, with the fifth and final chapter on limiting processes in analysis, measure theory, Borel and Souslin sets.
       

448. Dixon biography
     
     • In this respect his analysis is comparable in thoroughness with that of Carleman, Hardy, Hilbert and Schmidt.
       

449. Maschke biography
     
     • Moore was a fiery enthusiast, brilliant, and keenly interested in the popular mathematical research movements of the day; Bolza, a product of the meticulous German school of analysis led by Weierstrass, was an able, and widely read research scholar; Maschke was more deliberate than the other two, sagacious, brilliant in research, and a most delightful lecturer in geometry.
       

450. Fresnel biography
     
     • By applying mathematical analysis to his work Fresnel removed many of the objections to the wave theory of light.
       

451. Woodhouse biography
     
     • He demanded that analysis in general and the calculus specifically be placed upon a purely algebraic footing free of geometric and physical encumbrances such as limits or infinitesimals.
       

452. Wilder biography
     
     • The author quietly proposes that we study mathematics as a human artefact, as a natural phenomenon subject to empirical observation and scientific analysis, and, in particular, as a cultural phenomenon understandable in anthropological terms.
       

453. Bateman biography
     
     • He wrote a number of texts that have been reprinted as classics: The mathematical analysis of electrical and optical wave-motion on the basis of Maxwell's equations (1915, reprinted 1955); Partial differential equations of mathematical physics (1932, reprinted 1944 and 1959); (written with H L Dryden and F D Murnaghan), Hydrodynamics, National Research Council, Washington, D.C.
       

454. Burkhardt biography
     
     • His main work was in analysis, particularly the theory of trigonometric series, and on the history of mathematics.
       

455. Mineur biography
     
     • He contributed to many areas of astronomy and mathematics including celestial mechanics, analytic mechanics, statistics and numerical analysis.
       

456. Cantelli biography
     
     • Cantelli's work in astronomy involved statistical analysis of data and his interests turned more towards the statistical style of mathematics and to applications of probability to astronomy and other areas.
       

457. Coolidge biography
     
     • A great number of special topics are briefly or amply discussed, from the geometry of the spider's web to modern criticism of enumerative geometry, Douglas' work on the Plateau problem, quaternions and some tensor analysis.
       

458. Ramanujam biography
     
     • This was agreed and he taught analysis in Bangalore but, again in the depths of depression caused by his illness, he tried again to leave the Institute and obtain a university teaching post.
       

459. Cesaro biography
     
     • He remained at Palermo until 1891, moving then to Naples where he held the chair of mathematical analysis until his death.
       

460. Zhukovsky biography
     
     • The field of hydrodynamic phenomena which can be explored with exact analysis is more and more increasing.
       

461. Andreev biography
     
     • Andreev is best known for his work on geometry, although he also made contributions to analysis.
       

462. Kaluznin biography
     
     • The school provided a solid background in mathematics, including topics in the foundations of analysis, differential equations and complex variables.
       

463. Boggio biography
     
     • In 1918 D'Ovidio retired and Boggio took over teaching algebraic analysis and analytic geometry.
       

464. Petryshyn biography
     
     • Petryshyn's main achievements are in functional analysis.
       

465. Lah biography
     
     • The binding coefficients L(n, k) = n! (n-1)!/(k-1)!/(n-k)!/k! were called unsigned Lah numbers by J Riordan in his book An Introduction to Combinatorial Analysis (1958).
       

466. Frattini biography
     
     • His work on differential geometry is important as is his papers on the analysis of second degree indeterminates.
       

467. Plemelj biography
     
     • He was taught analysis by von Escherich while Gegenbauer (appointed a professor in Vienna in 1893) and Mertens (appointed to Vienna in 1894) taught him algebra and number theory.
       

468. Wright Sewall biography
     
     • An important method which he had worked out by 1918 was a new statistical approach called path analysis.
       

469. Steklov biography
     
     • He reduced problems of this type to boundary-value problems of Dirichlet type using rigorous mathematical analysis.
       

470. Lindelof biography
     
     • In it he examines the role which residue theory (Cauchy) plays in function theory as a means of access to modern analysis.
       

471. Descartes biography
     
     • the Praxis was read by Descartes, and every line of Descartes' analysis bears token of the impression.
       

472. Kolosov biography
     
     • 31 (1989), 52-75.',2)">2] contains details of the interesting correspondence and a detailed analysis of Kolosov's work.
       

473. Jacobsthal biography
     
     • He has written papers in such diverse fields as algebra, analysis, function theory and number theory.
       

474. Pask biography
     
     • His research teams carried out research on skill acquisition, styles and strategies of learning, learning in groups, knowledge and task analysis, processes of design, decision-making, problem-solving and learning to learn.
       

475. Legendre biography
     
     • all failed because he always relied, in the last analysis, on propositions that were "evident" from the Euclidean point of view.
       

476. Menabrea biography
     
     • During this period of politics he continued to do excellent scientific work, giving the first precise formulation of methods of structual analysis based on the principle of virtual work first presented in 1857.
       

477. Stevin biography
     
     • A careful analysis of the problem situation in the science of music around 1600, reveals that Stevin's treatise highlights a particular stage in the history of what has always been the core issue of the science of music, namely, the problem of consonance.
       

478. Kruskal William biography
     
     • The paper A nonparametric test for the several sample problem was authored by Kruskal alone while the second Use of ranks in one-criterion analysis of variance was a joint publication with Wallis.
       

479. Kellogg biography
     
     • Kellogg also wrote a number of papers on the existence of certain sets of functions in analysis as well as generalisations of polynomials due to Sergi Bernstein.
       

480. Laguerre biography
     
     • His most important work was in the areas of analysis and geometry.
       

481. Peierls biography
     
     • It "presents a number of examples in which a plausible explanation is not borne out by a more careful analysis".
       

482. De Bruin biography
     
     • In 1969 he joined the group of Leen van Wijngaarden at the department of Applied Physics where he was the first expert on numerical analysis and applied mathematics.
       

483. Beatty biography
     
     • There are many books dealing in an individual way with elementary aspects of Algebra, Geometry, or Analysis.
       

484. Cantor biography
     
     • At Halle the direction of Cantor's research turned away from number theory and towards analysis.
       

485. Novikov biography
     
     • Novikov headed the Department of Analysis at Moscow State Teachers Training Institute from 1944.
       

