Gratzer, G., University of Manitoba,
Winnipeg, Canada
1999. Approx. 136 pages. Softcover
ISBN 3-7643-4132-7
Due in September 1999
This book is for the mathematician,physicist, engineer,
scientist, or
technical typist who needs to quickly learn how to typeset
articles containing
mathematical formulas. "First Steps in LaTeX" will
provide a quick introduction
to LaTeX, including the American Mathematical Society's
enhancements,
so that your first article can be typeset in only a few hours.
Like the author's more comprehensive text "Math into
LaTeX", this concise, first-step
handbook contains well-organized material enriched by practical
examples, making it an
indispensable guide for the novice user.
Features
* simple and direct approach,
*"formula building blocks" to learn how to type math,
* a "formula gallery" to practise math formulas,
* samples to demonstrate the basic structure of LaTeX and AMS
articles,
* useful appendices containing mathematical and text symbol
tables, and a brief discussion of
TeX, LaTeX, and the Internet,
* a unique "Quick Finder" - supplementing a detailed
table of contents and index - to look
up common terms used in word processing and desktop publishing
applications.
Krantz, S.G., Washington University,
St. Louis, USA
1999. Approx. 352 pages. Hardcover
ISBN 3-7643-4011-8
Due in September 1999
"Handbook of Complex Variables" is a comprehensive
reference work for
scientists and engineers who need to know and use essential
information and
methods involving complex variables and analysis. Its focus is on
basic concepts
and informational tools for mathematical 'practice': solving
problems in applied
mathematics, science and engineering.
The information is self-contained and accessible to a broad
readership. All the
indispensable ideas are presented, as well as applications topics
and a brief survey of
available computer software. The material has been carefully
organized for quick, convenient
reference by specialists and non-specialists alike.
This handbook is an essential reference and authoritative
resource for all professionals,
practitioners, and researchers in mathematics, physical sciences
and engineering. Specialists
and non-specialists will find its practical, problem-solving
style both accessible and useful for their work.
Contents
The Complex Plane/ Complex Line Integrals/Applications of the
Cauchy Theory/ Isolated
Singularities and Laurent Series/ The Argument Principle/
Holomorphic Functions as
Geometric Mappings/ Harmonic Functions/ Infinite Series and
Products/ Applications of
Infinite Sums and Products/ Analytic Continuation/ Rational
Approximation Theory/
Special Classes of Holomorphic Functions/ Special Functions/
Applications that Depend on
Conformal Mapping/ Transform Theory/ Computer Packages for
Studying Complex
Variables/ Glossary of Terms from ComplexVariable Theory and
Analysis
Features
* Comprehensive table of notation
* Extensive glossary of key terms
* Detailed subject index
* A catalog of conformal maps
* Extensive examples of evaluating indefinite integrals using the
calculus of residues
* Generously illustrated with helpful figures and graphs
* Brief survey of available computer software
* Carefully worked examples for all key concepts
* Tables and charts to summarize information for ease of use,
i.e., conformal mappings,
equivalent definitions and equivalent concepts
* Conformal mapping applications
* Coverage of basic transform theory.
Gelfand, I.M., Rutgers Univ., New
Brunswick, USA / Saul, M., Bronxville
Schools, USA
1999. Approx. 280 pages. Softcover
ISBN 3-7643-3914-4
Due in September 1999
This book is the result of the successful collaboration between
two experienced pre-college teachers, one
of whom, I.M. Gelfand, is considered the most distinguished
living mathematician. Gelfand's impact on generations of
young people, some now mathematicians of renown, continues to be
remarkable.
All basic topics in Trigonometry are covered with an emphasis on
beautiful illustrations and
examples that treat elementary trigonometry as an outgrowth of
geometry, but stimulate the
reader to think of all of mathematics as a unified subject. The
definitions of the
trigonometric functions are geometrically motivated. Geometric
relationships are
rewritten in trigonometric form and extended. The text then makes
a transition to a study of
the algebraic and analytic properties of trigonometric functions,
in a way that provides
a solid foundation for more advanced mathematical discussions.
Like other publications by Gelfand, "Algebra",
"Functions and Graphs", and "The Method of
Coordinates", "Trigonometry" is written in an
engaging style, and approaches the material in a unique fashion
that will motivate students and teachers alike.
