Colloquium Publications, Series

Benyamini, Y. / Lindenstrauss, J.:

Geometric Nonlinear Functional Analysis

The book presents a systematic and unified study of geometric nonlinear functional analysis.

This area has its classical roots in the beginning of the twentieth century
and is now a very active research area, having close connections to geometric measure theory,
probability, classical analysis, combinatorics, and Banach space theory.

The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces
(e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.).

This study leads naturally also to the classification of Banach space
and of their important subsets (mainly spheres) in the uniform and Lipschitz categories.

Nov. 1999 313 pp.

0-8218-0835-4

A. M. S.


Graduate Studies in Mathematics, Vol. 20:

Gompf, R. / Stipsicz, A.:

4-Manifolds and Kirby Calculus

The past two decades have brought explosive growth in 4-manifold theory.

Many books are currently appearing that approach the topic from viewpoints such as
gauge theory or algebraic geometry.

This volume, however, offers an exposition from a topological point of view.

It bridges the gap to other disciplines and presents classical
but important topological techniques that have not previously appeared in the literature.

Part I of the text presents the basics of the theory at the second-year graduate level
a offers an overview of current research.

Part II is devoted to an exposition of Kirby calculus, or handlebody theory on 4-manifolds.
It is both elementary and comprehensive.

Part III offers in depth a broad range of topics from current 4-manifold research.

Oct 1999 576 pp.
0-8218-0994-6

A. M. S.


Higgins, R. / Stens, L.:

Sampling Series in Fourier Analysis and Signal Theory, Vol. 2

Volume 1 in this series laid the mathematical foundations of sampling theory;

Volume 2 surveys the many applications of the theory both within mathematics and in other areas of science.

Topics range over a wide variety of areas, and each application is given a modern treatment.

Contents
* 1 Applications of sampling theory to combintorial analysis,
Stirling numbers, special functions and the Riemann zeta function.
* 2 Sampling theory and the arithmetic Fourier transform
* 3 Derivative sampling - a pardigm example of multi-channel methods
* 4 Computational methods in linear prediction for band-limited signals based on past samples
* 5 Interpolation and sampling theories, and linear ordinary boundary value problems
* 6 Sampling by generalized kernels
* 7 Sampling theory and wavelets
* 8 Approximation by translates of a radial function
* 9 Almost sure sampling restoration of band-limited stochastic signals
* 10 Abstract harmonic analysis & the sampling theorem

July 1999 304 pp.

0-19-853496-5 .

Oxford University Press


Springer VideoMath, Series

Aposto1, T. /Bourguignon, I.-P. / Emmer, E. /Hege, H.-C. / Polthier, K. (eds.):

Springer VideoMath is a series ofvideos covering topics from mathematics and its related fields such
as computational science, scientific visualisation and mathematical physics. The level ranges from
research to teaching, and some ofthe videos address not only the experts but all who have an
interest in science.

Bourguignon, J.-P. / F.Tisseyre, F. /Weingarten, C.:

The New Shepherd's Lamp

Astronomy and celestial mechanics alwoys initated great
breakthroughs in the development of science and mathematics.

The authors of the film describe these developments starting with Ptolemy
and ending with contemporary sotellite-streering techniques.

The explanations come via conversations, illustrations,
famous scentific publication and animation.
The film is of interest to everyone with an interest
in mathematics and science, from school students to researshers.

July 1999 30 minutes

3-540-92638-2

Springer


Springer VideoMath, Series

Costa, A. / Gomez, B.:

Arabesques and Geometry

The authors of this film explain the topic of
symmetry in mathematics with examples from Islamic art.

The mathemtiical background - plane crystallographic groups -
is spectacularly illustrated by examples at the Alhambra in Granada, Spain.

This film will be enjoyed by everyone interested in
mathematics, from school students to researchers.

July 1999 20 minutes

3-540-92639-9

Springer


Springer VideoMath, Series
Csicsery, G. P.:

N is a Number

A man with no home and nojob, Poul Erdos was the most prolific mathematician who ever lived.
A wondering genius, Erdos, who died in 1996 at the age of 83,
spent his life engaged in a cosmic struggle to uncovr truths hidden by a stubborn adversary-God.

In N is a Number he describes this metaphysical duel with
the same wry humor he applied to politics, relationship and death.

