2002. Approx. 144 pages. Softcover
ISBN 3-7643-4317-6
English
Due in November 2002
Combinatorial Problems consists of 102 carefully
selected
problems that have been used in the training
and testing of the
USA International Mathematical Olympiad (IMO)
team.
Key features:
Provides in-depth enrichment in the important
areas of
combinatorics by reorganizing and enhancing
problem-solving
tactics and strategies
Topics include: combinatorial arguments and
identities,
generating functions, graph theory, recursive
relations, sums and
products, probability, number theory, polynomials,
theory of
equations, complex numbers in geometry, algorithmic
proofs,
combinatorial and advanced geometry, functional
equations and
classical inequalities
The book is systematically organized, gradually
building
combinatorial skills and techniques and broadening
the student's
view of mathematics. Aside from its practical
use in training
teachers and students engaged in mathematical
competitions, it is
a source of enrichment that is bound to stimulate
interest in a
variety of mathematical areas that are tangential
to
combinatorics.
Table of Contents
Preface
Introduction
Abbreviations and Notation
Introductory Problems
Advanced Problems
Solutions to Introductory Problems
Solutions to Advanced Problems
Glossary
Further Reading
Progress in Nonlinear Differential Equations,
vol.52
2002. Approx. 264 pages. Hardcover
ISBN 3-7643-4309-5
English
Due in December 2002
A wide range of topics in partial differential
equations, complex
analysis, and mathematical physics are presented
to commemorate
the memory of the great French mathematician
Jean Leray.
Most articles contain complete proofs and
excellent
bibliographies. For graduate students and
mathematical physicists
as well as mathematicians in analysis and
PDEs.
The 17 invited research articles in this
volume, all written by
leading experts in their respective fields,
are dedicated to the
great French mathematician Jean Leray. A
wide range of topics
with significant new results---detailed proofs
- are presented in
the areas of partial differential equations,
complex analysis,
and mathematical physics.
Key subjects are treated from the mathematical
physics viewpoint:
nonlinear stability of an expanding universe
the compressible Euler equation
spin groups and the Leray-Maslov index
Linked to the Cauchy problem: an intermediate
case between
effective hyperbolicity and the Levi condition,
global Cauchy--Kowalewski
theorem in some Gevrey classes, the analytic
continuation of the
solution, necessary conditions for hyperbolic
systems, well
posedness in the Gevrey class, uniformly
diagonalizable systems
and reduced dimension, and monodromy of ramified
Cauchy problem.
Additional articles examine results on:
Local solvability for a system of partial
differential operators,
The hypoellipticity of second order operators
Differential forms and Hodge theory on analytic
spaces
Subelliptic operators and subriemannian geometry.
Contributors: R. Beals, Y. Choquet-Bruhat,
F. Colombini, M. De
Gosson, B. Gaveau, D. Gourdin, P. Greiner,
Y. Hamada, K.
Mizohata, T. Nishitani, T. Okaji, S. Ouchi,
Y. Ohya, S. Spagnolo,
J. Vaillant, C. Wagschal, S. Wakabayashi
The book is suitable as a reference text
for graduate students
and active researchers.
Table of Contents
Exact Solutions for Some Linear PDEs
Nonlinear Stability of an Expanding Universe
with S^1 Isometry
Group
On the Cauchy Problem for a Weakly Hyperbolic
Operator: an
Intermediate Case Between Effective Hyperbolicity
and Levi
Condition
Spin Groups and the Leray-Maslov Index
Differential Forms and Hodge Theory on Analytic
Spaces
A Global Cauchy--Kowalewski Theorem in Some
Gevrey Classes
Subelliptic Operators and Subriemannian Geometry
On the Analytic Continuation of the Solution
of the Cauchy
Problem
On the Compressible Euler Equation
Necessary Conditions for Hyperbolic Systems
Absence of Eigenvalues of Elliptic Systems
of the First Order
The Behaviors of Singular Solutions of PDEs
in Some Class in the
Complex Domain
Hyperbolic Cauchy Problem Well Posed in the
Class of Gevrey
Strong Gevrey Solvability for a System of
Linear PDEs
Systemes Uniformement Diagonalisables, Dimension
Reduite et
Systemes Presymetriques
Monodromy of Ramified Cauchy Problem
On Hypoellipticity of the Operator exp [-|x_1|^{-\sigma
}]D_1^2+x_1^4
D_2^2+1
Publication is planned for April 2003 | Hardback
| 580 pages
76 line diagrams 6 half-tones 12 tables 135
exercises | ISBN: 0-521-48022-1
Not yet published - available from April
2003 | Stock level
updated: 22 Oct 08:58BST
Geometric algebra is a powerful mathematical
language with
applications across a range of subjects in
physics and
engineering. This book is a complete guide
to the current state
of the subject with early chapters providing
a self-contained
introduction to geometric algebra. Topics
covered include new
techniques for handling rotations in arbitrary
dimensions, and
the links between rotations, bivectors and
the structure of the
Lie groups. Following chapters extend the
concept of a complex
analytic function theory to arbitrary dimensions,
with
applications in quantum theory and electromagnetism.