Contents
Preface / Geometry Sets The Stage / Definitions Of The
Trigonometric Functions /
Relations Among The Trigonometric Functions / Trigonometry And
Geometry / Generalizing
The Trigonometric Ratios / Radian Measure / Addition Formulas /
More About The Addition
Formulas / Graphs Of Trigonometric Functions / Functions And
Inverse Functions / MoreAbout Graphs
Features
Carefully chosen exercises and beautiful illustrations throughout
* Treatment of
elementary trigonometry as an outgrowth of geometry * Broad range
of material covered
extending the traditional trigonometry curriculum * Unique
progression of topics
stimulating readers to think of mathematics as a unified subject.
All the basic topics are
covered in this engaging book in which the simple material of
elementary trigonometry
leads to deeper insights about algebra, functions, and calculus,
providing a solid
foundation for more advanced mathematical study.
Birkhauser Advanced Texts
Holz, M., Steffens, K., Weitz, E.,
University of Hannover, Germany
1999. 312 pages. Hardcover
ISBN 3-7643-6124-7
This book is an introduction into modern cardinal arithmetic in
the frame of the
axioms of Zermelo-Fraenkel set theory together with the axiom of
choice.
A first part describes the classical theory developed by
Bernstein, Cantor, Hausdorff,
K?nig and Tarski between 1870 and 1930. Next, the development in
the seventies led by Galvin,
Hajnal and Silver is characterized. The third part presents the
fundamental investigations in
pcf theory which have been worked out by Shelah to answer the
questions left open in the seventies.
This text is the first self-contained introduction to cardinal
arithmetic which alsoincludes pcf theory.
It is aimed at undergraduates, and also at postgraduate students
and researchers who want to broaden
their knowledge of cardinal arithmetic. It gives a relatively
complete survey of results provable in ZFC.
Trends in Mathematics
Eklof, P., Univ. of California at Irvine,USA /
Gobel, R., Universit?t GH Essen,Germany (Ed.)
International Conference in Dublin,August 10-14, 1998
1999. Approx. 384 pages. Hardcover
ISBN 3-7643-6172-7
This volume contains the refereed proceedings of the
International Conference on Abelian Groups and
Modules held at the Dublin Institute of Technology in Ireland,
from August 10 until August 14, 1998.
The meeting brought together more than 50 researchers and
graduate students from 14
countries around the world. In a series of eight invited survey
talks, experts in the field
presented several active areas of research, including:
* Almost completely decomposable abelian groups, Butler groups
and almost free groups
* the classification problem, and invariants of special classes
of torsion-free abelian groups.
* Totally projective groups, their automorphism groups and their
group rings
* questions about unique passage between these categories.
* Radicals commuting with products.
* The Ziegler spectra of Neumann regular rings and the class
(semi-) groups of Pr?fer domains.
* The Krull-Schmidt property for valuation domains.
These main talks were accompanied by many other presentations of
current research on
abelian groups and modules. Methods from model theory, category
theory, infinite
combinatorics, representation theory, classical algebra and
geometry were applied to the study
of abelian groups and modules; conversely, results and methods
from abelian group theory
were applied to general module theory and non-commutative groups.
All this is reflected in the 30 articles in this volume, which
introduce the reader to an
active and attractive part of algebra that over the years has
gained much from its position at
the crossroads of mathematics. Lively discussions at the
conference influenced the
final work on the presented papers, which convey some sense of
the intellectual ferment
they generated and stimulate the reader to consider and actively
investigate the topics and
problems contained therein.
PNLDE 37
Progress in Non-Linear Differential Equations
Dacorogna, B., Ecole PolytechniqueFed. de
Lausanne, Switzerland /
Marcellini, P., University of Florence,Italy
1999. Approx. 288 pages. Hardcover
ISBN 3-7643-4121-1
Due in September 1999
This book is devoted to a large class of partial differential
equations and
systems which are nonlinear in the highest derivatives.
The authors present a new functional analytic method based on the
Baire category theorem
for handling the existence of solutions to these equations.
Comparison with other methods:
essentially that of viscosity solutions, and also briefly that of
convex integration is discussed.
Results obtained by this new method have important applications
to the calculus of
variations, geometry, nonlinear elasticity, problems of phase
transitions, and optimal design.
The book is divided into four parts. Part I examines first and
second order partial
differential equations while Part II considers systems. Building
on the theory presented, Part
III is devoted to applications, including the singular values
case, the case of potential wells,
and the complex eikonal equation. In Part IV the authors gather
some nonclassical Vitali type
covering theorems, as well as several fine results on
approximation of Sobolev functions
by piecewise affine or polynomial function. These results have
relevance in other
contexts, such as numerical analysis.
This monograph is intended for advanced graduate students and
researchers in nonlinear
analysis and its applications. The book is essentially
self-contained and contains many
mathematical examples derived from applications to the materials
sciences.