486. Marchenko biography
     
     • He also obtained fundamental results in the theory of inverse problems in spectral analysis for the Sturm-Liouville and more general equations.
       

487. Montucla biography
     
     • I begin to take M Montucla at his word when he tells us he has fallen out with learned analysis: I wait calmly for him to be reconciled with it.
       

488. Hodge biography
     
     • During this period he developed the relationship between geometry, analysis and topology and produced some of his best remembered work on the theory of harmonic integrals.
       

489. Aaboe biography
     
     • This work would put research into Babylonian astronomy on a firm foundation through the publication and systematic analysis of more than three hundred texts found on cuneiform tablets held in the British Museum, the Oriental Institute at Chicago, the Louvre in Paris, the Staatliche Museen in Berlin, the Arkeoloji Muzeleri in Instanbul, and several smaller collections in Europe and the United States.
       

490. Cowling biography
     
     • The results of the analysis are of much physical interest and a large part of the book is devoted to the comparison of theory and experiment for viscosity, thermal conduction and diffusion.
       

491. Kingman biography
     
     • Let us now sum up his mathematical contributions which were almost all in the area of mathematical statistics, more precisely stochastic analysis, random processes, regenerative phenomena and mathematical genetics.
       

492. Siegel biography
     
     • 85 (4) (1983), 158-173.',9)">9], discusses Siegel's contributions to complex analysis.
       

493. Guccia biography
     
     • The goal was to stimulate the study of higher mathematics by means of original communications presented by the members of the society on the different branches of analysis and geometry, as well as on rational mechanics, mathematical physics, geodesy, and astronomy.
       

494. Jacobi biography
     
     • It gives me great satisfaction to see two young mathematicians such as you and [Abel] cultivate with such success a branch of analysis which for such a long time has been my favourite topic of study but which had not been received in my own country as well as it deserves.
       

495. Brouwer biography
     
     • Point set theory was widely applied in analysis and somewhat less widely applied in geometry, but it did not have the character of a unified theory.
       

496. Neyman biography
     
     • He put forward the theory of confidence intervals, the importance of which in statistical theory and analysis of data cannot be overemphasised.
       

497. Schwerdtfeger biography
     
     • His main fields of interest were Galois theory, matrix theory, theory of groups and their geometries and complex analysis.
       

498. Walker John biography
     
     • The three most important papers that Walker wrote were on the analysis of plane curves and curved lines.
       

499. Griffiths Brian biography
     
     • We give the titles of a few of his mathematical education article which give an overview of his interests in that topic: Pure mathematicians as teachers of applied mathematicians (1968); Mathematics Education today (1975); Successes and failures of mathematical curricula in the past two decades (1980); Simplification and complexity in mathematics education (1983); The implicit function theorem: technique versus understanding (1984); A critical analysis of university examinations in mathematics (1984); Cubic equations, or where did the examination question come from? (1994); The British Experience of Teaching Geometry since 1900 (1998); and The Divine Proportion, matrices and Fibonacci numbers (2008).
       

500. Keen biography
     
     • The details of how the pleating planes fill out quasi-Fuchsian punctured torus space and how their boundaries meet the space of Fuchsian punctured torus groups are determined by the combinatorial patterns of how the laminations intersect and the analysis of their length functions.
       
     • Among other contributions made by Keen, we should mention her editorial work with publications such as the Journal of Geometric Analysis, the Annales of the Finnish Academy of Sciences, and the Proceedings of the American Mathematical Society.
       

501. Wheeler biography
     
     • This work was done in the days when functional analysis was in its infancy and much of her work has lessened in importance as it became part of the more general theory.
       

502. Titeica biography
     
     • Mihaileanu [\'Gheorghe Titeica and Dimitrie Pompeiu\' Symposium on Geometry and Global Analysis, Bucharest, 1973 (Romanian) (Editura Acad.
       

503. Le Paige biography
     
     • He taught courses on the theory of determinants, which is not surprising since this was Catalan's speciality, and he also taught higher analysis.
       

504. Whittaker John biography
     
     • He then did some of his most important work on complex analysis.
       

505. Poinsot biography
     
     • Poinsot took on another appointment, in addition to the one with the Imperial University, when he accepted the position of assistant professor of analysis and mechanics at the Ecole Polytechnique on 1 November 1809.
       

506. Nash-Williams biography
     
     • The course notes for his courses at Reading could be extremely long and detailed, and the notes on one course 'Introduction to Analysis' in particular provoked a protest at the Staff/Student Committee that the quantity of notes handed out (averaging 17 closely written pages per lecture) were unreasonable, and no student could have sufficient time to actually read them.
       

507. Mathieu Claude biography
     
     • Mathieu was appointed professor of analysis at the Ecole Polytechnique in 1828, a position he held for ten years when he resigned to take up an appointment as an examiner for students completing their courses at the Ecole.
       

508. Steiner biography
     
     • He attended lectures at the Universities of Heidelberg on combinatorial analysis, differential and integral calculus and algebra.
       
     • Steiner disliked algebra and analysis and believed that calculation replaces thinking while geometry stimulates thinking.
       

509. Clarke Joan biography
     
     • Professor Jack Good, who also worked on Banburismus, has since said that it was the first example of Sequential Analysis and describes it as [6]:- .
       

510. Dixon Arthur biography
     
     • In the latter part of his career, Dixon published a series of around twelve joint papers with W L Ferrar on analytic number theory, summation formulae, Bessel functions and other topics in analysis.
       

511. Yau biography
     
     • Yau, in joint work, constructed minimal surfaces, studied their stability and made a deep analysis of how they behave in space-time.
       

512. Faa di Bruno biography
     
     • In 1871 Faa di Bruno became a professor at the University of Turin, being appointed to the Chair of Higher Analysis there in 1876.
       

513. Sokhotsky biography
     
     • The magister's thesis of Sokhotskii was the first research paper on complex analysis published in Russian.
       

514. Bondi biography
     
     • he could look at old problems with great freshness of mind, and overturn accepted ideas with a disarming combination of sheer speed, clear and incisive analysis and a childlike, bubbling sense of fun.
       

515. Thiele biography
     
     • He published this in 1909 in his book which made a major contribution to numerical analysis.
       

516. Droz-Farny biography
     
     • He studied mathematics in the canton of Neufchatel and then continued his studies in Munich where he attended analysis lectures by Klein.
       

