Jeffrey A. Barrett, Associate Professor of Philosophy, University of California, Irvine

The Quantum Mechanics of Minds and Worlds

284 pages, line figures, 216mm x 138mm

Paperback, 0-19-924743-9

Jeffrey Barrett presents the most comprehensive study yet of a problem that has puzzled physicists and philosophers since the 1930s. Quantum mechanics is in one sense the most successful physical theory ever, accurately predicting the behaviour of the basic constituents of matter. But it has an apparent ambiguity or inconsistency at its heart; Barrett gives a careful, clear, and challenging evaluation of attempts to deal with this problem.

Readership: Philosophers and physicists; graduate and advanced undergraduate students of quantum mechanics or of philosophy of physics.

Contents/contributors
1 A Brief Introduction
2 The Standard Formulation of Quantum Mechanics
3 The Theory of the Universal Wave Function
4 The Bare Theory and Determinate Experience
5 Selecting a Branch
6 Many Worlds
7 Many Minds
8 Many Histories
9 The Determinate-Experience Problem
Appendices
References
Index

Denis Weaire, Physics Department, Trinity College, Dublin,
and Stefan Hutzler, Physics Department, Trinity College, Dublin

The Physics of Foams

・Coherent and comprehensive introduction to the topic.
・Lasting value as reference for definitions, procedures, and theorems.
・Informal, accessible style of presentation.
・Extensive use of illustrated examples and computer simulations.
・Reference lists at chapter ends covering most of the important books and papers in the field.

272 pages, 178 line figs, 24 halftones, 234mm x 156mm

Paperback, 0-19-851097-7

Publication date: September 2001

Contents/contributors
Preface
1 Introduction
2 Local equilibrium rules
3 Foam structure
4 Making foams
5 Imaging and probing foam structure
6 Simulation and modelling
7 Coarsening
8 Rheology
9 Electrical conduction in a foam
10 Equilibrium under gravity
11 Drainage
12 Foam collapse
13 Ordered foams
14 Some applications of liquid foams
15 Some analogous physical systems
16 Solid foams
17 Some natural foams
18 Envoi
Appendices
A. The shape of single soap films and bubbles
B. The Theorem of Lamarle
C. Bubble Clusters
D. The decoration theorum
E. The conductivity formula of Lemlich
F. The drainage equation
G. Phyllotaxis
H. Simulation of liquid foams
I. Bibliography
Appendices

Hans Rott, Professor of Philosophy, University of Regensburg, Germany

Change, Choice and Inference
A study of Belief Revision and Nonmonotonic Reasoning

・Unifies theory of logic and rational choice.
・Provides philosophical foundations for significant research.
・Carefully presented research monograph.
・Contains detailed proofs of all central theorems.

384 pages, 18 black/white line, 234mm x 156mm
Series: Oxford Logic Guides (019-961138-6)
Hardback, 0-19-850306-7
Publication date: November 2001

Readership: Researchers and advanced students

Contents/contributors
0 Overview
1 Doxastic States and Their Representation
2 Epistemology and Belief Change
3 Changing Doxastic States: Two Complementary Perspectives
4 Concepts of Theoretical Rationality: Postulates for Belief Change and Nonmonotonic Reasoning
5 Foundational Belief Change Using Nonmonotonic Inference
6 A General Concept of Practical Rationality: Constraints for Coherent Choice
7 Coherentist Belief Change as a Problem of Rational Choice
8 Revealed Preferences: Understanding the Theory of Epistemic Entrenchment
Appendices A; B; C; D; E
References/Bibliography
Index of Symbols
Index of Names
Subject Index

Takesaki, M., University of California, Los Angeles, CA, USA

Theory of Operator Algebras I

1st ed. 1979. 2nd printing 2001. XII, 415 pp. Hardcover
3-540-42248-X

Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a two volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.
The books unifying theme is the Banach space duality for operator algebras. This allows the reader to recognize the affinity between operator algebras and measure theory on locally compact spaces. Very technical sections are clearly labeled and there are extensive comments by the author, a good historical background and excercises.
This book is part of the new subseries of the EMS on Operator Algebras and Non-Commutative Geometry.

Keywords: operator algebras, von Neumann algebras, C * -algebras

Contents: Fundaments of Banach Algebras and C*-Algebras.- Topologies and Density Theorems in Operator Algebras.- Conjugate Spaces.- Tensor Products of Operator Algebras and Direct Integrals.- Types of von Neumann Algebras and Traces.- Appendix: Polish Spaces and Standard Borel Spaces.

Series: Encyclopaedia of Mathematical Sciences. VOL. 124

Cheney, W., University of Texas at Austin, TX, USA

Analysis for Applied Mathematics

2001. Approx. 450 pp. 27 figs. Hardcover
0-387-95279-9

This textbook is designed for a course at the beginning graduate level, serving students of mathematics, engineering, physics, and other sciences. Its goal is to provide the analytical tools, concepts, and viewpoints needed for modern applied mathematics. The book begins with a gentle introduction to normed linear spaces and Hilbert spaces, taking the reader as far as the Spectral Theorem for compact normal operators on a Hilbert space. It then discusses calculus in normed linear spaces, leading up to topics in the calculus of variations and optimization theory.
Next, the book treats various practical methods for solving problems that arise in applied mathematics, such as differential equations, boundary value problems, and integral equations. Here the reader finds the Galerkin method, the method of iteration, Newton's method, projection techniques, homotopy methods, and other pragmatic approaches to the difficult equations confronting applied mathematicians. To prepare the reader for work in the modern theory of partial differential equations, the subject of distributions is taken up next. A chapter on the Fourier transform and its applications follows, and includes a section on Sobolev spaces. Another chapter discusses topics that are related to those in the earlier parts of the book but are more specialized, such as separation theorems, selection theorems, Fredholm theory, and linear topological spaces. The final chapter provides a concise account of measure theory and integration.

Contents: Normed Linear Spaces.- Hilbert Spaces.- Calculus in Banach Spaces.- Approximate Methods of Analysis.- Distributions.- The Fourier Transform.- Additional Topics.- Measure and Integration.- References.- Index.

Series: Graduate Texts in Mathematics. VOL. 208