Martin, G.E., State University of New York at Albany, NY, USA

Counting: The Art of Enumerative Combinatorics

2001. Approx. 265 pp. 56 figs. Hardcover
0-387-95225-X

Counting is hard. "Counting" is short for "Enumerative Combinatorics," which certainly doesn't
sound easy. This book provides an introduction to discrete mathematics that addresses questions
that begin, How many ways are there to... . At the end of the book the reader should be able to
answer such nontrivial counting questions as, How many ways are there to stack n poker chips,
each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1
green chip? There are no prerequisites for this course beyond mathematical maturity. The book can
be used for a semester course at the sophomore level as introduction to discrete mathematics for
mathematics, computer science, and statistics students. The first five chapters can also serve as a
basis for a graduate course for in-serivce teachers.

Contents: Elementary Enumeration.- The Principle of Inclusion and Exclusion.- Generating
Functions.- Groups.- Actions.- Recurrence Relations.- Mathematical Induction.- Graphs.- The Back
of the Book.

Series: Undergraduate Texts in Mathematics.

Yang, Y., Polytechnic University, Brooklyn, NY, USA

Solitons in Field Theory and Nonlinear Analysis

2001. Approx. 575 pp. Hardcover
0-387-95242-X

This book is on soliton solutions of elliptical partial differential equations arising in quantum field
theory, such as vortices, instantons, monopoles, dyons, and cosmic strings. The book presents
in-depth description of the problems of current interest, forging a link between mathematical
analysis and physics and seeking to stimulate further research in the area. Physically, it touches
the major branches of field theory: classical mechanics, special relativity, Maxwell equations,
superconductivity, Yang-Mills gauge theory, general relativity, and cosmology. Mathematically, it
involves Riemannian geometry, Lie groups and Lie algebras, algebraic topology (characteristic
classes and homotropy) and emphasizes modern nonlinear functional analysis. There are many
interesting and challenging problems in the area of classical field theory, and while this area has
long been of interest to algebraists, geometers, and topologists, it has gradually begun to attract
the attention of more analysts. This book written for researchers and graduate students will appeal
to high-energy and condensed-matter physicists, mathematicians, and mathematical scientists.

Contents: Preface.- Primer of Field Theory.- Sigma Models.- Multiple Instantons and Characteristic
Classes.- Generalized Abelian Higgs Equations.- Chern-Simons Systems: Abelian Case.-
Chern-Simons Systems: Non-Abelian Case.- Electroweak Vortices.- Dyons.- Ordinary Differential
Equations.- Strings in Cosmology.- Vortices and Antivortices.- Born-Infeld Solutions.- References.-
Bibliography.- Index.

Series: Springer Monographs in Mathematics.

Godsil, C., University of Waterloo, ON, Canada
Royle, G.F., University of Western Australia, Nedlands, WA, Australia

Algebraic Graph Theory

2001. Approx. 465 pp. 120 figs. Hardcover
0-387-95241-1
2001. Approx. 465 pp. 120 figs. Softcover
0-387-95220-9

Algebraic graph theory is a combination of two strands. The first is the study of algebraic objects
associated with graphs. The second is the use of tools from algebra to derive properties of graphs.
The authors' goal has been to present and illustrate the main tools and ideas of algebraic graph
theory, with an emphasis on current rather than classical topics. While placing a strong emphasis
on concrete examples they tried to keep the treatment self-contained.

Contents: Graphs.- Groups.- Transitive Graphs.- Arc-Transitive Graphs.- Generalized Polygons and
Moore Graphs.- Homomorphisms.- Kneser Graphs.- Matrix Theory.- Interlacing.- Strongly Regular
Graphs.- Two-Graphs.- Line Graphs and Eigenvalues.- The Laplacian of a Graph.- Cuts and Flows.-
The Rank Polynomial.- Knots.- Knots and Eulerian Cycles.- Glossary of Symbols.- Index.

Series: Graduate Texts in Mathematics.VOL. 207

Ammann, M., University of St. Gallen, Switzerland

Credit Risk Valuation
Methods, Models, and Applications

2nd ed. 2001. Approx. 320 pp. Hardcover
3-540-67805-0

This book offers an advanced introduction to the models of credit risk valuation. It concentrates on
firm-value and reduced-form approaches and their applications in practice. Additionally, the book
includes new models for valuing derivative securities with credit risk, focussing on options and
forward contracts subject to counterparty default risk, but also treating options on credit-risky
bonds and credit derivatives. The text provides detailed descriptions of the state-of-the-art
martingale methods and advanced numerical implementations based on multi-variate trees used to
price derivative credit risk. Numerical examples illustrate the effects of credit risk on the prices of
financial derivatives.

Series: Springer Finance.

Ewens, W., University of Pennsylvania, Philadelphia, PA, USA
Grant, G., University of Pennsylvania, Philadelphia, PA, USA

Statistical Methods in Bioinformatics
An Introduction

2001. Approx. 465 pp. 30 figs. Hardcover
0-387-95229-2

Advances in computers and biotechnology have had an immense impact on the biomedical fields,
with broad consequences for humanity. Correspondingly, new areas of probability and statistics are
being developed specifically to meet the needs of this area. There is now a necessity for a text that
introduces probability and statistics in the bioinformatics context. This book also describes some
of the main statistical applications in the field, including BLAST, gene finding, and evolutionary
inference, much of which has not yet been summarized in an introductory textbook format.
The earlier chapters introduce the concepts of probability and statistics at an elementary level, and
will be accessible to students who have only had introductory calculus and linear algebra. Later
chapters are immediately accessible to the trained statistician. Only a basic understanding of
biological concepts is assumed, and all concepts are explained when used or can be understood
from the context. Several chapters contain material independent of that in other chapters, so that
the reader interested in certain areas can proceed directly to those areas.

Contents: An Introduction to Probability Theory: One Random Variable.- An Introduction to
Probability Theory: Many Random Variables.- Statistics: An Introduction to Statistical Inference.-
Stochastic Processes: An Introduction to Poisson Processes and Markov Chains.- The Analysis of
DNA Sequence Patterns: One sequence.- The Analysis of DNA Sequences: Multiple sequences.-
Stochastic Processes: Random Walks.- Statistics: Classical Estimation and Hypothesis Testing.-
BLAST.- Stochastic Processes: Markov Chains.- Hidden Markov Models.- Computationally
intensive methods.- Evolutionary models.- Phylogenetica tree estimation.

Series: Statistics for Biology and Health.