(Hardback)
ISBN-10: 0-19-856913-0, ISBN-13: 978-0-19-856913-8
(Paperback)
ISBN-10: 0-19-852793-4, ISBN-13: 978-0-19-852793-0
Estimated publication date: December 2007
352 pages, 10 line figures, 234x156 mm
Review(s) from previous edition:
'This clearly written exposition is accompanied by well-chosen exercises. This book should be useful as a textbook for most undergraduates courses on algebra.' -
'This is an extremely engaging introduction to abstract algebra by one of this country's most prolific and creative algebraists. Recognising that although the axiomatic method is unavoidable it is intially uncomfortable for many students, he adopts a relatively informal style which is constantly encouraging without ever lapsing into imprecision. Aided by a relaxed, friendly expository style, his expertise, sureness of touch and contagious enthusiasm for algebra shine through on every page this is a book to study, savour and enjoy' -
''Altogether this is a concise but solid introduction into algebra and linear algebra' Internationale mathematische Nachrichten' -
Description
Comprehensive introductory chapters developed to meet students' needs
New material on the Axiom of Choice, p-groups and local rings
Covers applications and theory
Over 300 exercises
Solutions presented on author's website
An extensive further reading section
New to this edition
Comprehensive introductory chapters
New material on the Axiom of Choice, p-groups and local rings
Many new exercises
Solutions presented on a companion website
Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics.
Readership: All undergraduates taking a basic algebra course.
Contents
1. Introduction
2. Rings
3. Groups
4. Vector spaces
5. Modules
6. The number systems
7. Further topics
8. Applications
Further reading
Index
NEW IN PAPERBACK
(paper)
ISBN-10: 0-19-923652-6
ISBN-13: 978-0-19-923652-7
Estimated publication date: November 2007
352 pages, 84 line drawings, 240x168 mm
Review(s) from previous edition:
'Renormalization Methods should be an excellent source of material for anyone who plans to lead advanced undergradutes and first-year graduate students beyond the standard course material toward current research topics.' - Physics Today
'I think this book is the best introductory textbook on techniques of renormalization available. It will be a delight to read for anyone who is encountering the topic for the first time and is wishing to exploit the methods to pass an exam or in one's field.' - Contemporary Physics
Description
Easy introduction to the use of renormalization methods.
Bridges the gap between elementary texts and advanced texts on statistical field theory and critical phenomena.
Uses only basic physics and mathematics; accessible to a wide readership of scientists, engineers and mathematicians.
Addresses deep fundamental concepts whilst remaining a careful exposition for students of all levels of ability.
Supplemented with exercises and appendices to give a complete understanding of the main text.
This book is unique in occupying a gap between standard undergraduate texts and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation (and motivation), including mean-field theories and high-temperature and low-density expansions. It then proceeds by easy steps to the famous epsilon-expansion, ending up with the first-order corrections to critical exponents beyond mean-field theory. Nowadays there is widespread interest in applications of renormalization methods to various topics ranging over soft condensed matter, engineering dynamics, traffic queueing and fluctuations in the stock market. Hence macroscopic systems are also included, with particular emphasis on the archetypal problem of fluid turbulence. The book is also unique in making this material accessible to readers other than theoretical physicists, as it requires only the basic physics and mathematics which should be known to most scientists, engineers and mathematicians.
Contents
What is renormalization?
Chapter 1. The bedrock problem:why we need renormalization methods
Chapter 2. Easy applications of renomalization group (RG) to simple models
Chapter 3. Mean-field theories for simple models
Renormalization perturbation theories (RPT)
Chapter 4. Perturbation theory using a control parameter
Chapter 5. Classical nonlinear systems driven by random noise
Chapter 6. Application of RPT to turbulence and related problems
Renormalization group
Chapter 7. Setting the scene: critical pehnomena
Chapter 8. Real-space RG
Chapter 9. Momentum-space RG
Chapter 10. Field-theoretic RG
Chapter 11. Dynamical RG applied to classic nonlinear systems
Appendices
Chapter A. Statistical ensembles
Chapter B. From statistical mechanics to thermodynamics
Chapter C. Exact Solutions in one and two dimensions
Chapter D. Quantum Treatment of the Hamiltonian N-body assembly
Chapter E. Generalization of the Bogoliubov variational method to a spatially-varying magnetic field
(Hardback)
ISBN-10: 0-19-856599-2
ISBN-13: 978-0-19-856599-4
Estimated publication date: January 2008
304 pages, 234x156 mm
Series: Oxford Graduate Texts in Mathematics number 15
Description
Established author with international research reputation.
