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Eleven of the fourteen invited speakers at a symposium held by the Oxford Mathematical Institute in June 1972 have revised their contributions and submitted them for publication in this volume. The present papers do not necessarily closely correspond with the original talks, as it was the intention of the volume editor to make this book of mathematical rather than historical interest. The contributions will be of value to workers in topology in universities and polytechnics.

This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in the field of combinatorics. A section of problems illustrates some of the topics in need of further investigation.

This set of notes, for graduate students who are specializing in algebraic topology, adopts a novel approach to the teaching of the subject. It begins with a survey of the most beneficial areas for study, with recommendations regarding the best written accounts of each topic. Because a number of the sources are rather inaccessible to students, the second part of the book comprises a collection of some of these classic expositions, from journals, lecture notes, theses and conference proceedings. They are connected by short explanatory passages written by Professor Adams, whose own contributions to this branch of mathematics are represented in the reprinted articles.

Nobel laureate Erwin Schrödinger's What is Life? is one of the great science classics of the twentieth century. It was written for the layman, but proved to be one of the spurs to the birth of molecular biology and the subsequent discovery of DNA. What is Life? appears here together with Mind and Matter, his essay investigating a relationship which has eluded and puzzled philosophers since the earliest times. Brought together with these two classics are Schrödinger's autobiographical sketches, which offer a fascinating account of his life as a background to his scientific writings.

Professor Ziman's classic textbook on the theory of solids was first pulished in 1964. This paperback edition is a reprint of the second edition, which was substantially revised and enlarged in 1972. The value and popularity of this textbook is well attested by reviewers'opinions and by the existence of several foreign language editions, including German, Italian, Spanish, Japanese, Polish and Russian. The book gives a clear exposition of the elements of the physics of perfect crystalline solids. In discussing the principles, the author aims to give students an appreciation of the conditions which are necessary for the appearance of the various phenomena. A self-contained mathematical account is given of the simplest model that will demonstrate each principle. A grounding in quantum mechanics and knowledge of elementary facts about solids is assumed. This is therefore a textbook for advanced undergraduates and is also appropriate for graduate courses.

This 1972 book is a collection of Durkheim's writings drawing upon the whole body of his work. Dr Giddens takes his selections from a wide variety of sources and includes a number of items from untranslated writings in the Revue Philosophique, Annee Sociologique and from L'evolution pedagogue en France. Selections from previously translated writings have been checked against the originals and amended or re-translated where necessary. Dr Giddens arranges his selections thematically rather than chronologically. However, extracts from all phases of Durkheim's intellectual career are represented, giving the date of their first publication, which makes the evolution of his thought easily traceable. In his introduction Dr Giddens discusses phases in the interpretation of Durkheim's thought, as well as the main themes in his work, with an analysis of the effects of his thinking on modern sociology. The book is for students at any level taking courses in sociology, social anthropology and social theory in which Durkheim is one of the major writers studied.

The theory of the numerical range of a linear operator on an arbitrary normed space had its beginnings around 1960, and during the 1970s the subject has developed and expanded rapidly. This book presents a self-contained exposition of the subject as a whole. The authors develop various applications, in particular to the study of Banach algebras where the numerical range provides an important link between the algebraic and metric structures.

The study of abelian manifolds forms a natural generalization of the theory of elliptic functions, that is, of doubly periodic functions of one complex variable. When an abelian manifold is embedded in a projective space it is termed an abelian variety in an algebraic geometrical sense. This introduction presupposes little more than a basic course in complex variables. The notes contain all the material on abelian manifolds needed for application to geometry and number theory, although they do not contain an exposition of either application. Some geometrical results are included however.

These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of K-theory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences.

Numerical Ranges II is a sequel to Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras written by the same authors and published in this series in 1971. The present volume reflects the progress made in the subject, expanding and discussing topics under the general headings of spatial and algebra numerical ranges and further ranges.

How does an inventor set about designing a piece of machinery to make a particular product? Are they any basic principles to guide him? Glegg believes that there are and, in his short book, draws on his own wide-ranging experience as an inventor, consulting engineer, company director and university lecturer, to define them. Most books on engineering design are concerned with either mathematical analysis or some individual technique related to a narrow field. This book is neither: it defines the general laws which underlie all creative design, from the philosophy and psychology of inventiveness to the point at which an invention is commercially exploited. It thus cuts across the frontiers of specialised studies and specialised industries. Glegg finds engineering fun and feels that learning about it need not be dull. His book, with many illustrations from the battleground of industry, is both entertaining and profitable reading for engineering designers of the future and for those in general management responsible for design departments.