517. Konigsberger biography
     
     • He contributed to many fields of mathematics, most notably to analysis and analytic mechanics.
       

518. Vagner biography
     
     • His research activities were connected with the Seminar on Vector and Tensor Analysis at Moscow University.
       

519. Peirce Benjamin biography
     
     • To support his claims he did a statistical analysis of the angles of the downstrokes in 42 genuine Sylvia Ann Howland signatures.
       

520. Dyson biography
     
     • Dyson had three papers published in 1943, Three identities in combinatory analysis and On the order of magnitude of the partial quotients of a continued fraction are consecutive papers in the Journal of the London Mathematical Society while A note on kurtosis appeared in the Journal of the Royal Statistical Society.
       

521. Novikov Sergi biography
     
     • At this time the Faculty of Mathematics and Mechanics of Moscow University was a world leading centre for research in real analysis, with Kolmogorov the major influence.
       

522. Atwood biography
     
     • He also published a second work in the same year Analysis of a Course of Lectures on the Principles of Natural Philosophy which was an expanded version of his Cambridge course which he had first given detail of in 1776.
       

523. Johnson biography
     
     • In the area of logic he published papers such as The logical calculus (1892) and Analysis of thinking (1918), both of which appeared in Mind.
       

524. Pearson Egon biography
     
     • Neyman had already left London in 1938 for a post in Berkeley and with the outbreak of war Pearson began to undertake war work for the Ordinance Board undertaking statistical analysis of the fragmentation of shells hitting aircraft and similar work.
       

525. Arnold biography
     
     • In recognition of his basic contribution to the stability theory of Dynamical Systems, his pioneering work on singularity theory and seminal contributions to analysis and geometry.
       

526. Playfair biography
     
     • Playfair was among the first in Britain to teach modern analysis.
       

527. Chowla biography
     
     • He wrote on additive number theory (lattice points, partitions, Waring's problem), analysis, Bernoulli numbers, class invariants, definite integrals, elliptic integrals, infinite series, the Weierstrass approximation theorem), analytic number theory (Dirichlet L-functions, primes, Riemann and Epstein zeta functions), binary quadratic forms and class numbers, combinatorial problems (block designs, difference sets, Latin squares), Diophantine equations and Diophantine approximation, elementary number theory (arithmetic functions, continued fractions, and Ramanujan's tau function), and exponential and character sums (Gauss sums, Kloosterman sums, trigonometric sums).
       

528. Malcev biography
     
     • Ideas from these papers were later to reappear in Robinson's work on non-standard analysis.
       

529. Ruan Yuan biography
     
     • Experts in textual analysis studied the texts while other experts tried to reconstruct lost texts from quotations in surviving works.
       

530. Beltrami biography
     
     • Beltrami indirectly influenced the development of tensor analysis by providing a basis for the ideas of Ricci-Curbastro and Levi-Civita on the topic.
       

531. Teichmuller biography
     
     • Teichmuller's habilitation thesis Untersuchungen uber konforme und quasikonforme Abbildungen was not influenced by Hasse, but rather was sparked by lectures that he had attended by Rolf Nevanlinna on complex analysis.
       
     • He introduced quasi-conformal mappings and differential geometric methods into complex analysis.
       

532. Lukacs biography
     
     • He was an associate editor of the Journal of the American Statistical Association (1951-55, 1961-63), the Annals of Mathematical Statistics (1958-64,1968-70), and the Journal of Multivariate Analysis (1970-83).
       

533. Poncelet biography
     
     • (7) Analysis of transversals applied to geometric curves and surfaces.
       

534. Rajagopal biography
     
     • Here he gained an outstanding reputation as a teacher of classical analysis.
       

535. Nevanlinna biography
     
     • However he read Lindelof's Introduction to Higher Analysis before going to university and became an enthusiastic analyst for the whole of his life.
       

536. Schmidt biography
     
     • Schmidt's ideas were to lead to the geometry of Hilbert spaces and he must certainly be considered as a founder of modern abstract functional analysis.
       

537. Weyl biography
     
     • It united analysis, geometry and topology, making rigorous the geometric function theory developed by Riemann.
       

538. Green biography
     
     • In the Press, and shortly will be published, by subscription, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism.
       

539. Turnbull biography
     
     • concrete and formal in the sense that he sought to solve problems by an effective formalism rather than by a conceptual analysis of the underlying structures.
       

540. Neumann Carl biography
     
     • Neumann entered the University of Konigsberg where he became close friends with two of his teachers, Otto Hesse and F J Richelot who taught mathematical analysis.
       

541. Mengoli biography
     
     • analyse a little-known aspect of Pietro Mengoli's mathematical activity: the difficulties he faced in trying to solve some problems in Diophantine analysis suggested by J Ozanam.
       

542. Zorawski biography
     
     • One can say that, thanks to these two scientists, Polish mathematics ceased being a mere consumer of foreign thinking and analysis.
       

543. Whyburn biography
     
     • Later major texts by Whyburn were Topological analysis (1958) and Dynamic topology which was jointly authored by Edwin Duda and was published 10 years after Whyburn's death.
       

544. Saks biography
     
     • Mathematical analysis, and especially those of its branches which used modern methods of set theory and topology, became his main field of interest.
       

545. Bouquet biography
     
     • With Briot he worked from 1853 onwards on deep studies of Cauchy's ideas of analysis and produced many fundamental papers on series expansions of functions and on elliptic functions.
       

546. Sprague biography
     
     • This article was a most thorough analysis of the contributions, including those of de Witt, Halley, and de Moivre, to the advancement of actuarial science.
       

547. Mersenne biography
     
     • His main reason to study combinatorial analysis was, however, to optimise musical composition as he explains in The book on the art of singing well which is Book Six of Harmonie universelle (1636).
       

548. Delambre biography
     
     • In almost all branches of Mathematics one is blocked by insurmountable difficulties (but) the spectacle of analysis and mechanics in our time (convinces me that) the generations to come will not see anything impossible in what remains to be done.
       

549. Youden biography
     
     • In that position he again was deeply involved in devising experimental arrangements for a wide range of different tasks from spectral analysis to thermometer and other instrument calibration.
       

550. Arbogast biography
     
     • Arbogast won the prize with his essay and his notion of discontinuous function became important in Cauchy's more rigorous approach to analysis.
       