Contents
Preface
1. Introduction
2. First Order Equations
3. Second Order Equations
4. Comparisons with Viscosity Solutions
5. Some Preliminary Results
6. Existence Theorems for Systems
7. The Singular Values Case
8. The Case of Potential Wells
9. The Complex Eikonal Equation
10. Appendix: Piecewise Approximations
References
Index
Features
* Clear, concise, and systematic exposition
* Organization of book into three main parts with introductory
material presented in the first
two sections and the last third devoted to applications, followed
by an appendix
* Excellent choice of topics covered: different notions of
convexity involved in the vectorial
calculus of variations, the Vitali type covering theorems or
approximation of Sobolev
functions by piecewise affine functions, the singular values
case, the case of potential wells,
and the complex eikonal equation.
ISNM 133
International Series of Numerical Mathematics
Hoffmann, K.-H., Techn.University ofMunich,
Germany /
Leugering, G., University of Bayreuth, Germany /
Tr?ltzsch, F., Techn.University of Chemnitz, Germany (Ed.)
International Conference in Chemnitz,
Germany, April 20?25, 1998
1999. 336 pages. Hardcover
ISBN 3-7643-6151-4
This volume contains the contributions of participants of the
conference
"Optimal Control of Partial Differential Equations"
held at the Wasserschloss
Klaffenbach near Chemnitz (Saxony, Germany) from April 20 to 25,
1998.
The conference was organized by the editors of this volume. Along
with the dramatic increase
in computer power, the application of PDE-based control theory
and the corresponding numerical algorithms to
industrial problems has become more and more important in recent
years.
This development is reflected by the fact that researchers focus
their interest on challenging
problems such as the study of controlled fluid-structure
interactions, flexible structures,
noise reduction, smart materials, the optimal design of shapes
and material properties and
specific industrial processes.
All of these applications involve the analytical and numerical
treatment of nonlinear partial
differential equations with nonhomogeneous boundary or
transmission conditions along with
some cost criteria to be minimized. The mathematical framework
contains modelling and
analysis of such systems as well as the numerical analysis and
implemention of
algorithms in order to solve concrete problems. This volume
offers a wide spectrum of aspects
of the discipline and is of interest to mathematicians as well as
to scientists working in the fields of applications.
LM
Lectures in Mathematics, ETH Zurich
Le Gall, J.-F., Ecole Normale
Superieure, Parius, France
Random Snakes and Partial
Differential Equations
1999. 176 pages. Hardcover
ISBN 3-7643-6126-3
The text includes a presentation of the measure-valued branching
processes
also called superprocesses and of their basic properties. In the
important
quadratic branching case, the path-valued process known as the
Brownian snake is used to give a concrete and powerful
representation of superprocesses.
This representation is applied to several connections with a
class of semilinear partial
differential equations. On the one hand, these connections give
insight into properties of
superprocesses. On the other hand, the probabilistic point of
view sometimes leads to
new analytic results, concerning for instance the trace
classification of positive solutions in a smooth domain.
An important tool is the analysis of random trees coded by linear
Brownian motion. This includes the so-called
continuum random tree and leads to the fractal random measure
known as ISE, which has appeared recently in several
limit theorems for models of statistical mechanics.
This book is intended for postgraduate students and researchers
in probability theory. It will also
be of interest to mathematical physicists or specialists of PDE
who want to learn about
probabilistic methods. No prerequisites are assumed except for
some familiarity with
Brownian motion and the basic facts of the theory of stochastic
processes. Although the
text includes no new results, simplified versions of existing
proofs are provided in several instances.
OT 109
Operator Theory: Advances and Applications
Rossmann, J., Tak?c, P., Wildenhain, G.,
University of Rostock, Germany (Ed.)
Volume 1
On Maz'ya's Work in Functional
Analysis, Partial Differential Equations and Applications
1999. Approx. 384 pages. Hardcover
ISBN 3-7643-6201-4 Due in September 1999
Volume 2
Rostock Conference on Functional Analysis, Partial Differential
Equations and Applications
1999. Approx. 368 pages. Hardcover
ISBN 3-7643-6202-2 Due in September 1999
2 Vols. Set
1999. Approx. 752 pages. Hardcover
ISBN 3-7643-6203-0 Due in September 1999
This is the first volume of a collection of articles dedicated to
V.G Maz'ya on the occasion of his 60th birthday. It
contains surveys on his work in different fields of mathematics
or on areas to which he made essential
contributions. Other articles of this book have their origin in
the common work with Maz'ya.