A comprehensive overview of the basic principles of vortex dynamics in superfluids, this book addresses the problems of vortex dynamics in all three superfluids available in laboratories (4He, 3He, and BEC of cold atoms) alongside discussions of the elasticity of vortices, forces on vortices, and vortex mass. Beginning with a summary of classical hydrodynamics, the book guides the reader through examinations of vortex dynamics from large scales to the microscopic scale. Topics such as vortex arrays in rotating superfluids, bound states in vortex cores and interaction of vortices with quasiparticles are discussed. The final chapter of the book considers implications of vortex dynamics to superfluid turbulence using simple scaling and symmetry arguments. Written from a unified point of view that avoids complicated mathematical approaches, this text is ideal for students and researchers working with vortex dynamics in superfluids, superconductors, magnetically ordered materials, neutron stars and cosmological models.

A critical study of Persius'poetic aims, aversions and techniques, based mainly on an extended analysis of Satires I. John Bramble shows how Persius'discontent with conventional literary language led him to compress the existing satiric idiom and create a powerful individual style. The author situates Persius'work in the tradition of Roman satire, and shows how he takes the concepts and metaphors of literary criticism back to their physical origins, to indict moral and literary decadence through a series of images connected with, for example, gluttony and sexual excess. This is a model study of a classical text, which makes consistent sense of a difficult and subtle manner, and answers questions posed by the potentially constricting nature of Roman poetic form. It also reconstructs the referential framework of ideas and associations upon which a sophisticated writer addressing a discriminating audience could draw.

This critical Flora provides a definitive account of the native species, naturalised species, frequent garden escapes and casuals found in the British Isles. Full keys and descriptions should enable the user to name all plants occurring in the wild, plus some ornamental trees and shrubs. For the first time detailed accounts of all the large apomictic genera are given and many infraspecific variants included. Each species entry begins with the accepted latin name, synonyms and the common English name. A detailed description follows, with separate descriptions being given for infraspecific taxa. Information on status, ecology and distribution is also included. Clear black and white line drawings illustrate an extensive glossary and also illuminate the diagnostic features of a number of groups of plants.

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a'black hole'in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

In his preface Mr Wilson writes'I feel that a great many adults … would do better to spend less time in simply accepting the concepts of others uncritically, and more time in learning how to analyse concepts in general'. Mr Wilson starts by describing the techniques of conceptual analysis. He then gives examples of them in action by composing answers to specific questions and by criticism of quoted passages of argument. Chapter 3 sums up the importance of this kind of mental activity. Chapter 4 presents selections for the reader to analyse, followed by questions of university entrance/scholarship type. This is a book to be worked through, in a sense a text-book.

Shows that current elitist theories are based on an inadequate understanding of the early writings of democratic theory and that much sociological evidence has been ignored.

A good grasp of the theory of structures - the theoretical basis by which the strength, stiffness and stability of a building can be understood - is fundamental to structural engineers and architects. Yet most modern structural analysis and design is carried out by computer, with the user isolated from the processes in action. Plastic Design of Frames; Volume 1. Fundamentals provides a broad introduction to the mathematics behind a range of structural processes. Some of the techniques used in this book may be familiar to the reader, and some may not, but each of the topics examined will give the structural engineer valuable insight into the basis of the subject. This companion book Plastic Design of Frames; Volume 2. Applications provides additional advanced topics and case studies. This lucid second volume provides a valuable read for structural engineers and others who wish to deepen their knowledge of the structural analysis and design of buildings.

An international conference on complex analysis was held in Canterbury in July 1973. Some of the world's most prominent complex analysts attended and some outstanding open problems had their first solutions announced there. These are reflected in this set of Proceedings. Almost all of the contributions are abstracts of talks given at the symposium. The final part of this volume is a section on research problems contributed by members of the conference and a report on a previous collection of problems edited by Professor W. K. Hayman after an earlier conference in 1964. This book is essential reading for research workers and graduate students interested in complex analysis.

These notes provide a reasonably self-contained introductory survey of certain aspects of harmonic analysis on compact groups. The first part of the book seeks to give a brief account of integration theory on compact Hausdorff spaces. The second, larger part starts from the existence and essential uniqueness of an invariant integral on every compact Hausdorff group. Topics subsequently outlined include representations, the Peter–Weyl theory, positive definite functions, summability and convergence, spans of translates, closed ideals and invariant subspaces, spectral synthesis problems, the Hausdorff-Young theorem, and lacunarity.