551. Takagi biography
     
     • His two most important books from this time are Introduction to analysis (1938), Algebraic number theory (1948) and an important work on the history of mathematics in the 19th century.
       

552. Halphen biography
     
     • He examined problems in the areas of systems of lines, classification of space curves, enumerative geometry of plane conics, singular points of plane curves, projective geometry and differential equations, elliptic functions, and assorted questions in analysis.
       

553. Tibbon biography
     
     • Harper's analysis in [Isis 62 (1) (1971), 61-68.',4)">4] suggested that Tibbon's Almanach was based on original work but Toomer in [Isis 64 (223) (1973), 351-355.
       

554. Bernoulli Daniel biography
     
     • This work contains for the first time the correct analysis of water flowing from a hole in a container.
       

555. De Prony biography
     
     • Prony, lecturer in analysis, director of the Cadastre, member of the Institute.
       

556. De Vries Henrik biography
     
     • His lectures took in algebra and analysis, but from 1921-22 onwards, he focussed increasingly on his preferred field, giving public lectures on the development of geometry.
       

557. Laszlo biography
     
     • He published many other articles on the history of mathematics such as Lajos David (1881-1962), historian of Hungarian mathematics (1981), Great female figures of Hungarian mathematics in 19th-20th centuries (1983), The development, and the developing of the concept of a , fraction (2001), The genesis of Eudoxus's infinity lemma and proportion theory (2001), From Fejer's disciples to Erdos's epsilons - change over from analysis to combinatorics in Hungarian mathematics (2002), and Irrationality and approximation of √2 and √3 in Greek mathematics (2004).
       

558. Mohr biography
     
     • It had been sent to him by Oldenburg, the secretary of the Royal Society in London, in 1675 and Leibniz replied to Oldenburg in the following year praising Mohr's skill in geometry and analysis.
       

559. Parry biography
     
     • Bill was the first appointment in analysis at Warwick.
       

560. Malone-Mayes biography
     
     • In 1966 when she was awarded a doctorate for her thesis A Structure Problem in Asymptotic Analysis by the University of Texas at Austin she became the fifth African-American woman to receive a Ph.D.
       

561. Ingham biography
     
     • He was elected a Fellow of the Royal Society in 1945 and became a Reader in Mathematical Analysis in 1953.
       

562. Scherk biography
     
     • At Halle, Scherk taught a wide range of courses such as: analytic geometry of lines and the conic sections; analytic geometry of lines and surfaces of the first and second degree; algebra and algebraic geometry; plane and spherical trigonometry; integral calculus; and differential calculus and its application to algebra, analysis and geometry.
       

563. Fock biography
     
     • The articles presented also possess a great historical value, most of them representing important steps in the development of quantum mechanics and quantum field theory during the first half of last century, and should be subject to careful and detailed analysis from historians of science.
       

564. Lehmer Derrick N biography
     
     • A little counter which records the number of revolutions made by the main shaft, gives a number from which the factors of the large number under analysis can readily be obtained.
       

565. Ricci-Curbastro biography
     
     • Ricci-Curbastro's absolute differential calculus became the foundation of tensor analysis and was used by Einstein in his theory of general relativity.
       

566. Gregory David biography
     
     • the analysis of these notes suggests that the copy is the one annotated by David Gregory.
       

567. Thompson Robert biography
     
     • Editorial work was important to Thompson: he was a contributing editor of Linear Algebra and its Applications and an editor of the Society for Industrial and Applied Mathematics Journal on Matrix Analysis.
       

568. Saunderson biography
     
     • Its full title is The Method of fluxions applied to a Select Number of Useful Problems, together with the Demonstration of Mr Cotes's forms of Fluents in the second part of his Logometria, the Analysis of the Problems in his Scholium Generale, and an Explanation of the Principal Propositions of Sir Isaac Newton's Philosophy.
       

569. Milne William biography
     
     • These included: The geometrical meaning of the triad of points (1910); A property of the complete quadrangle (1911); The teaching of limits and convergence to scholarship candidates (1911); The teaching of limits and convergence to scholarship candidates (1912); The teaching of limits and convergence to scholarship candidates (1913); Another proof and generalisation of the theorem given in note 339 (1913); The teaching of modern analysis in secondary schools (1915); The graphical treatment of power series (1918); The uses and functions of a school mathematical library (1918); Mathematics and the pivotal industries (1919); The training of the mathematical teacher (1920); and Noether's canonical curves (1920).
       

570. Bessel biography
     
     • Bessel also worked out a method of mathematical analysis involving what is now known as the Bessel function.
       

571. Warschawski biography
     
     • With careful scholarship, he made lasting contributions to the theory of complex analysis, particularly to the theory of conformal mappings.
       

572. Hellinger biography
     
     • This Seminar is described in [Studies in numerical analysis : papers in honour of Cornelius Lanczos on the occasion of his 80th birthday (London, 1974), 7-13.
       

573. Pacioli biography
     
     • In [Sciences of the Renaissance (Paris, 1973), 93-106.',10)">10] the importance of Pacioli's work is discussed, in particular his computation of approximate values of a square root (using a special case of Newton's method), his incorrect analysis of certain games of chance (similar to those studied by Pascal which gave rise to the theory of probability), his problems involving number theory (similar problems appeared in Bachet's compilation), and his collection of many magic squares.
       

574. Witten biography
     
     • Of course, quantum physics had from the beginning a marked influence in many areas of mathematics - functional analysis and representation theory, to mention just two.
       

575. Robinson Julia biography
     
     • She was unhappy teaching statistics, which was allowed by the rules, but despite this her first publication A note on exact sequential analysis came out of her teaching in the statistics laboratory at Berkeley.
       

576. Herbrand biography
     
     • He lived constantly absorbed in the analysis of the conflicts and duties which gave birth to an inescapable sensitivity within him.
       

577. Bohr Niels biography
     
     • With it he won the Gold Medal for 1906 from the Royal Danish Academy of Sciences for his analysis of vibrations of water jets as a means of determining surface tension.
       

578. Volterra biography
     
     • He continued to study functional analysis applications to integral equations producing a large number of papers on composition and permutable functions.
       

579. Curry biography
     
     • In order to improve his chances of financial support, Curry wrote up his ideas on combinators for publication and this became his first paper An analysis of logical substitution which appeared in the American Journal of Mathematics in 1929.
       

