by Miguel de Guzman (Universidad Complutense de Madrid)
Games and beauty are found in the origin of a major part of
mathematics. If mathematicians throughout history have had such a
good time playing and contemplating theirgames and their science,
why not try to learn mathematics and pass it on through games and
beauty?
That is the fundamental idea which underlies the stories and
games presented in this book. You will be surprised and enticed
by the interesting concepts and the novelty of thebook. The
author has intended that you apply to it the same playful spirit
with which he has written it. In fact, if you open the book, you
will soon find that certain mathematicaldevelopments that may
seem at first sight rather imposing can be presented in a way
that anybody can understand and contemplate with pleasure. They
may even act like abridge in finding the same pleasure in other
mathematical endeavors that may look more serious and complicated
but, if we look carefully, display basically the same
playfulspirit.
Contents:
The Mathematics of a Sandwich
Nim
A Capricious Walk Through Königsberg
A Group for Solitary Players
The Mathematician as a Naturalist
Four Colors Suffice
The Jumping Frog
A Cutoff in the Chessboard
The Secret of the Oval Hall
Readership: General.
130pp (approx.)
Pub. date: Autumn 1999
ISBN 981-02-4032-5
ISBN 981-02-4033-3(pbk)
by Y Fan, Q Y Xiong & Y L Zheng (Wuhan University, P R
China)
This volume is based on the lectures given by the authors at
Wuhan University and Hubei University in courses on abstract
algebra.
It presents the fundamental concepts and basic properties of
groups, rings, modules and fields, including the interplay
between them
and other mathematical branches and applied aspects.
Contents:
Preliminaries: Sets
Logic
Relations
Maps
Zorn's Lemma
Groups: Transformations and Permutations
Groups
Subgroups
Homomorphisms, Isomorphisms
Cosets
Normal Subgroups, Quotient Groups
Homomorphism Theorems
Cyclic Groups, Orders of Elements
Direct Products
Rings: Fundamentals
Zero Divisors, Inverse Elements
Ideals, Residue Rings
Homomorphism Theorems
Prime Ideals, Maximal Ideals
Direct Sums
Fraction Fields of Integral Domains
Polynomial Rings
Factorial Rings
Polynomial Rings over Factorial Rings
Modules: Modules and Endomorphism Rings of Additive Groups
Submodules, Quotient Modules, and Homomorphisms
Direct Products, Direct Sums
Exact Sequences of Homomorphisms
Free Modules, Matrices over Rings
Vector Spaces and Matrices over Division Rings
Modules and Matrices over Commutative Rings
Algebras over Commutative Rings
Tensor Products
Projective Modules and Injective Modules
Fields: Subfields and Extensions
Single Extensions
Algebraic Extensions
Splitting Field of Polynomials, Normal Extensions
Applications
Separability, Multiple Roots
Finite Fields
Coding
p-adic Numbers
Quaternions
Readership: First- and second-year students in algebra.
280pp (approx.)
Pub. date: Spring 2000
ISBN 981-02-4061-9
Proceedings of the Conference
Wuhan, China 5 - 9 April 1999
edited by Chen Hua (Wuhan University, China) & L Rodino
(UniversitE di Torino, Italy)
This volume reports the recent progress in linear and nonlinear
partial differential equations, microlocal analysis,
singular partial differential operators, spectral analysis
andhyperfunction theory.
Contents:
On the Asymptotics of the Counting Function for Irregular Drums
(Chen Hua)
Formation-Construction of Shock in Compressive Simple Wave of N x
N Hyperbolic System (S-X Chen)
Blow-up Curve of Solutions of Semilinear Hyperbolic Equations in
One Space Dimension (P J M Godin)
Convergence of Binomial Tree Method for American Options (L
Jiang)
Boundary Value Problems for Isometric Embedding in R3 of Surfaces
(J-X Hong)
Convolutions of Hyperfunctions of One Variable and Laplace
Hyperfunctions (H Komatsu)
Fourier Transforms in Spaces of Hyperfunctions and Hartog's Type
Phenomena (O Liess)
Borel Summability of Divergent Solutions of the Cauchy Problem to
Non-Kowalevskian Equation (M Miyake)
Hadamard's Fundamental Solution and Conical Refraction (M-Y Qi)
Nonlinear Microlocal Analysis (L Rodino)
Asymptotics of Edge and Corner Distributions (B-W Schulze)
Asymptotic Behaviour for Minimizers of a GinzburgLandau-Type
Functional (Z-Q Wu)
Traveling Wave Front Solutions for ReactionDiffusion Systems
(Q-X Ye)
Well Posedness of the Cauchy Problem for Nonlinear Weakly
Hyperbolic Equations (L Zanghirati)
and other papers
Readership: Graduate students and researchers in the field of
partial differential equations.
