Books in the Cambridge Mathematical Library series

The classic textbook from Burkill and Burkill, now available in the Cambridge Mathematical Library. This straightforward course is intended for students who already have a working knowledge of calculus. Clear exposition, logical development and a wealth of illuminating examples ensure that this book will appeal to students of analysis.

Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. In most books, this diversity of interest is often ignored, but here Dr Korner has provided a shop-window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy, and electrical engineering. Each application is placed in perspective by a short essay. The prerequisites are few (the reader with knowledge of second or third year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. In short, this stimulating account will be welcomed by all who like to read about more than the bare bones of a subject. For them this will be a meaty guide to Fourier analysis.

In this substantial revision of his excellent book, Professor Biggs has taken the opportunity to clarify and update the text, whilst leaving the structure unchanged. Like the first edition, this will be essential reading for all combinatorialists.

This classic, now in paperback, discusses the mathematical theory of viscosity, thermal conduction and diffusion in non-uniform gases, based on the solutions of the Maxwell-Boltzmann equations. The theories of Chapman and Enskog, the quantum theory of collisions and the theory of conduction and diffusion in ionized gases in electric and magnetic fields are also detailed.

Originally published in 1934 in the Cambridge Tracts, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. The major part of the book is devoted to the analytical theory founded on the zeta-function of Reimann. This tract remains unsurpassed as an introduction to the field.

Designed for non-specialists, this classic text by a world expert is an invaluable reference for those seeking a basic understanding of the subject. Exercises, notes and exhaustive references follow each chapter, making it outstanding both as a text and reference for students and researchers in graph theory and its applications.

This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and exhaustively both the statement and proof of all the standard inequalities of analysis. The authors were well known for their powers of exposition and were able here to make the subject accessible to a wide audience of mathematicians.

Baker's 1897 classic book on algebraic geometry and allied theory.

Many of the ideas introduced by Macaulay in this book have developed into central concepts of modern theory. Originally published over 75 years ago, the wealth of thinking expounded here by Macaulay will still be a source of inspiration to all workers in commutative algebra.

An English translation of the notes from David Hilbert's course in 1897 on Invariant Theory at the University of Gottingen taken by his student Sophus Marxen.

First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. This new edition has been revised by the author, to include several new sections and a new appendix.

This comprehensive text describes the science of waves in liquids and gases. It will be invaluable to engineers, physicists, geophysicists, applied mathematicians and researchers concerned with wave motions or fluid flows. It is especially suitable as a textbook for final year undergraduates or graduates.

Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors' aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

Many questions involving the theory of surfaces, such as the classification of quartic surfaces, the description of moduli spaces for abelian surfaces, and the automorphism group of a Kummer surface, are touched upon in this volume.

This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.

Now available in the Cambridge Mathematical Library, this classic text is a systematic exposition of the theory and a compilation of its important results. Can be used to complement courses on differential geometry, Lie groups, probability or differential geometry. An ideal text and reference and for those entering the field.

This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principal transcendental functions.

This classic book is a encylopaedic and comprehensive account of the classical theory of analytical dynamics. The treatment is rigorous yet readable, starting from first principles with kinematics before moving to equations of motion and specific and explicit methods for solving them, with chapters devoted to particle dyanmics, rigid bodies, vibration, and dissipative systems. Hamilton's principle is introduced and then applied to dynamical systems, including three-body systems and celestial mechanics. Very many examples and exercisies are supplied throughout.

The great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part 1 (in which the logical properties of propositions, propositional functions, classes and relations are established); section 6 of Part 2 (dealing with unit classes and couples); and Appendices A and B (which give further developments of the argument on the theory of deduction and truth functions).

Hydrodynamic stability is of fundamental importance in fluid mechanics and is concerned with the problem of transition from laminar to turbulent flow. Drazin and Reid emphasise throughout the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, relate the theory to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems not only provide exercises for students but also provide many additional results in a concise form. This new edition of this celebrated introduction differs principally by the inclusion of detailed solutions for those exercises, and by the addition of a Foreword by Professor J. W. Miles.

All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

This celebrated volume gives an accessible introduction to stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Together with its companion, it helps equip graduate students for research into a subject of great intrinsic interest and wide application.

This classic in stochastic network modelling is back in print for a new generation. The author's clear and easy-to-read style makes it enjoyable reading for anyone interested in stochastic processes. Elementary probability is the only prerequisite and exercises are interspersed throughout.

The third edition of Professor Zygmund's classic Trigonometric Series, featuring a foreword by Robert Fefferman. Both volumes of the 1959 edition are bound as one. The rigorous treatment of this important subject presented here is a reference work of enduring value for mathematicians at graduate level and above.

This reissue of the classic 1932 edition of Lamb's Hydrodynamics is an indication of this work's lasting value. Constantly in use since its publication in 1892, it has proved to be the definitive reference for all fluid dynamicists. A new foreword highlights the prominence of the publication in the field.

Now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive characteristic, moduli spaces of principal bundles and of complexes, Hilbert schemes of points on surfaces, derived categories of coherent sheaves, and moduli spaces of sheaves on Calabi-Yau threefolds. The authors review changes in the field since the publication of the original edition in 1997 and point the reader towards further literature. References have been brought up to date and errors removed. Developed from the authors' lectures, this book is ideal as a text for graduate students as well as a valuable resource for any mathematician with a background in algebraic geometry who wants to learn more about Grothendieck's approach.

There are few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since publication in 1908, successive generations of budding mathematicians have turned to this classic work. This Centenary edition includes a Foreword by T. W. Koerner, describing the huge influence the book has had on mathematics worldwide.

Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism. Background material on mathematics has been collected in appendices to help the reader. Contains a new preface specially written for this edition by the author, updates on open problems and exercises.

Combinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. This classic volume is the first to attempt to present a thorough treatment of this theory.