C.G. Broyden , Ipswich, Suffolk, UK
M.T. Vespucci , University of Bologna, Italy

Krylov Solvers for Linear Algebraic Systems

Included in series
Studies in Computational Mathematics, 11

Hardbound, ISBN: 0-444-51474-0, 300 pages, publication date: 2004

Description

The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of the block conjugate-gradient algorithm and it is this observation that permits the unification of the theory. The two major sub-classes of those methods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as natural generalisations of the Orthodir (GCR) and Orthomin algorithms. These are themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt algorithm and their properties, in particular their stability properties, are determined by the two matrices that define the block conjugate-gradient algorithm. These are the matrix of coefficients and the preconditioning matrix.
In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms.
In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM.
Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices.

Key features:
comprehensive and unified approach
up-to-date chapter on preconditioners
complete theory of stability
includes dual and reverse methods
comparison of algorithms on CD-ROM
objective assessment of algorithms


T.W. Cusick , SUNY, Department of Mathematics, NY 14260, USA
C. Ding , The Hong Kong University of Science and Technology, Kowloon, China
A. Renvall , University of Turku, Department of Mathematics, Finland

Stream Ciphers and Number Theory
Revised edition

Included in series North-Holland Mathematical Library, 66

Hardbound, ISBN: 0-444-51631-X, 492 pages, publication date: 2004

Description

This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields.
Thomas W. Cusick is Professor of Mathematics at the State University of New York Buffalo. Cunsheng Ding is Associate Professor of Computer Science at the Hong Kong University of Science and Technology. Ari Renvall is Senior Assistant of Mathematics at the University of Turku.

Key features:

Unique book on interactions of stream ciphers and number theory.
Research monograph with many results not available elsewhere.
A revised edition with the most recent advances in this subject.
Over thirty research problems for stimulating interactions between the two areas.
Written by leading researchers in stream ciphers and number theory.

Audience
Cryptographers, mathematicians.



Kazuo Fujikawa, Dept of Physics, University of Tokyo, Japan,
and Hiroshi Suzuki, Dept of Mathematical Sciences, Ibaraki University, Japan

Path Integrals and Quantum Anomalies

(Hardback) 0-19-852913-9
Publication date: May 2004
Clarendon Press 288 pages, 10 line drawings, 234mm x 156mm
Series: International Series of Monographs on Physics

Succinct introduction to path integrals and Schwinger's action principle
Clear conceptual basis of the path integral method in the analyses of anomalies
Explicit and elementary calculations of all the examples
Path integral formulation of Weyl anomalies (which is not commonly available)
Analyses of two-dimensional theory such as bosonization and conformal field theory
Covers most recent developments in lattice gauge theory

Description

'Definitely a book that will fill a need at the graduate and research level. ' -Ian Aitchison, University of Oxford
'An excellent addition to the literature by one of the pioneers in understanding anomalies. ' -Roman Jackiw, Massachusetts Institute of Technology

Self-contained introduction to the path integral method in field theory and its applications to quantum anomalies. The subjects covered in the book are relevant to particle and high-energy nuclear theory, conformal field theory, applications to condensed matter theory, and string theory. No previous knowledge beyond the advanced undergraduate quantum mechanics is assumed.

Readership: Beginning graduate students and researchers in theoretical physics, mathematics, and chemistry, in particular particle physics theory, high energy nuclear theory, condensed matter theory, and string theory.

Contents/contributors
1 Genesis of quantum anomalies
2 Feynman path integrals and Schwinger's action principle
3 Quantum theory of photons and phase operators
4 Regularization of field theory and chiral anomalies
5 Jacobians in path integrals and quantum anomalies
6 Quantum breaking of gauge symmetry
7 Weyl anomaly and renormalization group
8 Two-dimensional field theory and bosonization
9 Index theorem on the lattice and chiral anomalies
10 Gravitational anomalies
11 Concluding remarks
A Basics of quantum electrodynamics
B Field theory in curved space-time
C References with brief comments

Scott Soames

Philosophical Analysis in the Twentieth Century, Volume 1:
The Dawn of Analysis

Cloth | 2003 | ISBN: 0-691-11573-7
432 pp. | 6 x 9

This is a major, wide-ranging history of analytic philosophy since 1900, told by one of the tradition's leading contemporary figures. The first volume takes the story from 1900 to mid-century. The second brings the history up to date.

