A textbook suitable for undergraduate courses.
The materials are presented very explicitly so that students will
find it very easy to read. A wide range of examples, about 500
combinatorial problems taken from various mathematicial
competitions and exercises are also included.
Contents:
Permutations and Combinations
Binomial Coefficients and Multinomial Coefficients
The Pigeonhole Principle and Ramsey Numbers
The Principle of Inclusion and Exclusion
Generating Functions
Recurrence Relations
Readership: Undergraduates, graduates and mathematicians.
312pp
Pub. date: Jul 1992
ISBN 981-02-1114-7
ISBN 981-02-1139-2(pbk)
Paper | 2000 |
Cloth | 2000 |
328 pp. | 6 x 9
This book introduces new methods in the theory of partial
differential equations derivable from a Lagrangian. These methods
constitute, in part, an extension to partial differential
equations of the methods of symplectic geometry and
Hamilton-Jacobi theory for Lagrangian systems of ordinary
differential equations. A distinguishing characteristic of this
approach is that one considers, at once, entire families of
solutions of the Euler-Lagrange equations, rather than
restricting attention to single solutions at a time. The second
part of the book develops a general theory of integral
identities, the theory of "compatible currents," which
extends the work of E. Noether. Finally, the third part
introduces a new general definition of hyperbolicity, based on a
quadratic form associated with the Lagrangian, which overcomes
the obstacles arising from singularities of the characteristic
variety that were encountered in previous approaches. On the
basis of the new definition, the domain-of-dependence theorem and
stability properties of solutions are derived. Applications to
continuum mechanics are discussed throughout the book. The last
chapter is devoted to the electrodynamics of nonlinear continuous
media.
Table of Contents
General Introduction 3
1
1.0 Introduction 7
1.1 The Lagrangian Picture 8
1.2 The Hamiltonian Picture 19
1.3 Examples 28
2
2.0 Introduction 51
2.1 The Canonlicd and Symplectic Forms 57
2.2 Symplectic Transformations 62
2.3 The Equations of Variation 79
2.4 The Circulation Theorem 84
2.5 The Euler System 87
2.6 Irrotational Solutions 96
2.7 The Equation of Continuity 99
3
3.0 Introduction 105
3.1 Compatible Currents 108
3.2 Null Currents and Null Lagragians 125
3.3 The Source Equations 128
3.4 The Generic Case n > 1 & m > 2 133
3.5 The Separable Case m > 2 141
3.6 The Case m = 2 144
3.7 Lie Flows and the Noether Current 146
4
4.1 Sections of Vector Bundles 159
5
5.0 Introduction 191
5.1 Relative Lagrangians 195
5.2 Ellipticity and Hyperbolicity 220
5.3 The Domain of Dependence 240
6
6.1 The Electromagnetic Field 263
6.2 Electromagnetic Symplectic Structure 272
6.3 Electromagnetic Compatible Currents 282
6.4 Causality in Electromagnetic etic Theory 299
Bibliography 315
Index 317
Series: Annals of Mathematics Studies vol.146.
Volume 1. Papers Dedicated to C. T. C. Wall
Paper | 2000 |
Cloth | 2000 |
448 pp. | 6 x 9
Surgery theory, the basis for the classification theory of
manifolds, is now about forty years old. There have been some
extraordinary accomplishments in that time, which have led to
enormously varied interactions with algebra, analysis, and
geometry. Workers in many of these areas have often lamented the
lack of a single source that surveys surgery theory and its
applications. Indeed, no one person could write such a survey.
The sixtieth birthday of C. T. C. Wall, one of the leaders of the
founding generation of surgery theory, provided an opportunity to
rectify the situation and produce a comprehensive book on the
subject. Experts have written state-of-the-art reports that will
be of broad interest to all those interested in topology, not
only graduate students and mathematicians, but mathematical
physicists as well.
Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance,
E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton,
L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J.
Roe, J. Milgram, and C. Thomas.
Table of Contents
The Editors Preface vii
The Editors C. T. C. Wall's contributions to the topology of
manifolds 3
C. T. C. Wall's publication list 17
J. Milnor Classification of (n - l)-connected 2n-dimensional
manifolds and the discovery of exotic spheres 25
S. Novikov Surgery in the 1960's 31
W. Browder Differential topology of higher dimensional manifolds
41
T. Lance Differentiable structures on manifolds 73
E. Brown The Kervaire invariant and surgery theory 105
A Kreck A guide to the classification of manifolds 121
J. Klein Poincare duality spaces 135
A Davis Poincare duality groups 167
J. Davis Manifold aspects of the Novikov Conjecture 195
I. Hambleton and L. Taylor A guide to the calculation of the
surgery obstruction groups for finite groups 225
C. Stark Surgery theory and infinite fundamental groups 275
E. Pedersen Continuously controlled surgery theory 307
W. Mio Homology manifolds 323
J. Levine and K. Orr A survey of applications of surgery to knot
and link theory 345
J. Roe Surgery and C*-algebras 365
R. J. Milgram The classification of Aloff-Wallach manifolds and
their generalizations 379
C. Thomas Elliptic cohomology 409
Series: Annals of Mathematics Studies vol.145.
ISBN: 0-471-34976-3
Paperback
Pages: 408
Published: Nov 1999
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ISBN: 0-471-32969-X
Hardcover
Projected Pub Date: Jan 2000
In one of the most startling discoveries in cosmology in the
century, astronomers last year determined that the universe is
flying apart at an ever faster rate. This
"acceleration" has smashed the popular idea of a
perfectly balanced "beautiful" universe and kicked off
what Scientific American has proclaimed as a new revolution in
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Telescope scientist Mario Livio introduces the new findings and
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universe to Galileo's inquisitors.
Mario Livio, PhD (Baltimore, MD), is a senior scientist at the
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Subject:
Physics / General & Introductory Physics /
ISBN: 0-471-87438-8
Hardcover
Projected Pub Date: Jun 2000
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