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Transformation Groups
The theory of transformation groups studies symmetries of various mathematical objects such as topological spaces, manifolds, polyhedra and function spaces. It is thus a central concept in many branches of mathematics. This volume contains 25 of the papers submitted at the conference on transformation groups held at the University of Newcastle upon Tyne in August 1976.
A First Course in Algebraic Topology
This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.
Several Complex Variables, Part 1
Contains sections on Singularities of analytic spaces, Function theory and real analysis, Compact complex manifolds, and Survey papers.
Several Complex Variables, Part 2
Contains sections on Non compact complex manifolds, Differential geometry and complex analysis, Problems in approximation, Value distribution theory, Group representation and harmonic analysis, and Survey papers.
Homology Theory
This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.
Permutation Groups and Combinatorial Structures
The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth chapter, a theory of maps on orientable surfaces is developed within a combinatorial framework. This simplifies and extends the existing literature in the field. The book is designed both as a course text and as a reference book for advanced undergraduate and graduate students. A feature is the set of carefully constructed projects, intended to give the reader a deeper understanding of the subject.
Fun Mathematics on Your Microcomputer
Have you ever wondered how you can use your microcomputer to learn something useful whilst still having fun? If you have then you will certainly enjoy this entertaining guide to the fascinating world of mathematics. And you do not need to be an expert in mathematics or computing! Each chapter introduces an important part of mathematics. The basic ideas are explained in a lively and instructive style, and then incorporated into computer games and 'fun' programs. Find out how to make snowflakes and about polar honey bees; discover hidden treasure, and learn what bouncing balls, rockets and bacteria have in common; create amazing patterns on screen. All of the computer programs are written in BASIC, and in such a way that they are readily adaptable to your own microcomputer; conversion notes are provided. The programs have been tested on several different microcomputers and the programs listings have been printed directly from running programs. The book will provide an endless source of ideas, and what you learn will enable you to write your own even more sophisticated programs.
Brownian Motion, Hardy Spaces and Bounded Mean Oscillation
This exposition of research on the martingale and analytic inequalities associated with Hardy spaces and functions of bounded mean oscillation (BMO) introduces the subject by concentrating on the connection between the probabilistic and analytic approaches. Short surveys of classical results on the maximal, square and Littlewood-Paley functions and the theory of Brownian motion introduce a detailed discussion of the Burkholder-Gundy-Silverstein characterization of HP in terms of maximal functions. The book examines the basis of the abstract martingale definitions of HP and BMO, makes generally available for the first time work of Gundy et al. on characterizations of BMO, and includes a probabilistic proof of the Fefferman-Stein Theorem on the duality of H11 and BMO.