V.G Maz'ya is author or co-author of more than 300 scientific
works on various fields of
functional analysis, function theory, numerical analysis, partial
differential equations and their
application. The reviews in this book show his enormous
productivity and the large variety of his work.
The scond volume contains most of the invited lectures of the
Conference on Functional
Analysis, Partial Differential Equations and Applications held in
Rostock in September 1998
in honor of V.G Maz'ya. Here different problems of functional
analysis, potential theory, linear
and nonlinear partial differential equations, theory of function
spaces and numerical
analysis are treated. The authors, who are outstanding experts in
these fields, present
surveys as well as new results.
Kallianpur, G., University of North Carolina,
Chapel Hill, USA /
Karandikar, R.L., Indian Statistical Institute, New Dehli, India
1999. Approx. 280 pages. Hardcover
ISBN 3-7643-4108-4
Due in September 1999
Since the appearance of seminal works by R. Merton, and F. Black
and M.
Scholes, stochastic processes have assumed an increasingly
important role
in the development of the mathematical theory of finance. This
work examines,
in some detail, that part of stochastic finance pertaining to
option pricing
theory. Thus the exposition is confined to areas of stochastic
finance that are
relevant to the theory, omitting such topics as futures and
term-structure.
This self-contained work begins with five introductory chapters
on stochastic analysis, making it accessible to
readers with little or no prior knowledge of stochastic processes
or stochastic analysis. These chapters cover
the essentials of Ito's theory of stochastic integration,
integration with respect to semimartingales, Girsanov's Theorem,
and a brief introduction to stochastic differentialequations.
Subsequent chapters treat more specialized topics,
including option pricing in discrete time, continuous time
trading, arbitrage, complete markets, European options
(Black and Scholes Theory), American options, Russian options,
discrete approximations, and asset pricing with
stochastic volatility. In several chapters, new results are
presented. A unique feature of the book is its emphasis on
arbitrage, in particular, the relationship between arbitrage and
equivalent martingale measures (EMM), and the derivation
of necessary and sufficient conditions for no arbitrage (NA).
"Introduction to Option Pricing Theory" is intended for
students and researchers in
statistics, applied mathematics, business, or economics, who have
a background in measure
theory and have completed probability theory at the intermediate
level. The work lends itself to
self-study, as well as to a one-semester course at the graduate
level.
Contents
Preface * 1. Stochastic Integration * 2. Ito's Formula and its
Applications * 3.
Representation of Square Integrable Martingales * 4. Stochastic
Differential
Equations * 5. Girsanov's Theorem and its Extensions * 6. Option
Pricing in Discrete Time
* 7. Introduction to Continuous Time Trading * 8. Arbitrage and
Equivalent Martingale Measures
* 9. Complete Markets * 10. The Black and Scholes Theory * 11.
Discrete Approximations
* 12. American Options * 13. Asset Pricing with Stochastic
Volatility 14. The Russian Options
* Bibliography * Index
Features
* Accessible to readers with little or no prior knowledge of
stochastic processes or stochastic analysis,
* Five introductory chapters on stochastic analysis, followed by
chapters covering more
specialized topics and presenting new results (chapter on
stochastic volatility),
* Wide range of topics treated, such as option pricing in
discrete time, continuous time
trading, arbitrage, complete markets, European options (Black and
Scholes Theory), American
options, discrete approximations, and asset pricing with
stochastic volatility,
* Unique emphasis on arbitrage, in particular, the relationship
between arbitrage and
equivalent martingale measures (EMM), and the derivation of
necessary and sufficientconditions for no arbitrage (NA),
* a separate chapter on Russian options for the first time in
book literature, in particular, the
complete proof of the theorem pertaining to Russian call options
is presented, from theperspective of a
free boundary problem.
Falb, P., MIT, Cambridge, USA
1999. Approx. 368 pages. Hardcover
ISBN 3-7643-4113-0
Due in September 1999
An introduction to the ideas of algebraic geometry in the
motivated context of system theory ? this describes this two
volume work which has been specifically written to serve the
needs of researchers and students of systems,
control, and applied mathematics.
Without sacrificing mathematical rigor, the author makes the
basic ideas of algebraic geometry accessible to engineers and
applied
scientists. The emphasis is on constructive methods and clarity
rather than on abstraction. While familiarity with Part I is
helpful,
it is not essential, since a considerable amount of relevant
material is included here. Part I "Scalar Linear Systems and
Affine Algebraic Geometry" contains a clear presentation,
with an applied flavor, of the core ideas in the
algebro-geometric treatment of scalar linear system theory. Part
II extends the theory to multivariable systems. After delineating
limitations of the scalar theory through carefully chosen
examples, the author introduces seven representations of a
multivariable linear s ystem and establishes the major results of
the underlying theory. Of key importance is a clear, detailed
analysis of the structure of the space of linear systems
including the full set of equations defining the space. Key
topics also
covered are the Geometric Quotient Theorem and a highly geometric
analysis of both state and output feedback.