580. Coriolis biography
     
     • After his father died Coriolis had to support the family and, with his health already poor, he decided to accept a post in the Ecole Polytechnique in 1816 tutoring analysis.
       

581. Koszul biography
     
     • Many new ideas have also been derived with the help of a great variety of notions from modern algebra, differential geometry, Lie groups, functional analysis, differentiable manifolds and representation theory.
       

582. Spencer biography
     
     • In Princeton he was always surrounded by a group of mathematicians who shared his enthusiasm and collaborated in the research of complex analysis (I was one of them).
       

583. Behrend biography
     
     • In A contribution to the theory of magnitudes and the foundations of analysis (1956) Behrend characterised the additive semigroup of positive real numbers, the "magnitudes" of the title.
       

584. Neuberg biography
     
     • At Liege he taught analysis, higher algebra, descriptive geometry, projective geometry, analytic geometry, and the foundations of mathematics.
       

585. Drach biography
     
     • After an appointment at Toulouse, Drach was appointed to the Chair of Analytical Mechanics and Higher Analysis at the Sorbonne in Paris in 1913.
       

586. Liouville biography
     
     • In 1838 Liouville was appointed Professor of Analysis and Mechanics at the Ecole Polytechnique.
       

587. Floquet biography
     
     • In July 1880 he was given a permanent chair and by the end of the year he was holding the chair of pure mathematics and analysis.
       

588. Petersen biography
     
     • His research was on a wide variety of topics from algebra and number theory to geometry, analysis, differential equations and mechanics.
       

589. Bring biography
     
     • There are eight volumes of his hand written mathematical work on various questions in algebra, geometry, analysis and astronomy preserved in the library at Lund.
       

590. Schoenberg biography
     
     • Schoenberg is noted worldwide for his realisation of the importance of spline functions for general mathematical analysis and in approximation theory, their key relevance in numerical procedures for solving differential equations with initial and/or boundary conditions, and their role in the solution of a whole host of variational problems.
       

591. Spence David biography
     
     • He described some of his analysis of the potential flow about a body representing the airfoil plus its boundary layer and viscous wake in the paper Prediction of the characteristics of two dimensional airfoils which appeared in 1954.
       

592. Hopkinson biography
     
     • Hopkinson's application of Maxwell's electromagnetic theories to the analysis of residual charge and displacement in electrostatic capacity led to his election as a fellow of the Royal Society in 1877.
       

593. Stormer biography
     
     • The chief results obtained from the analysis of a vast number of parallactic photographs are discussed in this book.
       

594. Jeffery Ralph biography
     
     • In chapter VII properties of the non-differentiable functions of Weierstrass and of Besicovitch are established, followed by an exhaustive analysis of the distribution of the derivates and approximate derivates of an arbitrary function of one variable.
       

595. Qin Jiushao biography
     
     • Chapter 1 is on indeterminate analysis; it contains remarkable work on the Chinese remainder theorem which occurs right at the beginning of the text.
       

596. Steenrod biography
     
     • From a position of minor importance, as compared as compared with the traditional areas of analysis and algebra, its concepts came to exert a profound influence, and it is now commonplace that a mathematical problem is "solved" by reducing it to a homology-theoretic one.
       

597. Lyapin biography
     
     • Analysis, algebra, geometry, and topology being rich in examples of the latter, their abstract theory deserves recognition.
       

598. Koksma biography
     
     • One then finds a discussion of Minkowski's analysis, his 'Geometry of Numbers' and applications to homogeneous and non-homogeneous linear forms.
       

599. Alexander biography
     
     • In the same year the American Mathematical Society awarded Alexander the Bocher Prize for his memoir, Combinatorial analysis situs published in the Transactions of the American Mathematical Society two years earlier.
       

600. Boole biography
     
     • Boole had begun to correspond with De Morgan in 1842 and when in the following year he wrote a paper On a general method of analysis applying algebraic methods to the solution of differential equations he sent it to De Morgan for comments.
       

601. Bruhat biography
     
     • Another lecture course, this time given in India, was published as Lectures on some aspects of p-adic analysis in 1963.
       

602. Aepinus biography
     
     • These appointments were apparently merely a device for establishing Aepinus, who had begun to acquire a reputation, in Frederick's capital: he was neither especially interested nor experienced in astronomy, and his closest published approach to the subject during his Berlin sojourn was a mathematical analysis of a micrometer adapted to a quadrant circle.
       

603. Zeuthen biography
     
     • It looked in detail at the work of Descartes, Viete, Barrow, Newton and Leibniz as he traced the development of algebra, analytic geometry and analysis.
       

604. Linnik biography
     
     • Later Linnik made major contributions to probability with his work on limit theorems and was the first to use powerful techniques from analysis in mathematical statistics.
       

605. Orshansky biography
     
     • She published an analysis of the poverty population using these thresholds in a January 1965 Social Security Bulletin article.
       

606. Doppler biography
     
     • After recommending Doppler's paper on applied analysis for publication, Bolzano commented about Doppler himself.
       

607. Bohr Harald biography
     
     • Harald Bohr worked on Dirichlet series, and applied analysis to the theory of numbers.
       

608. Jia Xian biography
     
     • This is because Yang Hui wrote Xiangjie Jiuzhang Suanfa (A detailed analysis of the mathematical rules in the Nine Chapters) in 1261 with the intention of explaining, and making better known, the work of Jia Xian.
       

609. De Vries Hendrik biography
     
     • His lectures took in algebra and analysis, but from 1921-22 onwards, he focussed increasingly on his preferred field, giving public lectures on the development of geometry.
       

610. Grosswald biography
     
     • An analyst, specializing in analytic number theory, Grosswald also wrote on classical analysis and related topics.
       

611. Biot biography
     
     • was endowed to the highest degree with all the qualities of curiosity, finesse, penetration, precision, ingenious analysis, method, clarity, in short with all the essential and secondary qualities, bar one, genius, in the sense of originality and invention.
       

612. Newton biography
     
     • The title page of Analysis per quantitatum series, fluxiones (1711) .
       

613. Walsh biography
     
     • He takes up some known method or formula of analysis, makes in it a slight and quite unimportant change (for every theorem admits of some variety in the mode of its expression) and views the result to which he is led as an original discovery.
       

