Edited by D. J. Hand / Imperial College of Science, Technology and Medicine, London
A. M. Herzberg / Queen's University, Ontario

Selected Statistical Papers of Sir David Cox 2 Volume Set
David Cox Nuffield College, Oxford

1 Hardback, 1 Hardback (ISBN-10: 052185816X)

Not yet published - available from October 2005

Sir David Cox is one of the seminal statistical thinkers of the twentieth and twenty-first centuries. In this selection of his work, Professor Cox reviews his most influential and interesting papers published before 1993. Each paper is the subject of a candid commentary written especially for this collection. In these he describes the context in which the papers arose and their subsequent influence. He also identifies avenues for future research. Organised in two volumes and grouped by theme, the papers and commentaries provide excellent coverage of many of the most significant advances in statistics in recent times. But this collection is more than a record of scientific achievement. Professor Cox’s writing is characterised by clarity and wit, so these volumes can be read as much for enjoyment as for edification.

? Sir David Cox is one of the greatest scientists of the twentieth century

? Each paper the subject of a candid commentary by Professor Cox written especially for this collection

? Includes the most important and most interesting papers published by Professor Cox before 1993

Contents

Volume I: Foreword D. R. Cox; Preface; Part I. Design of Investigations: Design of experiments; Sampling. Part II. Statistical Methods: Point process data; Binary data; Survival data; Multivariate analysis; Miscellaneous. Part III. Applications. Publications of Sir David Cox. Volume II: Part IV. Foundations of Statistical Inference. Part V. Theoretical Statistics: Part VI. Time Series: Part VII. Stochastic Processes: Publications of Sir David Cox.

Contributors

Volume I: R. M. Anderson, S. L. Anderson, M. Atiqullah, L. Billard, K. H. V. Booth, G. E. P. Box, L. Brandwood, V. Farewell, R. Fitzpatrick, A. E. Fletcher, S. M. Gore, D. R. Jones, P. A. W. Lewis, G. F. Medley, N. J. H. Small, E. J. Snell, P. J. Solomon, D. J. Spiegelhalter, E. Spjotvoll, A. Stuart, N. Wermuth

Volume II: A. Azzalini, O. E. Barndorff-Nielsen, P. Bloomfield, A. C. Davison, P. S. Eagleson, A. M. Herzberg, D. V. Hinkley, V. Isham, P. McCullagh, N. Reid, I. Rodriguez-Iturbe, W. L. Smith, N. Wermuth

Edited by George Ellis / Antonio Lanza / John Miller
Universita degli Studi di Trieste

The Renaissance of General Relativity and Cosmology
A Survey to Celebrate the 65th Birthday of Dennis Sciama

Paperback (ISBN-10: 0521021081)
Hardback (ISBN-10: 0521433770)

Not yet published - available from October 2005

The past forty years have have been a time of spectacular development in the study of general relativity and cosmology. A special role in this has been played by the influential research groups led by Dennis Sciama in Cambridge, Oxford, and Trieste. In April 1992 many of his ex-students and collaborators came to Trieste (where he is currently Professor) for a review meeting to celebrate his 65th birthday. This book consists of written versions of the talks presented which, taken together, comprise an authoritative overview of developments which have taken place during his career to date. The topics covered include fundamental questions in general relativity and cosmology, black holes, active galactic nuclei, galactic structure, dark matter, and large scale structure.

? Comprises reviews of important topics in astrophysics and relativity

? Top rank contributors

Contents

Introduction; 1. Exact and inexact solutions of the Einstein field equations G. F. R. Ellis; 2. Inertial forces in general relativity M. A. Abramovicz; 3. Relativistic radiation hydrodynamics A. M. Anile and V. Romano; 4. Relativistic gravitational collapse J. Miller; 5. The cosmic censorship hypothesis C. J. S. Clarke; 6. The Kerr metric: a gateway to the roots of gravity? F. de Felice; 7. Galactic astronomy since 1950 J. J. Binney; 8. Galaxy distribution functions W. C. Saslow; 9. Nonlinear galaxy clustering B. J. T. Jones; 10. Quasars: progress and prospects M. J. Rees; 11. Decaying neutrinos in astronomy and cosmology D. W. Sciama; 12. Cosmological principles J. D. Barrow; 13. Anisotropic and inhomogeneous cosmologies; 14. M. A. H. MacCallum, Mach’s principle and isotropic singularities P. K. Tod; 15. Implications of superconductivity in cosmic string theory B. Carter; 16. The formation and evaporation of primordial black holes B. J. Carr; 17. Evaporation of two dimensional black holes S. W. Hawking; 18. Topology and topology change in general relativity G. W. Gibbons; 19. Decoherence of the cluttered quantum vacuum D. J. Raine; 20. Quantum nonlocality and complex reality R. Penrose; 21. The different levels of connections between science and objective reality N. Dallaporta.

Review

‘Libraries should make sure they have a copy, so that the younger generation are able to learn something about the achievements of a man who has probably strongly influenced their research.’ The Observatory

Contributors

G. F. R. Ellis, M. A. Abramovicz, A. M. Anile, V. Romano, J. Miller, C. J. S. Clarke, F. de Felice, J. J. Binney, W. C. Saslow, B. J. T. Jones, M. J. Rees, D. W. Sciama, J. D. Barrow, M. A. H. MacCallum, P. K. Tod, B. Carter, B. J. Carr, S. W. Hawking, G. W. Gibbons, D. J. Raine, R. Penrose, N. Dallaporta.

