... the first attempt to carry out coset enumeration on a digital computer. It was prompted by discussion with Todd after experiments with enumeration of elements of groups by expressing them as words in the computer.

The problem of stellar evolution is expressed, mathematically, by a set of non-linear partial differential equations describing the variation of density and temperature as a function of time and of distance from the star centre. This problem is tackled in the paper under review on the following assumptions: i) spherical symmetry of the star; ii) hydrostatic equilibrium; iii) negligible stirring of material except where convectively unstable; there, "well mixed". The computer employed was one of only moderate storage and speed, viz. the Cambridge EDSAC I; thus, considerable ingenuity was required in defining subsidiary variables.

There was a rheostat up on the wall just outside the machine room door, which was used to adjust the voltage if the mains wasn't right. ... One night even the rheostat adjustment wasn't enough and Fred Hoyle, with whom my husband Brian Haselgrove was working on stellar evolution, rang up the electricity board and said "Can you hike your volts up a bit?". I can't remember if they did!

In 1957 [Max Newman] appointed Haselgrove ... to promote research in mathematical computing in Manchester. Some of the applications of computers were immediately obvious; many well-formulated problems in science and engineering which required numerical solutions could benefit directly from faster computation. This was particularly true in astronomy, a classical area for numerical work, where the research at Jodrell Bank called for major computing support. But there was also the prospect of using automatic machines to solve analytical and logical problems in new ways, which were not simply accelerated versions of existing methods.

This is the first table of the Royal Society to be produced automatically by electronic computers. Any other method would not have been feasible. A great many terms of the Euler-Maclaurin or Riemann-Siegel series were used to calculate each entry. For some cases 15 figure logarithms were needed as input data to obtain barely 6 decimal accuracy. The large zeros of Table IV required inverse interpolation involving 14th differences.

The tables will be very helpful in future exploration of inequalities involving certain numerical functions ...

Brian Haselgrove's research interests ranged over many areas of mathematics both pure and applied. ... at Manchester he published papers on Dirichlet functions and the Riemann hypothesis, ray paths in the ionosphere, numerical integration using quasi-random numbers, two-point boundary-value problems, and some geometrical puzzles. The paper on boundary-value problems illustrates an early stage of what was to become a major interest of numerical analysts at Manchester and elsewhere, the development of general algorithms. This work involves the elucidation of classes of mathematical problems which are suitable for solution by a standardised approach. The solution methods have to be studied analytically and tested on an extensive range of problems, to determine their applicability and limitations. In the early 1960's the potential for general solvers was becoming apparent, but the programming languages available did not provide enough flexibility for implementation.

In this paper we shall give an account of some methods developed for the numerical evaluation of multidimensional integrals. These methods are based on the theory of Diophantine approximation. They are suitable for some problems for which the Monte Carlo method is commonly used and, like the Monte Carlo method, are well fitted for use with an electronic digital computer.

A receiver mounted on a satellite in orbit above the maximum of the F2 layer can receive radiation of frequencies that are totally reflected by the ionosphere. Two effects of reflection in the upper part of the ionosphere are discussed in this paper; both occur particularly when the satellite enters or leaves a region in which it can receive radiation from a point source.

On the teaching side, Haselgrove initiated a postgraduate Diploma in Computing in 1959 in collaboration with Tony Brooker and other members of the Computing group. In 1964 Computer Science became a separate Department, and the postgraduate course began to concentrate on the more mathematical aspects of computing, retaining some options from Computer Science. Student numbers were relatively small at first, but the course provided a source of research students in Numerical Analysis. Haselgrove also introduced an undergraduate course in numerical methods and computer programming, but it was not possible to include realistic practical work until autocodes were designed.