Anatole Beck, Michael N. Bleicher, Donaldd W. Crowe
Excursions into Mathematics : The Millenium Edition
Since it was first published three decades ago, Excursions Into Mathematics has been one of the most
popular mathematical books written for a general audience. Taking the reader for short Excursions
into several specific disciplines of mathematics, it makes mathematical concepts accessible to a wide
audience. The Millennium Edition is updated with current research and new solutions to outstanding
problems that have been discovered since the last edition was printed, such as the solution to the
well-known 吐our-color problem.・Excursions Into Mathematics: The Millennium Edition is an exciting
revision of the original, much-loved classic. Everyone with an interest in mathematics should read this
book.
2000 ISBN 1-56881-115-2
JULIAN BARBOUR
Absolute or Relative Motion?
The Deep Structure of General Relativity Volume 2
This is the second of a two volume series discussing the theories of Einstein, Newton and other ideas of late 19th and early 20th century physics as in-depth research and basis for Barbour's theory that
time is an illusion. This volume gives a comprehensive survey of the major issues associated with the transition in our understanding of the nature of space and motion that came with Einstein's theory of
general relativity. Einstein's work and thoughts are critically reexamined in their historical context of Mach's earlier reinterpretation of Newton's arguments for absolute space, and other ideas in physics of the time. Along with its new interpretations, this book is an excellent guide to the deeper philosophical implications of
general relativity, and has much to contribute to the studies relevant to the current effort to create a quantum theory of gravity.
0195132033
2001 Not Yet Published
Sara Billey, M.I.T., Cambridge, MA
V. Lakshmibai, Northeastern University, Boston, MASingular Loci of Schubert Varieties
0-8176-4092-4 * 1999 * $49.95 * Hardcover * 240 pages
Singular Loci of Schubert Varieties is a unique work at the crossroads of representation theory, algebraic geometry, and combinatorics. Over the past 20 years, many research articles have been written on the subject in notable journals. In this work, Billey and Lakshmibai have recreated and restructured the
various theories and approaches of those articles and present a clearer understanding of this important subdiscipline of Schubert varieties - namely singular loci.
The main focus, therefore, is on the computations for the singular loci of Schubert varieties and corresponding tangent spaces. The methods used include standard monomial theory, the nil Hecke ring, and Kazhdan--Lusztig theory. New results are presented with sufficient examples to emphasize key points. A
comprehensive bibliography, index, and tables - the latter not to be found elsewhere in the mathematics literature - round out this concise work.
After a good introduction giving background material, the topics are presented in a systematic fashion to engage a wide readership of researchers and graduate students and include: generalities on G/B and G/Q; the Grassmannian and the Flag Variety SL_n/B; the tangent space and smoothness; rational smoothness and Kazhdan--Lusztig theory; root system description of T(w, \tau); determination of the singular locus of X(w) ・la Kumar; patterns, smoothness and rational smoothness.
Series: Progress in Mathematics, Vol. 182
Contents
0.1 Preface
0.2 Notation
Chapter 1. Introduction
Chapter 2. Generalities on G/B and G/Q
Chapter 3. The Grassmannian and the Flag Variety SLn/B
Chapter 4. The Tangent Space and Smoothness
Chapter 5. Rational Smoothness and Kazhdan--Lusztig Theory
Chapter 6. Root System Description of T(\omega, \tau)
Chapter 7. More Results on T(\omega, \tau)
Chapter 8. Determination of the Singular Locus of X(\omega) ・la Kumar
Chapter 9. Patterns, Smoothness and Rational Smoothness
Chapter 10. Irreducible Components of the Singular Locus of a Schubert Variety
Chapter 11. Multiplicity at a Point
Chapter 12. Rank Two Results
Chapter 13. Related Combinatorial Results
Chapter 14. Related Varieties
Chapter 15. Addendum
Index
Jeremy J. Gray, The Open University, Milton Keynes, UK
Linear Differential Equations and Group Theory
from Riemann to Poincare ,Second Edition
0-8176-3837-7 * 1999 * Hardcover * 384 pages * 36 Illustrations
This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and non-Euclidean geometry.