The documentary follows him through four countries to discover what makes mathematicians tick.
N is a Number presents Erdos’ mathematical quest, its personal and philosophical dimensions,
and the tragic historical events that molded his life.
Two animated sequences illustrate kinds ff problems Erdos pursued throughout his life.

July 1999 60 minutes

3-540-92641-0 6,790.

Springer


Universitext, Series

Hsieh, P.-F.:

Basic Theory of Ordinary Differential Equations

The authors' aim is to provide the reader with the very basic knowledge necessary
to begin research on differential equations with professional ability.

The Selection of topics should provide the reader with methods and results
which are applicable in a variety of different fields.

The book is divided into four parts.

The first covers fundamental existence, uniqueness,
smoothness with respect to data, and nonuniqueness.

The second part describes the basic results concerning linear differential equations,
the third deals with nonlinear equations.

In the last Part the authors write about the basic results concerning power series solutions.

Aug. 1999 454 pp.

3-540-6594l-2
Springer


Undergraduate Texts in Mathematics,

Elaydi, S. A.:

An Introduction to Difference Equations, 2nd ed.

Integrating both classical and modern treatments of difference
equations, this book contains the most updated and comprehensive
material on stability, Z-transform, discrete control theory,
asymptotic theory, continued fractions and orthogonal polynomials.

Sep. 1999 470 pp.
0-387-98830-0
Springer


Undergraduate Texts in Mathematics,

Protter, M. / Weinberger, H.:

Maximum Principles in Differential Equations

Originally published by Prentice-Hall 1967

Maxilmum Principles are central fo the theory and applications of
second-order partial differen tiai equations and systems.

This self-contained text establishes the fundamental prlnciples and provides a variety of applitations.

July 1999 2nd rev. and exp. ed. 501 pp.June 1999 261 pp.

3-540-96068-6
Springer


Springer Texts in Statistics,

Bilodeau, M. / Brenner, D.:

Theory of Multivariate Statistics

Contents:
Linear Algebra: Random Vectors:
Gamma, Dirichlet and F Distributions.- Invariance.- Multivariate Normal.-
Multivariate Sampling.- Wishart Distributions.- Tests on Mean and Variance.-
Multivariate Regression.- Principal Components.- Canonical Correlations.-
Asymptotic Expansions.- Robustness.- Bootstrap Confidence Regions and Tests.

Intended as a textbook for students taking a first graduate course in the subject,
as well as for the general reference of interested research workers, this text discusses,
in a readable form, developments from recently published work on
certain brood topics not otherwise easily accessible,
such as robust inference and the use of the bootstrap in a multivariate setting.

A minimum background expected of the reader would include at least two courses in mathematical statistics,
and certainly some exposure to the calculus of several variables together
with the descriptive geometry of linear algebra.

Sep. 1999 315 pp.

0-387-98739-8

Springer


Springer Texts in Statistics,

Durrett, D.:

Essentials of Stochastic Processes


Designed for a Master's level course in stochastic processes,
this text features the introduction and use of martingales,
allowing much more to be done with Brownian motion,
e.g., option pricing, and queueing theory are integrated into
the Continuous Time Markov Chain and Renewal Theory chapters.

Sep. 1999 305 pp.

0-387-98836-X

Springer


Algorithms and Combinatorics, Vol. 19:

Kerber, A.:

Applied Finite Group Actions, 2nd., rev. and exp. ed. 1999.



Originally published by BI Wissenschafts-Verlag 1991

The topic of this book is finite group actions and their use in order to
approach finite unlabeled structures by defining them as orbits offinite groups of sets.

Well-known examples are graph, linear codes, chemical isomers, spin configurations,
isomorphism classes of combinatorial designs etc.

Aug.1999 454 pp.

3-540-6594l-2

Springer


Algorithms and Combinatorics, Vol. 12:

Padberg, M.:

Linear Optimization and Extensions, 2nd ed.

Revised by D. Alevras

This book offers a comprehensive treatment ofinear programming as well as
of the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces.

An introduction surveying fiffty years oflinear optimization is given.
The book can serve both as a graduate textbook for linearprogramming and as
a text for advanced topics classes or semilnars. Exercises as well as several case studies are included.
The book is based on the author’s long term experience in teaching and research.

July 1999 2nd rev. and exp. ed. 501 pp.

3-540165833-5

Springer