Mark Colyvan

The Indispensability of Mathematics

0-19-516661-2, paper, 192 pages

Description

The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with many influential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.

About the Author(s)

Mark Colyvan, Lecturer, School of Philosophy, University of Tasmania, Australia

Jim Baggott

Beyond Measure:
Modern Physics, Philosophy and the Meaning of Quantum Theory

(Hardback)0-19-852927-9
Paperback)0-19-852536-2
Publication date: 6 November 2003
396 pages, numerous figures, 240mm x 168mm

Description
''Jim Baggotts Beyond Measure is a lively tour through the major positions. in the foundations and interpretation of the quantum theory. It is not a prancing roshis tour but a carefully written and beautifully organized primer on virtually all the interesting issues.'' - Arthur Fine, Professor of Philosophy, Adjunct Professor of Physics, University of Washington, Seattle
''More than a revision of a classic account of quantum mechanics, Jim Baggotts book is the definitive non-technical account of the wonder and understandable strangeness of the theory that underlies all of physics - quantum mechanics'' -Roald Hoffmann-Nobel prize winner for chemistry in 1981. Department of Chemistry and Chemical Biology, Cornell University

Quantum theory is one of the most important and successful theories of modern physical science. A fact all the more remarkable because quatum theory is a theory that few understand.

Most academic textbooks on the subject are written for specialists, filled with complex jargon and dense mathematics. In contrast there are many popular presentations of the inherent 'weirdness' of the quantum world that are light on jargon and contain no mathematics.Together these presentations serve to create the impression that there are two theories - the 'serious, one and the 'wierd' one. Baggott successfully bridges the gulf between these presentations by grounding the discussion of the theory's profound problems directly in its mathematical formalism in a way that under-graduate students and interested individuals can follow.


Readership: Students of physical science (physics/ chemistry) Curiosity - they are taught quantum theory and often do not understand why they do not understand it. Informed lay readers (the proverbial "average New Scientist reader") - they will have read many popular treatments but are interested to penetrate more of the detail. Academic scientists and philosophers - because this is their field, the book represents a possible course text or, if this is not their field, because they are also curious.

Luigi Ambrosio, Scuola Normale Superiore, and Paolo Tilli, Scuola Normale Superiore

Topics on Analysis in Metric Spaces

(Hardback) 0-19-852938-4
Publication date: 18 December 2003
130 pages, none, 234mm x 156mm
Series: Oxford Lecture Series in Mathematics and Its Applications

Concise and clear coverage of analysis in metric spaces
Based on lecture notes from the Scuola Normale
Supplemented with exercises of varying difficulty
Coverage of classical and recent results

Description
''This would be an excellent basis for a one-semester graduate course. This is very much a good time for this book.' ' -Professor Stephen Semmes (Rice University)
''[it is] above average and very important. The selected topics provide a good start in the field.'' -Professor Bernd Kirchheim (University of Oxford)

Based on lecture notes from the Scuola Normale this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers.

Readership: Graduate students in in applied mathematics and engineering undertaking a course on analysis in metric spaces.

Contents/contributors

1 Some preliminaries in measure theory
2 Hausdorff measures and covering theorems in metric spaces
3 Lipschitz functions in metric spaces
4 Geodesic problem and Gromov-Hausdorff convergence
5 Sobolev spaces in a metric framework
6 A quick overview on the theory of integration

John C Gower, Professor, Open University, Walton Hall, Statistics Department, Milton Keynes, and Garmt B Dijksterhuis, Senior Scientist, WUR Wageningen University and Research Centre,

Procrustes Problems

(Hardback) 0-19-851058-6
Publication date: 22 January 2004
256 pages, 234mm x 156mm
Series: Oxford Statistical Science Series

First systematic overview of Procrustean methods in one volume
Multi-disciplinary - these matching methods are used in many fields involving data analysis at research level
Contains new algorithms
Presents a unifying ANOVA framework

Description

Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. The name derives from the Greek myth where Procrustes invited passers-by in for a pleasant meal and a night's rest on a magical bed that would exactly fit any guest. He then either stretched the guest on the rack or cut off their legs to make them fit perfectly into the bed. Theseus turned the tables on Procrustes, fatally adjusting him to fit his own bed. The text is the first systematic overview of Procrustean methods in one volume, presenting a unifying Analysis of Variance framework for different matching methods and the development of statistical tests.


Readership: Statisticians, data analysts and research workers using Procrustean methods, graduate students of statistics and multivariate analysis, specialists in many other fields involved in analysing data

Contents/contributors
Preface
Contents
1 Introduction
2 Initial transformations
3 Two-set Procrustes problems: generalities
4 Orthogonal Procrustes problems
5 Projection Procrustes problems
6 Oblique Procrustes problems
7 Other two-sets Procrustes problems
8 Weighting, scaling and missing values
9 Generalised Procrustes problems
10 Analysis of variance framework
11 Incorporating information on variables
12 Accuracy and stability
13 Links with other methods
14 Some application areas, future and conclusion
A1 Configurations
A2 Rotations and reflections
A3 Orthogonal projections
A4 Oblique axes
A5 A minimisation problem
A6 Symmetric matrix products
References

Lucjan Jacak, Institute of Physics, Wroclaw University of Technology, Piotr Sitko, Institute of Physics, Wroclaw University of Technology, Konrad Wieczorek, Institute of Physics, Wroclaw University of Technology, and Arkadiusz Wojs, Institute of Physics, Wroclaw University of Technolog

Quantum Hall systems Braid groups, composite fermions and fractional charge

0-19-852870-1 Hardback

Description

This book presents cutting-edge topics in modern theoretical physics - quantum Hall systems - the subject of two Nobel Prizes in 1985 and 1998.


Readership: Graduate students and researchers working in theoretical physics and in particular, condensed matter physicists. Also of interest to mathematicians.

Contents/contributors
1 Introduction
2 Topological methods for description of quantum many-body systems
3 Quantization of many-particle systems and quantum statistics in lower dimensions
4 Topological approach to composite particles in two dimensions
5 Many-body methods for Chern-Simons systems
6 Anyon superconductivity
7 The fractional quantum Hall effect in composite fermion systems
8 Quantum Hall systems on a sphere
9 Pseudopotential approach to the fractional quantum Hall states


Charles S. Chihara, Department of Philosophy, University of California, Berkeley

A Structural Account of Mathematics

(Hardback)0-19-926753-7
Publication date: 20 November 2003
Clarendon Press 394 pages, 234mm x 156mm

Description

Charles Chihara's new book develops a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. In particular, this perspective allows Chihara to show that, in order to understand how mathematical systems are applied in science, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. He also advances several new ways of undermining the Platonic view of mathematics. Anyone working in the field will find much to reward and stimulate them here.

Readership: Scholars and students of the philosophy of mathematics; mathematicians interested in the foundations of their subject.

Contents/contributors
Introduction
1 Five Puzzles in Search of an Explanation
2 Geometry and Mathematical Existence
3 The Van Inwagen Puzzle
4 Structuralism
5 Platonism
6 Minimal Anti-Nominalism
7 The Constructibility Theory
8 Constructible Structures
9 Applications
10 If-Thenism
11 Field's Account of Mathematics and Metalogic
Appendix A: Some Doubts about Hellman's Views
Appendix B: Balaguer's Fictionalism