330pp (approx.)
Pub. date: Spring 2000
ISBN 981-02-4059-7
by M I Rabinovich (University of California, San Diego),
A B Ezersky (Russian Academy of Sciences)
& P D Weidman (University of Colorado)
Spirals, vortices, crystalline lattices, and other attractive
patterns are prevalent in Nature. How do such beautiful patterns
appear from the initial chaos? What universal dynamical rules are
responsible for their formation? What is the dynamical origin
of spatial disorder in nonequilibrium media? Based on the many
visual experiments in physics,hydrodynamics, chemistry, and
biology,
this invaluable book answers those and related intriguing
questions. The mathematical models presented for the dynamical
theory of
pattern formation are nonlinear partial differential equations.
The corresponding theory is not so accessible to a wide audience.
Consequently, the authors have made every attempt to synthesize
long and complex mathematical calculations to exhibit the
underlying physics. The book will be useful for final year
undergraduates, but is primarily aimed at graduate students,
postdoctoral
fellows, and others interested in the puzzling phenomena of
pattern formation.
Contents:
Prelude to a Dynamical Description of Pattern Formation
Examples of Instability
Model Equations
GinzburgLandau Equation
'Crystal' Formation
Quasicrystals
Breaking of Order
Localized Patterns
Spirals
Vortices in Soap Films
Patterns in Colonies of Microorganisms
Spatial Disorder
Regular Patterns in Nonregular Media
Living Matter and Dynamics Forms
Short Guide to Nonlinear Dynamics
Key Experiments in Pattern Formation
Readership: Graduate students of mathematical physics and
nonlinear science.
350pp (approx.)
Pub. date: Autumn 1999
ISBN 981-02-4055-4
ISBN 981-02-4056-2(pbk)
Proceedings of the Conference on Low-Dimensional Topology
University Park, Pennsylvania, USA May 1996
edited by A Banyaga, H Movahedi-Lankarani & R Wells (The
Pennsylvania State University)
Recent success with the four-dimensional PoincarEconjecture has
revived interest in low-dimensional topology,
especially the three-dimensional PoincarEconjecture and other
aspects of the problems of classifying three-dimensional
manifolds. These problems have a driving force, and have
generated a great body of research, as well as insight.
The main topics treated in this book include a paper by V Poenaru
on the PoincarEconjecture and its ramifications,
giving an insight into the herculean work of the author on the
subject. Steve Armentrout's paper on "Bing's dogbone
space"
belongs to the topics in three-dimensional topology motivated by
the PoincarEconjecture. S Singh gives a nice synthesis of
Armentrout's work. Also included in the volume are shorter
original papers, dealing with somewhat different aspects of
geometry,
and dedicated to Armentrout by his colleagues EAugustin Banyaga
(and Jean-Pierre Ezin), David Hurtubise, Hossein
Movahedi-Lankarani and Robert Wells.
Contents:
Mathematics of Steve Armentrout: A Review (S Singh)
Bing's Dogbone Space Is Not Strongly Locally Simply Connected (S
Armentrout)
A Program for the PoincarEConjecture and Some of Its
Ramifications (V Poénaru)
On the Foundation of Geometry, Analysis, and the Differentiable
Structure for Manifolds (D Sullivan)
A Conformal Invariant Characterizing the Sphere (A Banyaga &
J-P Ezin)
Spaces of Holomorphic Maps from CP1 to Complex Grassmann
Manifolds (D E Hurtubise)
Sets with Lie Isometry Groups (H Movahedi-Lankarani & R
Wells)
Readership: Researchers in mathematics and physics.
130pp (approx.)