614. Green Sandy biography
     
     • with First Class Honours in Mathematics in 1947 having taken the compulsory courses of Geometry, Algebra, Analysis, Statics, Dynamics and the optional courses of Special Functions, and Algebra in his final year of study.
       

615. Kato biography
     
     • emphasizes clear and simple explanations of the fundamental notions of functional analysis.
       

616. Mumford biography
     
     • may be described as follows "the analysis of the patterns generated by the world in any modularity, with all their naturally occurring complexity and ambiguity, with the goal of reconstructing the processes, objects and events that produced them and of predicting these patterns when they reoccur".
       

617. Born biography
     
     • Their work uses three dimensional Fourier analysis and periodic boundary conditions.
       

618. Cournot biography
     
     • Again with Poisson's recommendation, Cournot was appointed to a newly created chair in analysis at Lyon in 1834.
       

619. Vranceanu biography
     
     • His doctoral thesis, and all his earlier publications, concerned applications of analysis to mechanics.
       

620. Zeeman biography
     
     • And such discipline needs to be taught, needs specialists to teach it, and needs to be supported by research on curriculum reform and the analysis of learning techniques.
       

621. Kneser Hellmuth biography
     
     • I hope that this theory will also prove fruitful for the special functions used in analysis, this has to be required of a new theory, in particular, if one considers that the general theory of rational functions of one indeterminate came from the treatment of special functions, namely the gamma and sigma functions by Weierstrass and of the Riemann zeta function by Hadamard.
       

622. Friedmann biography
     
     • Friedmann began to study for his Master's Degree and, in 1911, became involved with a circle formed to study mathematical analysis and mechanics.
       

623. Fermi biography
     
     • In his essay Fermi derived the system of partial differential equations for a vibrating rod, then used Fourier analysis to solve them.
       

624. Severi biography
     
     • Severi maintains a balance between geometry and analysis - he has actually made outstanding contributions to function theory.
       

625. Selten biography
     
     • for their pioneering analysis of equilibria in the theory of non-cooperative games.
       

626. Rankine biography
     
     • While an apprentice engineer he made a mathematical analysis of the cooling of the earth (1840).
       

627. Darboux biography
     
     • Darboux made important contributions to differential geometry and analysis.
       

628. Nekrasov biography
     
     • In fact his deep understanding of mathematical analysis as developed by mathematicians such as Goursat enabled him to succeed in solving a whole range of concrete problems.
       

629. Stewart biography
     
     • In the mean time I wish you would as your leisure can permit find out as many as may be of them, and be sure to write down both analysis and composition, because when I publish an account of the "Porisms" I shall be glad to have your store to increase mine which shall every one of them be particularly acknowledged in the book.
       

630. Denjoy biography
     
     • He combined topological and metrical methods to attack problems of real analysis.
       

631. Ince biography
     
     • gave a modern presentation of the theory, using methods from algebra as well as analysis.
       

632. Cunningham biography
     
     • Although Cunningham's early papers were on analysis, he was soon to change topic.
       

633. Dehn biography
     
     • At that time topology was called 'analysis situs'.
       

634. Bell biography
     
     • He also made contributions to analytic number theory, Diophantine analysis and numerical functions.
       

635. Smale biography
     
     • With co-workers L Blum and M Shub, he has developed a model of computation which includes both the Turing machine approach and the numerical methods of numerical analysis.
       
     • In addition to the prizes mentioned above, Smale has been awarded the Chauvenet Prize by the Mathematical Association of America in 1988 for his paper On the Efficiency of Algorithms in Analysis.
       

636. Helly biography
     
     • During this period, he undertook research on functional analysis and proved the Hahn-Banach theorem in 1912, fifteen years before Hahn published essentially the same proof and 20 years before Banach gave his new setting.
       

637. Wolf biography
     
     • One of the reasons that he was able to be so confident was his understanding of statistics and the statistical analysis of the sunspot data.
       

638. Neumann Bernhard biography
     
     • Not only did he form a department of very able mathematicians at the ANU specialising in group theory and functional analysis, he also took a deep interest in the Australian Mathematical Society.
       

639. Wrinch biography
     
     • Von Neumann wrote in a letter to Norbert Wiener, which is discussed in [Kybernetes 21 (4) (1992), 7-10.',8)">8], that he would consult with Irving Langmuir and Wrinch regarding the possibility of using electronic computers to determine protein structure via X-ray crystallographic analysis.
       

640. Delone biography
     
     • He also did important work on the structural analysis of crystals.
       

641. Struik biography
     
     • Struik decided to change to the topic he was studying with Schouten, tensor analysis, for his doctoral thesis and he presented his dissertation on applications of tensor methods to Riemannian manifolds in 1922.
       

642. Morawetz biography
     
     • In a series of three significant papers in the late 1950s, Cathleen Morawetz used functional analysis coupled with ingenious new estimates for an equation of mixed type, i.e.
       

643. Doeblin biography
     
     • Doblin's masterful analysis of the domain of attraction (1939).
       

644. Smirnov biography
     
     • At the University a circle was formed in 1911 to study mathematical analysis and mechanics.
       

645. Urysohn biography
     
     • At this stage Urysohn was interested in analysis, in particular integral equations, and this was the topic of his habilitation.
       

646. Turing biography
     
     • The expectation was that Turing would lead the mathematical side of the work, and for a few years he continued to work, first on the design of the subroutines out of which the larger programs for such a machine are built, and then, as this kind of work became standardised, on more general problems of numerical analysis.
       

647. Polozii biography
     
     • Polozii's major pure mathematical contributions were to the theory of functions of a complex variable, approximation theory, and numerical analysis.
       

648. Durell biography
     
     • Before the outbreak of World War I, Durell published The arithmetic syllabus in secondary schools (1911) and Analysis and projective geometry (1911) in the Mathematical Gazette.
       

649. Rankin biography
     
     • Directly coming out of his teaching was the undergraduate text An introduction to mathematical analysis.
       

650. Cohen biography
     
     • In addition to his work on set theory, Cohen has worked on differential equations and harmonic analysis.
       

651. Francoeur biography
     
     • He entered the Ecole Polytechnique in 1794 and in 1798 he taught an analysis course for Lacroix.
       

652. Jeffreys Bertha biography
     
     • We maintain therefore that careful analysis is more important in science than in pure mathematics, not less.
       

