Editors:
David Jerison, Tom Mrowka, Richard Stanley - MIT
B. Mazur, W. Schmid, S.-T. Yau, Harvard

Current Developments in Mathematics 2001

ISBN 1-57146-101-9

AUTHORS:

Gunnar Carlsson / Stanford University
Recent Developments in Algebraic K-theory

Daniel Freed / University of Texas
K-Theory in Quantum Field Theory

Elliott H. Lieb / Princeton University
Jakob Yngvason / Universitat Wien
The Mathematical Structure of the Second Law of Thermodynamics

Elliott H. Lieb / Princeton University |Jan Philip Solovej / University of Copenhagen
Robert Seiringer / Princeton University |Jakob Yngvason / Universitat Wien
The Ground State of the Bose Gas

Shou-Wu Zhang / Columbia University
On Gross-Zagier Formula

Henk C. Tijms

A First Course in Stochastic Models

ISBN: 0-471-49880-7
Hardcover
ISBN: 0-471-49881-5
Paperback
488 pages
May 09, 2003

Description

The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved.
Provides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications.
Incorporates recent developments in computational probability.
Includes a wide range of examples that illustrate the models and make the methods of solution clear.
Features an abundance of motivating exercises that help the student learn how to apply the theory.
Accessible to anyone with a basic knowledge of probability.
A First Course in Stochastic Models is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations resear ch, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications.

Table of Contents

Preface.
The Poisson Process and Related Processes.
Renewal-Reward Processes.
Discrete-Time Markov Chains.
Continuous-Time Markov Chains.
Markov Chains and Queues.
Discrete-Time Markov Decision Processes.
Semi-Markov Decision Processes.
Advanced Renewal Theory.
Algorithmic Analysis of Queueing Models.
Appendices.

Dhammika Amaratunga, Javier Cabrera

Exploration and Analysis of DNA Microarray and Protein Array Data

ISBN: 0-471-27398-8
Hardcover
224 pages
September 2003

Description

The emergence of genomics, the study of genes, is one of the major scientific revolutions of this century. Microarrays, a method used to analyze numerous DNA samples rapidly, enables scientists to make sense of this mountain of data using statistical analysis. They are being used in such areas of biomedical research as studying patterns for gene activity that cause cancers to spread. This book presents a comprehensive methodology for analyzing DNA microarray and protein array data.

The most comprehensive treatment of this important emerging field, Exploration and Analysis of DNA Microarray and Protein Array Data includes:

A review of basic molecular biology and a chapter introducing microarrays and their preparation
Chapters on processing scanned images, preprocessing microarray data, group comparative experiments, and other designs
Discussions of clustering, protein arrays, and applications for diagnostic tools
Ample exercises assist absorbtion

Table of Contents

Preface.
A Brief Introduction.
Genomics Basics.
Microarrays.
Processing the Scanned Image.
Preprocessing Microarray Data.
Summarization.
Two-Group Comparative Experiments.
Model-Based Inference and Experimental Design Considerations.
Pattern Discovery.
Class Prediction.
Protein Arrays.
References.


J. C. Butcher

Numerical Methods for Ordinary Differential Equations , Second Edition

ISBN: 0-471-96758-0
Hardcover
440 pages
August 2003

Description

Second edition of the exceptionally popular Numerical Analysis of Ordinary Differential Equations
New exercises are included in each chapter
The author is widely regarded as the world expert on Runge-Kutta methods
"This book is...an indispensible reference for any researcher"
- American Mathematical Society review of the first edition.

Table of Contents

Preface.
1 Differential and Difference Equations.
2 Numerical Differential Equation Methods.
3 Runge-Kutta Methods.
4 Linear Multistep Methods.
5 General Linear Methods.
References.
Index.

Edited by Matthias Schirn, University of Munich

The Philosophy of Mathematics Today

NEW IN PAPERBACK
0-19-926262-4
Publication date: 22 May 2003
Clarendon Press 650 pages, 234mm x 156mm

Description

The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come.

Contributors Paul Benacerraf, George Boolos, John P. Burgess, Charles S. Chihara, Michael Detlefsen, Michael Dummett, Hartry Field, Kit Fine, Bob Hale, Richard G. Heck, Jnr., Geoffrey Hellman, Penelope Maddy, Karl-Georg Niebergall, Charles D. Parsons, Michael D. Resnik, Matthias Schirn, Stewart Shapiro, Peter Simons, W.W. Tait, Crispin Wright.

Readership: Scholars and students of the philosophy of mathematics.

Contents/contributors
Introduction.
PART I: ONTOLOGY, MODELS, AND INDETERMINACY
1 Paul Benacerraf: What Mathematical Truth Could Not Be--1
2 Bob Hale: Iis Platonism Epistemologically Bankrupt?
3 Hartry Field: Do We Have a Determinate Conception of Finiteness and Natural Number?
4 Stewart Shapiro: Logical Consequence: Models and Modality
5 Charles Chihara: Tarski's Thesis and the Ontology of Mathematics
PART II: MATHEMATICS, SCIENCE, AND METHOD
6 Penelope Maddy: Naturalizing Mathematical Methodology
7 John P. Burgess: Occam's Razor and Scientific Method
8 Geoffrey Hellman: Beyond Definitionism - But Not Too Far Beyond
9 Michael D. Resnik: Holistic Mathematics
PART III: FINITISM AND INTUITIONISM
10 Charles Parsons: Finitism and Intuitive Knowledge
11 Karl-Georg Niebergall and Matthias Schirn: Hilbert's Finitism and the Notion of Infinity
12 Michael Detlefsen: Constructive Existence Claims
PART IV: FREGE AND THE FOUNDATIONS OF ARITHMETIC
13 Crispin Wright: On the Harmless Impredicativity of N= (`Hume's Principle')
14 Michael Dummett: Neo-Fregeans: In Bad Company?
15 Crispin Wright: Response to Dummett
16 George Boolos and Richard G. Heck: Die Grundlagen der Arithmetik, 82-3
17 Richard G. Heck: The Finite and the Infinite in Frege's Grundgesetze der Arithmetik
PART V: SETS, STRUCTURE, AND ABSTRACTION
18 W. W. Tait: Zermelo's Conception of Set Theory and Reflection Principles
19 Peter Simons: Structure and Abstraction
20 Kit Fine: The Limits of Abstraction
Index