Ian Percival
Queen Mary, University of London

Quantum State Diffusion

Paperback (ISBN-10: 0521021200)

Not yet published - available from October 2005

This is the first book devoted to quantum state diffusion (QSD) and its applications to open quantum systems and to the foundations of quantum mechanics. Recent experiments with detailed control over individual quantum systems have changed the face of quantum physics. These systems include atoms at the low temperatures attained by the 1997 Nobel Laureates, they include entangled photons in cavities, and they include the quantum systems used in new and future technologies like quantum cryptography and quantum computation. The experiments have led to a revival of interest in the foundations of quantum mechanics. QSD is used both as a theoretical and computational tool to study these systems, and as the basis of new approaches to the foundations. The book will interest graduate students and researchers in quantum mechanics and its applications, including quantum optics, quantum statistics, the philosophy of quantum theory and theoretical molecular biology.

? The first book devoted to quantum state diffusion

? Describes basic tools and concepts

? Self-contained introduction

Contents

1. Introduction; 2. Brownian motion and Ito calculus; 3. Open quantum systems; 4. Quantum state diffusion; 5. Localisation; 6. Numerical methods and examples; 7. Quantum foundations; 8. Primary state diffusion; 9. Classical dynamics of quantum localisation; 10. Semiclassical theory and linear dynamics.

Reviews
‘Partha Ghose’s timely and valuable book … shows, although not yet testable, the coherent set of concepts embodied in the pilot-wave interpretation implies unambiguous predictions about transit times … Ghose reviews the current experimental basis of this emergent field, a blend of tests of classic quantum phenomena and specific interpretations. As far as I know it is the first book to attempt this comprehensively, with full technical details … highly recommended as a resource for graduate students and researchers … recommended as a very good introduction to stochastic methods in contemporary physics.’ The Times Higher Education Supplement

‘This is highly motivating and well-written book. Historical references are spread all over the text taking the reader along the endless debate on the foundations of quantum theory. The author has accomplished an admirable pedagogical effort. Each chapter starts with a small table of contents followed by a brief summary. The style is direct, avoiding superfluous technicalities. It is a good introduction for physicists to methods and concepts of classical stochastic analysis. To summarise, the book provides physicists with an appealing introduction to methods and concepts of stochastic analysis. Moreover, it illustrates a way of implementing specific numerical procedures for open quantum systems. That feature will certainly interest both physicists and mathematicians who will enjoy as well the philosophical discussion on the foundations of quantum mechanics.’ Rolando Rebolledo Berroe, Zentralblatt fur Mathematik

Edited by R. D. Canary / University of Michigan, Ann Arbor
A. Marden / University of Minnesota
D. B. A. Epstein / University of Warwick

Fundamentals of Hyperbolic 3-Manifolds
Selected Expositions

Series: London Mathematical Society Lecture Note Series (No. 328)

Paperback (ISBN-10: 0521615585 )

Not yet published - available from November 2005

Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

? Rigorous introduction to and exposition of some fundamental topics required in the study of hyperbolic manifolds

? Important material, not otherwise published, now brought up-to-date; original books frequently requested for advanced lecture courses in hyperbolic geometry

? Expositions of a number of topics which are of fundamental importance in the modern theory

Contents

Preface 2005; Preface; Part I. Notes on Notes of Thurston R. D. Canary, D. B. A. Epstein and P. Green; Part II. Convex Hulls in Hyperbolic Space, a Theorem of Sullivan, and Measured Pleated Surfaces D. B. A. Epstein and A. Marden; Part III. Earthquakes in Two-Dimensional Hyperbolic Geometry William P. Thurston; Part IV. Lectures on Measures on Limit Sets of Kleinian Groups S. J. Patterson.

Contributors

D. Canary, D. B. A. Epstein, P. Green, William P. Thurston, S. J. Patterson

J. E. Humphreys
University of Massachusetts, Amherst

Modular Representations of Finite Groups of Lie Type

Series: London Mathematical Society Lecture Note Series
Paperback (ISBN-10: 0521674549)

Not yet published - available from December 2005

Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne-Lusztig characters. One goal has been to make the subject more accessible to those working in neighbouring parts of group theory, number theory, and topology. Core material is treated in detail, but the later chapters emphasize informal exposition accompanied by examples and precise references.

? This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic

? Core material is covered in detail, while other topics and recent developments are surveyed

? One goal has been to make the subject more accessible to those working in neighboring parts of group theory, number theory, and topology: chapters are accompanied by examples and carefully selected references

Contents

1. Finite groups of Lie type; 2. Simple modules; 3. Weyl modules and Lusztig’s conjecture; 4. Computation of weight multiplicities; 5. Other aspects of simple modules; 6. Tensor products; 7. BN-pairs and induced modules; 8. Blocks; 9. Projective modules; 10. Comparison with Frobenius kernals; 11. Caran invariants; 12. Extensions of simple modules; 13. Lewy series; 14. Cohomology; 15. Complexity and support varieties; 16. Ordinary and modular representations; 17. Deligne-Lusztig characters; 18. The groups; 19. General and special linear groups; 20. Suzuki and Ree groups; Bibliography; Frequently used symbols; Index.

Daniel J. Velleman

How to Prove It, 2nd ed.
A Structured Approach

Hardback (ISBN-10: 0521861241)
Paperback (ISBN-10: 0521675995)

available from February 2006

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman’s successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed ‘scratch work’ sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

* Systematic and thorough, shows how several techniques can be combined to construct a complex proof

*Selected solutions and hints now provided, plus over 200 new exercises some using Proof Designer software to help students learn to construct their own proofs

* Covers logic, set theory, relations, functions and cardinality

Contents

1. Sentential logic: 2. Quantificational logic; 3. Proofs; 4. Relations; 5. Functions; 6. Mathematical induction 7. Infinite sets.