The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting...

Academic life in Cambridge especially in Trinity College is viewed through the eyes of one of its greatest figures. Most of Professor Littlewood's earlier work is presented along with a wealth of new material.

Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.

A straightforward introduction to Lebesgue's theory of integration.

The book provides an introduction to the theory of cluster sets, a branch of topological analysis which has made great strides in recent years. The cluster set of a function at a particular point is the set of limit values of the function at that point which may be either a boundary point or (in the case of a non-analytic function) an interior point of the function's domain. In topological analysis, its main application is to problems arising in the theory of functions of a complex variable, with particular reference to boundary behaviour such as the theory of prime ends under conformal...

Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical physics. Solutions of ordinary differential equations are frequently obtained in the form of a definite integral or contour integral, and this tract is concerned with the asymptotic representation of a function of a real or complex variable defined in this way. After a preliminary account of the...

Ideal theory is important not only for the intrinsic interest and purity of its logical structure but because it is a necessary tool in many branches of mathematics. In this introduction to the modern theory of ideals, Professor Northcott assumes a sound background of mathematical theory but no previous knowledge of modern algebra. After a discussion of elementary ring theory, he deals with the properties of Noetherian rings and the algebraic and analytical theories of local rings. In order to give some idea of deeper applications of this theory the author has woven into the connected...

Written in the wake of the advent of Relativity by an author who made important contributions to projective and differential geometry, and topology, this early Cambridge Tract in Mathematics and Theoretical Physics aimed to assist students of the time from the fields of differential geometry and mathematical physics. Beginning by introducing formal preliminaries, the text continues, bringing the underlying differential invariant theory that to this day remains relevant in a range of geometrical and physical applications, to the fore.

Stochastic approximation is a relatively new technique for studying the properties of an experimental situation; it has important applications in fields such as medicine and engineering. The subject can be treated either largely as a branch of pure mathematics, or else from an empirical and practical angle. In this book, Dr Wasan gives a rigorous mathematical treatment of the subject, drawing together the scattered results of a number of authors. He discusses the conditions under which the method gives a valid approximation to the required solution; methods for optimal choice of parameters to...