Topic stands at the centre of a number of key areas of mathematics and physics
Novel treatment of a rich and highly topical area
Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry.
Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework.
Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.
Readership: Graduate and research students in mathematics and physics.
Contents
1. The many faces of cohomology
2. Quantum cohomology
3. Quantum differential equations
4. Linear differential equations in general
5. The quantum D-module
6. Abstract quantum cohomology
7. Integrable systems
8. Solving integrable systems
9. Quantum cohomology as an integrable system
10. Integrable systems and quantum cohomology
References
1987; 247 pp; hardcover
ISBN-10: 0-8218-4422-9
ISBN-13: 978-0-8218-4422-9
Expected publication date is November 17, 2007.
S Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornass and Stensones look at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations. The first part of the book reviews some of the basics of the theory, in a self-contained introduction to several complex variables. The counterexamples cover a variety of important topics: the Levi problem, plurisubharmonic functions, Monge-Ampere equations, CR geometry, function theory, and the barpartial equation.
The book would be an excellent supplement to a graduate course on several complex variables.
Readership
Graduate students and research mathematicians interested in several complex variables.
Table of Contents
Some notations and definitions
Holomorphic functions
Holomorphic convexity and domains of holomorphy
Stein manifolds
Subharmonic/Plurisubharmonic functions
Pseudoconvex domains
Invariant metrics
Biholomorphic maps
Counterexamples to smoothing of plurisubharmonic functions
Complex Monge Ampere equation
H^infty-convexity
CR-manifolds
Pseudoconvex domains without pseudoconvex exhaustion
Stein neighborhood basis
Riemann domains over mathbb{C}^n
The Kohn-Nirenberg example
Peak points
Bloom's example
D'Angelo's example
Integral manifolds
Peak sets for A(D)
Peak sets. Steps 1-4
Sup-norm estimates for the bar{partial}-equation
Sibony's bar{partial}-example
Hypoellipticity for bar{partial}
Inner functions
Large maximum modulus sets
Zero sets
Nontangential boundary limits of functions in H^infty(mathbb{B}^n)
Wermer's example
The union problem
Riemann domains
Runge exhaustion
Peak sets in weakly pseudoconvex boundaries
The Kobayashi metric
Bibliography
Series: Chapman & Hall/CRC Texts in Statistical Science Series
ISBN: 9781420065213
ISBN 10: 1420065211
Publication Date: 1/15/2008
Number of Pages: 352
Provides a calculus-based introduction to probability and information fusion
Presents a probabilistic approach to concepts
Organizes the standard distributions that most often occur in probability using physical processes
Includes examples and exercises that compare and contrast different perspectives
Based on the popular probability course by Gian-Carlo Rota of MIT, Probability and Random Processes with R provides a calculus-based introduction to probability. The text systemically motivates and organizes the standard distributions that most often occur in probability using physical processes. Presenting a probabilistic approach that builds on other approaches such as geometry and physical processes, the book addresses sets, events, and probability; finite processes; random variables; statistics and normal distribution; conditional probability; the Poisson process; entropy and information; Markov chains; Markov processes; Bayesian networks; and the Bayesian web. Various exercises and examples compare different perspectives.
Table of Contents
Introduction. Sets, Events, and Probability. Finite Processes. Random Variables. Statistics and the Normal Distribution. Conditional Probability. The Poisson Process. Entropy and Information. Markov Chains. Markov Processes. Bayesian Networks. The Bayesian Web.