Pub. date: Autumn 1999
ISBN 981-02-4050-3
by A O Ivanov & A A Tuzhilin (Moscow State University)
This book deals with the new class of one-dimensional variational
problems Ethe problems with branching solutions.
Instead of extreme curves (mappings of a segment to a manifold)
we investigate extreme networks, which are mappings
of graphs (one-dimensional cell complexes) to a manifold. Various
applications of the approach are presented, such as
several generalizations of the famous Steiner problem of finding
the shortest network spanning given points of the plane.
Contents:
General Theory: General Notion of Networks
One-Dimensional Variational Problems and Problems of Optimal
Control on the Spaces of Networks
Applications: Geometry of Linear Networks in Euclidean Spaces
Local Minimal Networks: The State of the Art
Local Minimal Networks in Manhattan Metric
Readership: Researchers in differential geometry and topology.
400pp (approx.)
Pub. date: Spring 2000
ISBN 981-02-4060-0
Proceedings of the International Workshop
Zacatecas, Mexico 23 - 26 June 1999
edited by Andrew E Chubykalo, Valeri V Dvoeglazov (Universidad
Autónoma de Zacatecas, Mexico), David J Ernst (Vanderbilt
University, USA), Vladimir G
Kadyshevsky (Joint Institute for Nuclear Research, Russia) &
Y S Kim (University of Maryland, USA)
The topics in this volume range from mathematical aspects of the
theory of the PoincarEgroup, Clifford algebras and the CPT
theorem, through new theoretical physical
constructions and concepts (such as the physical significance of
the 4-potential, the interplay between quantum mechanics and
gravity, Majorana-like models, the photon as a
composite particle, action-at-a-distance and superluminal
phenomena), to experiments in neutrino physics. The book will be
of interest to graduate students and researchers
working in fundamental physics and phenomenology, and also to
experimentalists.
Readership: Researchers and graduate students in physics, as well
as engineers.
350pp (approx.)
Pub. date: Summer 2000
ISBN 981-02-4062-7
by V S Pugachev & I N Sinitsyn (Russian Academy of
Sciences, Moscow)
This book is intended for those having only a moderate background
in mathematics, who need to increase their
mathematical knowledge for development in their areas of work and
to read the related mathematical literature. The
material covered, which includes practically all the information
on functional analysis that may be necessary for those
working in various areas of applications of mathematics, as well
as the simplicity of presentation, differentiates this book
from others. About 300 examples and more than 500 problems are
provided to help readers understand and master the
theories presented. The list of references enables readers to
explore those topics in which they are interested, and
gather further information about applications used as examples in
the book.
Applications: Probability Theory and Statistics, Signal and Image
Processing, Systems Analysis and Design.
Contents:
Sets, Spaces and Functions
Measure Theory
Integrals
Topological Spaces
Spaces of Operators and Functionals
Linear Operators
Linear Operators in Hilbert Spaces
Spectral Theory of Linear Operators
Nonlinear Problems of Functional Analysis
Elements of Approximate Methods in Abstract Spaces
Readership: Undergraduates and researchers in applied
mathematics, and engineers.
752pp
Pub. date: Jul 1999
ISBN 981-02-3722-7
ISBN 981-02-3723-5(pbk)
Series on Knots and Everything - Vol. 20
Computer Programming for Knot Tabulation
by Charilaos Aneziris (Brookhaven National Laboratory)
One of the most significant unsolved problems in mathematics is
the complete classification of knots. The main purpose of this
book is to
introduce the reader to the use of computer programming to obtain
the table of knots. The author presents this problem as clearly
and
methodically as possible, starting from the very basics.
Mathematical ideas and concepts are extensively discussed, and no
advanced
background is required.
Contents:
A Knot Theory Primer: From Geometry to Topology to Knot Theory
Showing Knot Equivalence
Showing Knot Inequivalence
The Alexander-Conway Polynomial
The Nonlinear "Colorizations"
The HOMFLYPT Polynomial
The Kauffman Polynomial
The Tabulation of Knots: Defining the Problem
Ordering Notations
Calculating the HOMFLYPT Polynomials
More About Chirality and Orientation Reversal
From Knots to Links
The Table of Knots
Readership: Students and researchers in computer programming and
topology.
200pp (approx.)
Pub. date: Autumn 1999
ISBN 981-02-3878-9