Prerequisites are the basics of linear algebra, some simple
topological notions, the elementary properties of groups, rings
and
fields, and a basic course in linear systems. Exercises, which
are an integral part of the exposition throughout, combined with
an index
and extensive bibliography of related literature make this a
valuable classroom tool or good self-study resource.
Grundstudium Mathematik
Foata, D., Fuchs, A., University Louis Pasteur,
Strasbourg
?bersetzt aus dem Franz?sischen von
Volker Strehl
1999. 400 Seiten. Gebunden
ISBN 3-7643-6170-0
1999. 400 Seiten. Broschur
ISBN 3-7643-6169-7
Due in September 1999
Wahrscheinlichkeitstheorie ist ein wesentlicher Bestandteil jedes
Mathematik- und Physikstudiums und
spielt eine zentrale Rolle in der Wirtschaftswissenschaft und den
Naturwissenschaften.
Die vorliegende Einf?hrung richtet sich an Studenten, die bereits
einen Grundkurs in
Analysis besucht haben, und zeichnet sich durch einen
hervorragenden didaktischen
Aufbau aus. Sowohl die diskrete wie auch die masstheoretische
Wahrscheinlichkeitstheorie
werden in allen wesentlichen Elementen behandelt und alle
wichtigen S?tze werden
bewiesen. Viele ?bungen helfen den Stoff einzuarbeiten und zu
vertiefen. Alle L?sungen,
oftmals sehr detailliert, sind im Buch enthalten
Trends in Mathematics
Gyr, A., Kinzelbach, W., ETH Zurich, Switzerland
/
Tsinober, A., Tel Aviv University, Israel (Ed.)
1999. 496 pages. Hardcover
ISBN 3-7643-6150-6
The intention of the book is to highlight the problematic aspects
of turbulence.
The contributions treat a variety of mathematical, physical and
engineering
subjects related to turbulence.
The topics include mathematical issues, control and related
problems, observational aspects,
two- and quasi-two-dimensional flows, basic aspects of turbulence
modeling, statistical issues and passive scalars.
The main questions addressed are the controllability of turbulent
flows, possible qualitative differences between pure
two-dimensional and real quasi-two-dimensional turbulent flows,
common features of two-dimensional and
three-dimensional turbulence, universality (or not) of
small-scale turbulence and its relation to large scales, the
question
of how realistic the prospects of reduced description of
turbulent flows are, the necessity of dealing
more with the physics of turbulence in general, and in turbulence
modeling and (beyond) scaling properties, in particular.
Applied and Numerical Harmonic Analysis
Herman, G.T., University of Pennsylvania,
Philadelphia, USA /
Kuba, A., Jozsef Attial University, Szeged, Hungary (Ed.)
Foundations, Algorithms, and Applications
1999. Approx. 488 pages. Hardcover
ISBN 3-7643-4101-7
Due in September 1999
The visualization, construction and reconstruction of
multidimensional images are of intense interest in
science and engineering today, and discrete tomography-which
deals with the special case in which the object to
be reconstructed has a small number of possible values-offers
some significant new analytical and computational tools.
"Discrete Tomography" provides a critical survey of new
methods, algorithms and select applications that are the
foundations of multidimensional image construction and
reconstruction. The survey chapters, written
by leading international authorities, are self-contained and
present the latest researchand results in the field.
The book covers three main areas: important theoretical results,
available algorithms to utilize for
reconstructing, and key applications where new results are
indicative of greater utility. Following a thorough historical
overview of the field, the book provides a journey through the
various mathematical and computational
problems of discrete tomography. This is followed by a section on
numerous algorithmic techniques that can be used
to achieve real reconstructions from image projections.
The book is an essential resource for the latest developments and
tools in discrete tomography.
Professionals, researchers and practitioners in mathematics,
computer imaging, scientific
visualization, computer engineering, and multidimensional image
processing will find the
book an authoritative guide and reference to current research,
methods and applications.
Features
* Historical overview and summary chapter
* Uniqueness and complexity in discrete tomography
* Probabilistic modeling of discrete images
* Binary tomography using Gibb priors
* Discrete tomography on the 3-D Torus and crystals
* Binary steering
* 3-D tomographic reconstruction from sparse radiographic data
* Symbolic projections