As Scott Soames tells it, the story of analytic philosophy is one of great but uneven progress, with leading thinkers making important advances toward solving the tradition's core problems. Though no broad philosophical position ever achieved lasting dominance, Soames argues that two methodological developments have, over time, remade the philosophical landscape. These are (1) analytic philosophers' hard-won success in understanding, and distinguishing the notions of logical truth, a priori truth, and necessary truth, and (2) gradual acceptance of the idea that philosophical speculation must be grounded in sound prephilosophical thought. Though Soames views this history in a positive light, he also illustrates the difficulties, false starts, and disappointments endured along the way. As he engages with the work of his predecessors and contemporaries--from Bertrand Russell and Ludwig Wittgenstein to Donald Davidson and Saul Kripke--he seeks to highlight their accomplishments while also pinpointing their shortcomings, especially where their perspectives were limited by an incomplete grasp of matters that have now become clear.

Soames himself has been at the center of some of the tradition's most important debates, and throughout writes with exceptional ease about its often complex ideas. His gift for clear exposition makes the history as accessible to advanced undergraduates as it will be important to scholars. Despite its centrality to philosophy in the English-speaking world, the analytic tradition in philosophy has had very few synthetic histories. This will be the benchmark against which all future accounts will be measured.

Scott Soames is Professor of Philosophy at Princeton University. The author of Beyond Rigidity and Understanding Truth, he is coeditor of Propositions and Attitudes and coauthor of Syntactic Argumentation and the Structure of English.

Endorsements:

"A history of analytic philosophy and an excellent piece of analytic philosophy in its own right. We can all benefit from Soames's discussion of the central issues that have shaped the subject and his assessment of what we have achieved and where we might have gone wrong."--Kit Fine, New York University

"This monumental study is a careful assessment of the successes and the failures of twentieth-century analytic philosophy. Soames displays unfailingly sound judgment throughout. The work is invaluable to those of us who have contributed to this period of very recent history of thought, and more importantly, to our students who will build upon the triumphs and will profit from the defeats of ourselves and our predecessors, carrying philosophy forward into the new millennium. The work is also a comprehensive reality check in the face of persistent accusations (coming not only from those who do not understand analytic philosophy, but also from those who remain stuck in its recent failures) that analytic philosophy is a disease or a futile exercise in wheel spinning. Analytic philosophy is, and has always been, a rational quest for knowledge and understanding. Its tools are clarification, argument, and tutored intuition. Soames provides perspective concerning the best of recent philosophical thought, articulating its most important developments, dead ends, and discoveries."--Nathan Salmon, University of California, Santa Barbara

"Philosophical Analysis in the Twentieth Century is a critical examination of key texts and trends in analytic philosophy by one of its leading contemporary practitioners. Soames has applied his formidable forensic talents to highlight the insights and expose the errors of the major figures from Moore to Kripke. These two volumes are an essential resource for any serious student of analytic philosophy."--Alex Byrne, Massachusetts Institute of Technology

Scott Soames

Philosophical Analysis in the Twentieth Century, Volume 2:
The Age of Meaning

Cloth | 2003 | ISBN: 0-691-11574-5
488 pp. | 6 x 9

This is a major, wide-ranging history of analytic philosophy since 1900, told by one of the tradition's leading contemporary figures. The first volume takes the story from 1900 to mid-century. The second brings the history up to date.

As Scott Soames tells it, the story of analytic philosophy is one of great but uneven progress, with leading thinkers making important advances toward solving the tradition's core problems. Though no broad philosophical position ever achieved lasting dominance, Soames argues that two methodological developments have, over time, remade the philosophical landscape. These are (1) analytic philosophers' hard-won success in understanding, and distinguishing the notions of logical truth, a priori truth, and necessary truth, and (2) gradual acceptance of the idea that philosophical speculation must be grounded in sound prephilosophical thought. Though Soames views this history in a positive light, he also illustrates the difficulties, false starts, and disappointments endured along the way. As he engages with the work of his predecessors and contemporaries--from Bertrand Russell and Ludwig Wittgenstein to Donald Davidson and Saul Kripke--he seeks to highlight their accomplishments while also pinpointing their shortcomings, especially where their perspectives were limited by an incomplete grasp of matters that have now become clear.

Soames himself has been at the center of some of the tradition's most important debates, and throughout writes with exceptional ease about its often complex ideas. His gift for clear exposition makes the history as accessible to advanced undergraduates as it will be important to scholars. Despite its centrality to philosophy in the English-speaking world, the analytic tradition in philosophy has had very few synthetic histories. This will be the benchmark against which all future accounts will be measured.

Scott Soames is Professor of Philosophy at Princeton University. The author of Beyond Rigidity and Understanding Truth, he is coeditor of Propositions and Attitudes and coauthor of Syntactic Argumentation and the Structure of English.

Endorsement:

"A history of analytic philosophy and an excellent piece of analytic philosophy in its own right. We can all benefit from Soames's discussion of the central issues that have shaped the subject and his assessment of what we have achieved and where we might have gone wrong."--Kit Fine, New York University