Hardback (ISBN-13: 9780521887182)
One of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this new edition basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of ‘zero-square’, or ‘nilpotent’ infinitesimal - that is, a quantity so small that its square and all higher powers can be set, literally, to zero. The systematic employment of these infinitesimals reduces the differential calculus to simple algebra and, at the same time, restores to use the “infinitesimal” methods figuring in traditional applications of the calculus to physical problems - a number of which are discussed in this book. This edition also contains an expanded historical and philosophical introduction.
* Unique treatment of this material at this level * First elementary book
to employ ‘zero-square’ infinitesimals in presenting the calculus * This
new edition fully updated with new material on applications to physics
Contents
Introduction; 1. Basic features of smooth worlds; 2. Basic differential calculus; 3. First applications of the differential calculus; 4. Applications to physics; 5. Multivariable calculus and applications; 6. The definite integral: Higher order infinitesimals; 7. Synthetic geometry; 8. Smooth infinitesimal analysis as an axiomatic system; Appendix; Models for smooth infinitesimal analysis.
Paperback (ISBN-13: 9780521047517)
This book presents the human side of statistical consulting and illustrates the problems and opportunities that can arise for the modern consultant. Statistical problems occur in almost all areas of science, in medicine, in industry, in marketing, and in finance, and a wide range of interests is catered for by the twelve contributions to this unique volume. These contributions demonstrate that statistical consultancy provides a broad spectrum of intellectually stimulating problems, as well as being a vital tool in many aspects of modern life. The book will be valuable to university and college students of statistics and to all those who use statistical techniques in a consultancy environment of any kind.
Contents
Preface; List of contributors; 1. Statistical consultancy D. J. Hand and B. S. Everitt; 2. Consultants’ cameos: a chapter of encounters Tony Greenfield; 3. Straight consulting V. Barnett; 4. A two-period crossover trial D. Clayton and M. Hills; 5. Consultancy in a medical school, illustrated by a clinical trial for treatment of primary biliary cirrhosis D. G. Cook and S. J. Pocock; 6. The analysis of response latencies G. Dunn; 7. Acid rain and tree roots: an analysis of an experiment J. N. R. Jeffers; 8. On identifying yeasts and related problems J. C. Gower and R. W. Payne; 9. Uneven sex ratios in the light-brown apple moth: a problem in outlier allocation Toby Lewis; 10. Collaboration between university and industry B. J. T. Morgan, P. M. North and S. E. Pack; 11. Inspection for faulty components before or after assembly of manufactured items P. M. E. Altham; 12. Statistical modelling of the EEC Labour Force Survey: a project history M. Aitkin and R. Healey; Bibliography on statistical consulting D. J. Hand; Name index; Subject index.
Series: Cambridge Mathematical Library
Paperback (ISBN-13: 9780521720557)
There are few textbooks of mathematics as well-known as Hardy’s Pure Mathematics. Since its publication in 1908, this classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigour of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Celebrating 100 years in print with Cambridge, this edition includes a Foreword by T. W. Korner, describing the huge influence the book has had on the teaching and development of mathematics worldwide. Hardy’s presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to.
* The classic text on pure maths, by the author of A Mathematician's Apology
* This Centenary edition includes a new Foreword by T. W. Korner * Hardy’s
enthusiasm for his subject and his expository skill shine through the whole
book
Contents
Foreword by T. W. Korner; 1. Real variables; 2. Functions of real variables; 3. Complex numbers; 4. Limits of functions of a positive integral variable; 5. Limits of functions of a continuous variable: continuous and discontinuous functions; 6. Derivatives and integrals; 7. Additional theorems in the differential and integral calculus; 8. The convergence of infinite series and infinite integrals; 9. The logarithmic, exponential, and circular functions; 10. The general theory of the logarithmic, exponential, and circular functions; Appendices; Index.
Series: Cambridge Studies in Advanced Mathematics (No. 111)
Hardback (ISBN-13: 9780521856348)
Details
43 line diagrams 43 exercises 55 worked examples
Page extent: 224 pages
Size: 228 x 152 mm
Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have taken the standard first courses in real analysis, abstract algebra, and point-set topology. The book begins with a detailed discussion of vector bundles and related algebraic notions, followed by the definition of K-theory and proofs of the most important theorems in the subject, such as the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative structure of K-theory and the Adams operations are also discussed and the final chapter details the construction and computation of characteristic classes. With every important aspect of the topic covered, and exercises at the end of each chapter, this is the definitive book for a first course in topological K-theory.
* Needs no prior knowledge of K-theory or algebraic topology * Approaches
K-theory from both a topological and an algebraic viewpoint * Exercises
at the end of each chapter make this the definitive book for a first graduate
text on topological K-Theory
Contents
1. Preliminaries; 2. K-Theory; 3. Additional structure; 4. Characteristic classes; Bibliography; Symbol index; Subject index.
Hardback (ISBN-13: 9780521857918)
25 line diagrams 5 half-tones
Page extent: 304 pages
Size: 247 x 174
In recent years the interaction between dynamical systems theory and non-equilibrium statistical mechanics has been enormous. The discovery of fluctuation theorems as a fundamental structure common to almost all non-equilibrium systems, and the connections with the free energy calculation methods of Jarzynski and Crooks, have excited both theorists and experimentalists. This graduate level book charts the development and theoretical analysis of molecular dynamics as applied to equilibrium and non-equilibrium systems. Designed for both researchers in the field and graduate students of physics, it connects molecular dynamics simulation with the mathematical theory to understand non-equilibrium steady states. It also provides a link between the atomic, nano, and macro worlds. The book ends with an introduction to the use of non-equilibrium statistical mechanics to justify a thermodynamic treatment of non-equilibrium steady states, and gives a direction to further avenues of exploration.
* Connects molecular dynamics simulation and mathematical theory to understand
non-equilibrium steady states * Graduate level book on non-equilibrium
statistical mechanics * Links the atomic, nano, and macro worlds
Contents
1. Introduction; 2. Linear irreversible thermodynamics; 3. The microscopic connection; 4. The Green-Kubo relations; 5. Linear response theory; 6. Computer simulation algorithms; 7. Nonlinear response theory; 8. Dynamical stability; 9. Nonequilibrium fluctuations; 10. Thermodynamics of steady states; References; Index.