653. Reichenbach biography
     
     • In the year he arrived in the United States he published with the University of Chicago Press his book Experience and prediction: an analysis of the foundations and the structure of knowledge.
       

654. Lesokhin biography
     
     • Elements of language and speech system analysis as well as application peculiarities of fundamentals of modern mathematics to the setting of linguistic models are considered, major attention being focused on the arrangement of thesaurus semantic nets.
       

655. Lindemann biography
     
     • Lindemann's main work was in geometry and analysis.
       

656. Aleksandrov Aleksandr biography
     
     • Then, in 1934, he published a book Mathematical foundations of the structural analysis of crystals jointly written with Delone and N N Padurov.
       

657. Burali-Forti biography
     
     • As well as set theory and vector analysis, Burali-Forti also worked on linear transformations and their applications to differential geometry.
       

658. Guinand biography
     
     • As a student of Titchmarsh in Oxford in the years immediately before the second world war it was natural that Guinand's research interests should be directed into the field of Fourier analysis and the Riemann zeta function.
       

659. Delaunay biography
     
     • However this work was important in that it contained the beginnings of functional analysis.
       

660. Schmetterer biography
     
     • He became interested in mathematics when he was about twelve years old, his interest beginning when he read a book on analysis which defined logarithms of complex numbers.
       

661. Routh biography
     
     • The research areas which interested him most were geometry, dynamics, astronomy, waves, vibrations and harmonic analysis.
       

662. Wantzel biography
     
     • He became a lecturer in analysis at the Ecole Polytechnique in 1838 but, in addition, he was made an engineer in 1840 and from 1841 became professor of applied mechanics at the Ecole des Ponts et Chaussees.
       

663. Jarnik biography
     
     • He also wrote on rearrangement of infinite series, trigonometric series and other areas of analysis.
       

664. Davenport biography
     
     • He studied mathematics and chemistry at Manchester being taught complex analysis by Mordell and applied mathematics by Milne.
       

665. Yoccoz biography
     
     • He combines an extremely acute geometric intuition, an impressive command of analysis, and a penetrating combinatorial sense to play the chess game at which he excels.
       

666. Gibbs biography
     
     • Gibbs' work on vector analysis was also of major importance in pure mathematics.
       

667. Forsyth biography
     
     • However his preference for technical mastery rather than rigorous analysis meant that he failed to inspire future pure mathematicians.
       

668. Grunsky biography
     
     • Grunsky worked on complex analysis for his doctorate but he took a job before submitting his thesis.
       

669. Schwarzschild biography
     
     • The wide range of his contributions to knowledge suggests a comparison with Poincare; but Schwarzschild's bent was more practical, and he delighted as much in the design of instrumental methods as in the triumphs of analysis.
       

670. Camus biography
     
     • Charles-Etienne Camus related the force of rising and falling bodies to Bernoulli's Leibnizian analysis of expanding springs.
       

671. Rogers biography
     
     • His later work covered a wide range of different topics in geomery and analysis including Borel functions, Hausdorff measure and local measure, topological properties of Banach spaces and upper semicontinuous functions.
       

672. Bromwich biography
     
     • In 1908 he published his only large treatise An introduction to the theory of infinite series which was based on lectures on analysis he had given at Galway.
       

673. Eilenberg biography
     
     • The conceptual flavour of homological algebra derives less specifically from topology than from the general "naturalistic" trend of mathematics as a whole to supplement the study of the anatomy of any mathematical entity with an analysis of its behaviour under the maps belonging to the larger mathematical system with which it is associated.
       

674. Killing biography
     
     • Furthermore, he had permitted complex numbers into the calculations to facilitate the analysis, but eventually, for his classification of space forms, he must deal with the "real" case.
       

675. Ford biography
     
     • Some of the papers are related to the fields of Ford's major interests: complex functions, interpolation, differential equations, and numerical analysis.
       

676. Reizins biography
     
     • He graduated in 1948 with distinction and became a member of the Department of Mathematical Analysis at the University while he undertook research on differential equations under Arvids Lusis.
       

677. Valyi biography
     
     • Valyi was appointed professor of theoretical physics at Kolozsvar in 1884, and in the following year he also became professor of mathematics lecturing on analysis, geometry and number theory.
       

678. Bolyai biography
     
     • The 'Comments' to the 'Geometrical Examinations' are more than a critical analysis of the work.
       

679. Aristarchus biography
     
     • [His] thesis concerning the times when solar eclipses may occur rests on an analysis of Greek and Egyptian calendrical conventions, rather than on an appeal to observation of solar eclipses.
       

680. Neumann Franz biography
     
     • He used least squares methods of error analysis of instruments giving new precision to measurements.
       

681. Kneser biography
     
     • the first to introduce Hilbert's new methods into analysis in his textbook on integral equations.
       

682. Chen biography
     
     • The goal of Chen's iterated integrals program, which is a de Rham theory for path spaces, was to study the interaction of topology and analysis through path integration.
       

683. Schramm biography
     
     • (The spheres must have disjoint interiors, but they don't have to be the same size.) It's a standard theorem in classical geometry, also related to important work in hyperbolic geometry and complex analysis, that you can realize any planar simple graph by kissing circles in R2, i.e., the circles are the vertices and the kissing pairs are the edges.
       

684. Kronecker biography
     
     • Not only Dedekind, Heine and Cantor's mathematics was unacceptable to this way of thinking, and Weierstrass also came to feel that Kronecker was trying to convince the next generation of mathematicians that Weierstrass's work on analysis was of no value.
       

685. Zuse biography
     
     • After graduating Zuse joined the Henschel Aircraft Company where he worked on stress analysis.
       

686. Henrici biography
     
     • introduced projective geometry, vector analysis, and graphical statics into the University College mathematics syllabus - a radical departure from the analytically biased Cambridge-style course previously taught.
       

687. Kochin biography
     
     • He wrote textbooks on hydromechanics and vector analysis.Article by: J J O'Connor and E F Robertson .
       

688. Bevan-Baker biography
     
     • Part of Chapter II includes a useful discussion of an important type of definite integral which occurs in the analysis of diffraction problems.
       

689. Bott biography
     
     • The papers included in this book are united by one theme: topological constraints on analysis ..
       

690. Hesse biography
     
     • Both have major contributions to this field, which might be considered the doorstep of functional analysis.
       

