Computers in Mathematical Research

This collection of articles, by mathematicians from a wide range of disciplines, explores many ways in which computers are used in mathematical research, taken from the results of a conference on this subject at University College, Cardiff in 1986. The contributors highlight the ways in which computers are utilized as a mathematical tool both to explore and to prove results in a wide range of topics. There are sections on the impact of the computer on research in number theory (including the Riemann Zeta function), cryptography, combinatorics, symbolic manipulation, geometry, group theory, statistics and applied mathematics. The book aims to show how the computer has become a valuable research tool, able to perform otherwise tedious calculations which reveal interesting directions for further research and, on occasion, capable of providing the means of proof of particular results.Table of ContentPreface. Contributors. Some recent discoveries in number theory and analysis made by the use of a computer; some computations relating to the Riemann Zeta function; implementing data security; multi-dimensional continued fractions and their applications; probabilistic prime tests; Galois module structure of elliptic functions; computations for additive diophantine equations - pairs of quintic congruences 2; integration in closed form; some applications of computers in design theory; computing for the arithmetic of geometries; groups - a database for computational algebra; partially ordered sets and sorting; results in elasticity theory using complex FORTRAN; the influence of computers in statistics; integral equations in traffic noise simulation; industrial numerical analysis.