The text for this new edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann--Hilbert problem, the uniformization theorem, Picard-Vessiot theory, and the hypergeometric equation in higher dimensions. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
This work continues to be the only up-to-date scholarly account of the history of a branch of mathematics that continues to generate important research, for which the mathematics has been the occasion for some of the most profound work by numerous 19th century figures: Riemann, Fuchs, Dedekind, Klein, and Poincare
書評
"The volume...is one among the most interesting books on the history of mathematics published in recent times.... very stimulating reading for both historians of modern mathematics and mathematicians as well." ---Mathematical Reviews
"The book contains an amazing wealth of material relating to the algebra, geometry, and analysis of the nineteenth century.... Written with accurate historical perspective and clear exposition, this book is truly hard to put down." ---Zentralblatt fur Mathematik
"...must reading for every serious student of nineteenth century mathematics...represents a substantial contribution toward filling what is generally acknowledged to be an immense gap in the historical literature."---ISIS
Table of Contents
Chapter 1. Hypergeometric Equations and Modular Equations
Chapter 2. Lazarus Fuchs
Chapter 3. Algebraic Solutions to a Differential Equation
Chapter 4. Modular Equations
Chapter 5. Some Algebraic Curves
Chapter 6. Six Automorphic Functions
Appendices
Notes on Chapter I-VI
Notes on the Appendices
Bibliography
Index
by S S Chern (University of California, Berkeley), W H Chen (Beijing University)
& K S Lam (California State Polytechnic University)LECTURES ON DIFFERENTIAL GEOMETRY
This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.
Contents:
Differentiable Manifolds
Multilinear Algebra
Exterior Differential Calculus
Connections
Riemannian Geometry
Lie Groups and Moving Frames
Complex Manifolds
Finsler Geometry
Historical Notes
Differential Geometry and Theoretical Physics
Readership: Undergraduates, graduates and researchers in pure mathematics and mathematical physics.
368pp
Pub. date: Nov 1999
ISBN 981-02-3494-5
ISBN 981-02-4182-8(pbk)
J.M. Gracia-Bonda / J.C. Varilly /H. Figueroa,
all Universidad de Costa Rica, San JosElements of Noncommutative Geometry
0-8176-4124-6 * 2000 * Hardcover * 650 pages * Forthcoming May 2000...
Noncommutative geometry deals with the unification of mathematics under the aegis of the quantum apparatus, that is, the theory of operators and of C*-algebras. In recent years noncommutative geometry has been a rich topic of research with discoveries leading to an increasing number of applications in
mathematics and theoretical physics. Very little has appeared in book form since Alain Connes' work in the early 90s to deal with this subject. Elements of Noncommutative Geometry fills an important gap in the literature.
An introduction to the language and techniques of noncommutative geometry A unified and comprehensive presentation of core topics and key research results drawing from several branches of mathematics
Excellent exposition of introductory material; main topics covered repeatedly in the text at gradually more demanding levels of difficulty Many applications to diverse fields: index theory, foliations, number theory, particle physics, and fundamental quantum theory Proof of the noncommutative characterization of Riemannian spin manifolds Comprehensive bibliography and index
Rich in proofs, examples, exercises and solutions, this volume is an excellent self-study resource for mathematicians, physicists, and graduate students. As a textbook, the work is also useful in a graduate-level course in noncommutative geometry.
Series: Birkhauser Advanced Texts
Table of Contents
Preface
I Topology
1. Noncommutative Topology: Spaces
2. Noncommutative Topology: Vector Bundles
3. Some Aspects of K-theory
4. Fredholm Operators on C*-modules
II Calculus and Linear Algebra
5. Finite-dimensional Clifford Algebras and Spinors
6. The Spin Representation
7. The Noncommutative Integral
8. Noncommutative Differential Calculi
III Geometry
9. Commutative Geometries
10. Spectral Triples
11. Connes' Spin Manifold Theorem
IV Trends
12. Tori
13. Quantum Theory
14. Kreimer-Connes-Moscovici Algebras
References
Symbol Index