691. Heaviside biography
     
     • Heaviside results on electromagnetism, impressive as they were, were overshadowed by the important methods in vector analysis which he developed in his investigations.
       

692. Heegaard biography
     
     • Another important Heegaard contribution is his 1907 survey article (with Max Dehn) Analysis Situs where the authors set forth the foundations of combinatorial topology.
       

693. Carmeli biography
     
     • During his time in this post he published papers such as Group analysis of Maxwell's equations (1969), Infinite-dimensional representations of the Lorentz group (1970), and SL(2, C) symmetry of the gravitational field dynamical variables (1970).
       

694. Yates biography
     
     • In 1954 he purchased a computer to assist with the statistical analysis to the data at Rothamsted.
       

695. Schubert Hans biography
     
     • He remained at Halle for the rest of his career, being named Professor of Applied Mathematics in 1960 and Professor of Analysis in 1969.
       

696. Robins biography
     
     • Robins loved this geometrical approach to mathematics and retained a preference for geometry over algebra or analysis throughout his life.
       

697. Bolyai Farkas biography
     
     • His main work, the Tentamen, was an attempt at a rigorous and systematic foundation of geometry, arithmetic, algebra and analysis.
       

698. Harriot biography
     
     • He came very close to a vector analysis solution of the problem of finding the velocity of the projectile and, certainly by 1607, he came to the conclusion that the path of the projectile was a tilted parabola.
       

699. Spencer Tony biography
     
     • After introductory chapters on matrix algebra, vectors and Cartesian tensors, and an analysis of deformation and stress, the author examines the mathematical statements of the laws of conservation of mass, momentum and energy and the formulation of the mechanical constitutive equations for various classes of fluids and solids.
       

700. Kreisel biography
     
     • There is a different general program which does not seem to suffer the defects of [Hilbert's] consistency program: To determine the constructive (recursive) content or the constructive equivalent of the non-constructive concepts and theorems used in mathematics, particularly in arithmetic and analysis.
       

701. Iyanaga biography
     
     • He did publish a number of papers, however, which arose through the various courses such as algebraic topology, functional analysis, and geometry, which he taught.
       

702. Zeno of Elea biography
     
     • Zeno elaborated forty different paradoxes following from the assumption of plurality and motion, all of them apparently based on the difficulties deriving from an analysis of the continuum.
       

703. Lax Anneli biography
     
     • Lax's view on mathematics deeply influenced Marchisotto's approach to the subject, particularly in the areas of analysis and geometry.
       

704. Northcott biography
     
     • At Princeton rather than analysis which had been the main focus before the war, the main area had moved towards algebra.
       

705. Evans biography
     
     • His work dealt with potential theory, functional analysis, integral equations and the problem of minimal surfaces, the Plateau Problem.
       

706. Dickson biography
     
     • The three volumes cover: Divisibility and primality; Diophantine analysis; and Quadratic and higher forms.
       

707. Perron biography
     
     • His work in analysis is certainly remembered through the Perron integral.
       

708. Bour biography
     
     • Bour made many significant contributions to analysis, algebra, geometry and applied mechanics despite his early death from an incurable disease.
       

709. Bernoulli Jacob biography
     
     • Bernoulli was one of the most significant promoters of the formal methods of higher analysis.
       

710. Wright biography
     
     • He [was] interested in many different strands of analysis, being one of the first to work on difference-differential equations.
       

711. Van der Waerden biography
     
     • Van der Waerden worked on algebraic geometry, abstract algebra, groups, topology, number theory, geometry, combinatorics, analysis, probability theory, mathematical statistics, quantum mechanics, the history of mathematics, the history of modern physics, the history of astronomy and the history of ancient science.
       

712. Hopf Eberhard biography
     
     • His interests and principal achievements were in the fields of partial and ordinarydifferential equations, calculus of variations, ergodic theory, topological dynamics, integral equations, differential geometry, complex function theory and functional analysis.
       

713. Cooper biography
     
     • Alan Hill, the author of [Functional analysis and approximation, Oberwolfach, 1980, Internat.
       
     • He writes [Functional analysis and approximation, Oberwolfach, 1980, Internat.
       
     • His research was on a wide range of different but related topics: operator theory, transform theory, thermodynamics, functional analysis and differential equations.
       
     • As to his character, the quote above from Alan Hill's tribute [Functional analysis and approximation, Oberwolfach, 1980, Internat.
       
     • Here is another quote from [Functional analysis and approximation, Oberwolfach, 1980, Internat.
       
     • Paul Butzer writes in [ Functional analysis and approximation, Oberwolfach, 1980, Internat.
       

714. Sneddon biography
     
     • Written on a topic on which Sneddon published many papers, it was a comprehensive account of the mathematical analysis of the theoretical distribution of stresses induced in perfectly elastic bodies by the presence of cracks.
       

715. Wazewski biography
     
     • At about this time his interests shifted away from set theory and topology and he became interested in analysis.
       

716. Potapov biography
     
     • During the 1950s Potapov worked on the theory of J-contractive matrix functions and the analysis of matrix functions became his main work.
       

717. Lavrentev biography
     
     • From 1933 he held the chair of Analysis and Theory of Functions at Moscow State University.
       

718. Carnot Sadi biography
     
     • Carnot's work is distinguished for his careful, clear analysis of the units and concepts employed and for his use of both an adiabatic working stage and an isothermal stage in which work is consumed.
       

719. Hobbes biography
     
     • In 1660 Hobbes attacked the 'new' methods of mathematical analysis.
       

720. Gleason biography
     
     • In 1966 Gleason published Fundamentals of abstract analysis.
       

721. Vitali biography
     
     • This was as a result of him winning a competition for the chair of infinitesimal analysis in 1923.
       

722. Gromoll biography
     
     • The first five chapters comprise an introduction to Riemannian geometry, accessible to students with a background in real analysis, linear algebra and first concepts of general topology.
       

723. Sokolov biography
     
     • The next three parts look first at problems which can be modelled by nonlinear integral equations with constant limits and then extend the analysis to the situation where the upper limit is variable.
       

724. Buffon biography
     
     • 22 (6) (1980), 167-171.',6)">6] gives a new analysis of Buffon's needle experiment, and the author conducts an experiment with 2000 throws which gives π = 3.1430 ..