Dale Rolfsen, University of British Columbia, Vancouver, Canada

Knots and Links

Expected publication date is December 6, 2003

Description

Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds.

Besides providing a guide to understanding knot theory, the book offers "practical" training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements. It is characterized by its hands-on approach and emphasis on a visual, geometric understanding.

Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included.

Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds.

Contents

Introduction
Codimension and other matters
The fundamental group
Three-dimensional pl geometry
Seifert surfaces
Finite cyclic coverings and the torsion invariants
Infinite cyclic coverings and the Alexander invariant
Matrix invariants
3-manifolds and surgery on links
Foliations, branched covers, fibrations and so on
A higher-dimensional sampler
Covering spaces and some algebra in a nutshell
Dehn's lemma and the loop theorem
Table of knots and links
References
Index

Details:

Series: AMS Chelsea Publishing
Publication Year: 2003
ISBN: 0-8218-3436-3
Paging: 439 pp.
Binding: Hardcover

Patrick Dehornoy, Universite de Caen, France, Ivan Dynnikov, Moscow State University, Russia, Dale Rolfsen, University of British Columbia, Vancouver, BC, Canada, and Bert Wiest, Universite de Rennes I, France

Why Are Braids Orderable?

Description

In the decade since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several quite different approaches have been applied to understand this phenomenon. This book is an account of those approaches, involving self-distributive algebra, uniform finite trees, combinatorial group theory, mapping class groups, laminations, and hyperbolic geometry.

This volume is suitable for graduate students and research mathematicians interested in algebra and topology.

Contents

A linear ordering of braids
Self-distributivity
Handle reduction
Finite trees
Automorphisms of a free group
Curve diagrams
Hyperbolic geometry
Triangulations
Bi-ordering the pure braid groups
Open questions
Bibliography
Index
Index of notation

Details:

Series: Panoramas et Syntheses, Number: 14
Publication Year: 2002
ISBN: 2-85629-135-X
Paging: 190 pp.
Binding: Softcover


Ed. A Kundu, SAHA Institute of Nuclear Physics, Calcutta, India

Classical and Quantum Nonlinear Integrable Systems: Theory and Application

Publication Date Sep 2003
Length 312pp,
ISBN Hardback:0-7503-0959-8

Contents

Preface (A Kundu) A Journey Through the KdV Equation (M Lakshmanan) The Painleve methods (R Conte and M Musette) Discrete Integrability (K M Tamizhmani, A Ramani, B Grammaticos and T Tamizhmani) The D-BAR Method: A Tool for Solving Two-Dimensional Integrable Evolution PDEs (A S Fokas) Introduction to Solvable Lattice Models in Statistical and Mathematical Physics (T Deguchi)II. QUANTUM SYSTEMS Unifying Approaches in Integrable Systems: Quantum and Statistical, Ultralocal and Nonultralocal (A Kundu) The Physical Basis of Integrable Spin Models (I Bose) Exact Solvability in Contemporary Physics (A Foerster, J Links and H-Q Zhou) The Thermodynamics of the spin-1/2 XXX Chain: Free Energy and Low-temperature Singularities of Correlation Lengths (A KlEper and C Scheeren) Reaction-Diffusion Processes and Their Connection with Integrable Quantum Spin Chains (M Henkel)

Synopsis
Nonlinear integrable systems, covering both classical and quantum models, are of considerable theoretical and practical interest, with applications over a wide range of subjects from water waves to spin models, nonlinear optics to correlated electron systems, plasma physics to reaction-diffusion processes.

Classical and Quantum Nonlinear Integrable Systems reviews the advances made in various facets of this subject. Emphasis is placed on the underlying concepts rather than technicalities and it is intended to serve as an introduction to the subject for those interested in the field as well as being useful to specialists. The book divides into two parts, the first covering classical theories and applications, the second devoted to the quantum aspects of the subject.

Readership
Advanced graduate students and researchers in mathematical physics and applied mathematics

I J R Aitchison, Oxford University, UK; A J G
Hey, Southampton University, UK

Gauge Theories in Particle Physics, Volume 2:
3rd edition: QCD and the Electroweak Theory

Publication Date Dec 2003
Length c400pp, illus
ISBN Paperback:0-7503-0950-4

Contents

Part V Non-Abelian Symmetries Part VI Quantum Chromodynamics (QCD) Part VII Spontaneous Symmetry Breaking Part VII Weak Interactions and the Electroweak Theory
Full Text Contents

Synopsis

Gauge Theories in Particle Physics Volume 1: From Relativistic Quantum Mechanics to QED discussed the formulation and application of quantum electrodynamics, which is now regarded as simply the first part of the standard model of particle physics. In Gauge Theories in Particle Physics Volume 2: QCD and the Electroweak Theory the remaining two parts of the standard model, namely, quantum chromodynamics and the electroweak theory of Glashow, Salam and Weinberg are considered. These latter two theories are in some ways like QED but there are important differences, which create significant conceptual and technical difficulties for the student. The aim of the book is to ease the reader through these difficulties, keeping the level of accessibility comparable to that of volume 1, and thus provide a much more accessible introduction to these theories than is available elsewhere. As was also the case in volume 1, substantial attention is paid to calculations of physical quantities, and to comparison of the resulting predictions with experimental results.

The similarities between QED and the two theories studied in volume 2 include the facts that all three are gauge theories, that the calculation methods of Feynman graphs can be applied to all of them, and that they are all renormalizable. So the foundations of gauge theory, Feynman graphs and renormalization theory laid in volume 1 continue to be highly relevant in volume 2. Nevertheless, there are important differences between QED and the other two theories.

Readership

Graduate and senior undergraduate students taking courses on the standard model of particle physics. Postgraduate students and researchers in particle physics

Phillip I. Good, James W. Hardin

Common Errors in Statistics: (and How to Avoid Them)

ISBN: 0-471-46068-0
Paperback
240 pages
July 2003

Author Information

A guide to choosing and using the right techniques
High-speed computers and prepackaged statistical routines would seem to take much of the guesswork out of statistical analysis and lend its applications readily accessible to all. Yet, as Phillip Good and James Hardin persuasively argue, statistical software no more makes one a statistician than a scalpel makes one a surgeon. Choosing the proper technique and understanding the analytical context is of paramount importance to the proper application of statistics. The highly readable Common Errors in Statistics (and How to Avoid Them) provides both newly minted academics and professionals who use statistics in their work with a handy field guide to statistical problems and solutions.

Good and Hardin begin their handbook by establishing a mathematically rigorous but readily accessible foundation for statistical procedures. They focus on debunking popular myths, analyzing common mistakes, and instructing readers on how to choose the appropriate statistical technique to address their specific task. A handy checklist is provided to summarize the necessary steps.

Topics covered include:

Creating a research plan
Formulating a hypothesis
Specifying sample size
Checking assumptions
Interpreting p-values and confidence intervals
Building a model
Data mining
Bayesf Theorem, the bootstrap, and many others
Common Errors in Statistics (and How to Avoid Them) also contains reprints of classic articles from statistical literature to re-examine such bedrock subjects as linear regression, the analysis of variance, maximum likelihood, meta-analysis, and the bootstrap. With a final emphasis on finding solutions and on the great value of statistics when applied in the proper context, this book will prove eminently useful to students and professionals in the fields of research, industry, medicine, and government.