Later
chapters cover advanced topics such as non-Euclidean
geometry,
quantum entanglement, and gauge theories.
Applications such as
black holes and cosmic strings are also explored.
Suitable for
researchers working in the fields of relativity
and quantum
theory, it can also be used as a graduate
text for courses on the
physical applications of geometric algebra.
Contents
1. Introduction; 2. Geometric algebra in
two and three
dimensions; 3. Classical mechanics; 4. Foundations
of geometric
algebra; 5. Relativity and spacetime; 6.
Geometric calculus; 7.
Classical electrodynamics; 8. Quantum theory
and spinors; 9.
Multiparticle states and quantum entanglement;
10. Geometry; 11.
Further topics in calculus and group theory;
12. Lagrangian and
Hamiltonian techniques; 13. Symmetry and
gauge theory; 14.
Gravitation.
Publication is planned for August 2003 |
Paperback (Hardback)
| 200 pages 200 line diagrams | ISBN: 0-521-52574-8
available from August 2003
Flexagons are hinged polygons that have the
intriguing property
of displaying different pairs of faces when
they are flexed.
Workable paper models of flexagons are easy
to make and
entertaining to manipulate. Flexagons have
a surprisingly complex
mathematical structure and just how a flexagon
works is not
obvious on casual examination of a paper
model. Flexagons may be
appreciated at three different levels. Firstly
as toys or
puzzles, secondly as a recreational mathematics
topic and finally
as the subject of serious mathematical study.
This book is
written for anyone interested in puzzles
or recreational maths.
No previous knowledge of flexagons is assumed,
and the only pre-requisite
is some knowledge of elementary geometry.
An attractive feature
of the book is a collection of nets, with
assembly instructions,
for a wide range of paper models of flexagons.
These are printed
full size and laid out so they can be photocopied.
Contents
1. Making and flexing flexagons; 2. Early
history of flexagons; 3.
Geometry of flexagons; 4. Hexaflexagons;
5. Hexaflexagon
variations; 6. Square flexagons; 7. Introduction
to convex
polygon flexagons; 8. Typical convex polygon
flexagons; 9. Ring
flexagons; 10. Distorted polygon flexagons;
11. Flexahedra.
Soft cover, ISBN 3-88538-226-1, in production
Research and Exposition in Mathematics, Volume
26
Congruence relations play an important role
when investigating
universal algebras. On the one hand, the
structure of the
congruence lattice of a given algebra reveals
much information on
the underlying algebra. On the other hand,
via congruence
relations quotient algebras can be formed
which may have "nicer"
properties than the original algebras. Moreover,
in many cases
congruences are determined by some of their
classes. For instance
in the case of groups, rings and Boolean
algebras, congruences
are determined by each single one of their
classes. The aim of
the present book is to present the most important
results
concerning congruence classes, dependences
between them as well
as connections to subalgebras. Thus the reader
is informed on the
developments in this field during the last
decades.
406 p., soft cover, ISBN 3-88538-225-3, 2002
Research and Exposition in Mathematics, Volume
25
Lie Theory is known to play a crucial role
in many fields of
Mathematics and Physics. Apart from their
obvious geometric and
algebraic importance, Lie groups and Lie
algebras have turned out
to be of fundamental significance in Differential
Equations,
Quantum Mechanics, Algebraic Geometry, Topology
and the Theory of
Special Functions. The aim of this book is
to provide the reader
with a general view of recent research directions,
represented in
23 articles, in most of these topics.
Contents.
Foreword, v--viii
L. Aussenhofer: A Survey on Nuclear Groups
1--30
W. Banaszczyk: Theorems of Bochner and Levy
for Nuclear Groups 31--44
O. Blasco: Bilinear Maps and Convolutions
45--56
W. W. Comfort, S. Hernandez, D. Remus, F.
J. Trigos-Arrieta: Some
Open Questions on Topological Groups 57--76
E. Corbacho Rosas, D. Dikranjan, V. Tarieladze:
Absorption
Adjunctable Semigroups 77--104
D. Dikranjan: The Lattice of Group Topologies
and Compact
Representations 105--126
X. Dominguez, V. Tarieladze: GP-Nuclear Groups
127--162
H. Glockner, K.-H. Neeb: Minimally Almost
Periodic Abelian Groups
and Commutative W*-Algebras 163--186
P. Matysiak: Non-Reflexive Closed Connected
Subgroups of Banach
Spaces 187--196
M. G. Megrelishvili: Operator Topologies
and Reflexive
Representability 197--208
M. G. Megrelishvili, V. G. Pestov, V. V.
Uspenskij: A Note on the
Precompactness of Weakly Almost Periodic
Groups 209--216
R. Steglinski: Quotient Groups of Normed
Spaces for which the
Bochner Theorem Fails Completely 217--225
W. Wojtynski: An Introduction to String Lie
Theory 227--238
M. Wustner: A Short Survey on the Surjectivity
of Exponential Lie
Groups 239--250