Bøger i Cambridge Mathematical Library serien

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 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.

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.

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 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.

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).

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 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.

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 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.

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.

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.

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.

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.