P. J. Giblin

Peter Giblin describes, in the context of an introduction to the theory of numbers, some of the more elementary methods for factorization and primality testing; that is, methods independent of a knowledge of other areas of mathematics. Indeed everything is developed from scratch so the mathematical prerequisites are minimal. An essential feature of the book is the large number of computer programs (written in Pascal) and a wealth of computational exercises and projects, in addition to more usual theory exercises. The theoretical development includes continued fractions and quadratic residues, directed always towards the two fundamental problems of primality testing and factorization. There is time, all the same, to include a number of topics and projects of a purely "recreational" nature.

The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors cast the theory into a new light, that of singularity theory. This second edition has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added which covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to modern singularity theory.

The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors cast the theory into a new light, that of singularity theory. This second edition has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added which covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to modern singularity theory.

The interaction between computer and mathematics is becoming more and more important at all levels as computers become more sophisticated. This book shows how simple programs can be used to do significant mathematics. The purpose of this book is to give those with some mathematical background a wealth of material with which to appreciate both the power of the microcomputer and its relevance to the study of mathematics. The authors cover topics such as number theory, approximate solutions, differential equations and iterative processes, with each chapter self-contained. Many exercises and projects are included giving ready made material for demonstrating mathematical ideas. Only a fundamental knowledge of mathematics is assumed and programming is restricted to ‘basic BASIC’ which will be understood by any microcomputer. The book may be used as a textbook for algorithmic mathematics at several levels, with all the topics covered appearing in any undergraduate mathematics course.