Meinolf Geck, Institut Girard Desargues, Universite Lyon]

An Introduction to Algebraic Geometry and Algebraic Groups

(Hardback)
0-19-852831-0
Publication date: December 2003
Clarendon Press 235 pages, none, 234mm x 156mm

Series: Oxford Graduate Texts in Mathematics

Excellent coverage of the algebraic groups at graduate level
Ideal for year-long M.Math courses
Contains elegant worked examples and instructive exercises as well as bibliographical and historical remarks

Description

An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. The text contains numerous examples and proofs along with exercises and hints.

Readership: Graduates and researchers in pure mathematics seeking a comprehensive background in algebraic geometry; university teaching staff; advanced undergraduates in third and fourth year of university studies.

Contents

1 Algebraic sets and algebraic groups
2 Affine varieties and finite morphisms
3 Algebraic representations and Borel subgroups
4 Frobenius maps and finite groups of Lie type
Bibliography
Index

Robert Mattheij and Jaap Molenaar

Ordinary Differential Equations in Theory and Practice

Classics in Applied Mathematics 43

In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role.

Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which not only the general concepts of mathematical modeling but also illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained.

Audience

The book is intended for use as a textbook for both undergraduate and graduate courses, and it can also serve as a reference for students and researchers alike.

Contents

Preface to the Classics Edition; Preface; Chapter 1: Introduction; Chapter 2: Existence, Uniqueness, and Dependence on Parameters; Chapter 3: Numerical Analysis of One-Step Methods; Chapter 4: Linear Systems; Chapter 5: Stability; Chapter 6: Chaotic Systems; Chapter 7: Numerical Analysis of Multistep Methods; Chapter 8: Singular Perturbations and Stiff Differential Equations; Chapter 9: Differential-Algebraic Equations; Chapter 10: Boundary Value Problems; Chapter 11: Concepts from Classical Mechanics; Chapter 12: Mathematical Modelling; Appendices; References; Index.

2002 / xvii + 405 pages / Softcover / ISBN 0-89871-531-8

Shanti S. Gupta and S. Panchapakesan

Multiple Decision Procedures: Theory and Methodology of Selecting and Ranking Populations

Classics in Applied Mathematics 44

Multiple Decision Procedures: Theory and Methodology of Selecting and Ranking Populations provides an encyclopedic coverage of the literature in the area of ranking and selection procedures, summarizing and surveying in a unified manner a majority of more than 600 main references in the bibliography. It also deals with related problems, such as the estimation of unknown ordered parameters. A separate chapter is devoted to information about several tables available in the literature for carrying out various specific procedures. Examples are given in another chapter illustrating applications of these procedures in various practical contexts. Although several books have appeared to date in this area, many of them deal with specific aspects of the field and a limited number of topics. This book contains substantial material not discussed in other books.

Audience

This book can serve as a text for a graduate topics course in ranking and selection (as it has done at Purdue University for more than 30 years). It will also serve as a valuable reference for researchers and practitioners in various fields, such as agriculture, industry, engineering, and behavioral sciences.

Contents

Preface to the Classics Edition; Preface; List of Abbreviations and Symbols; Chapter 1: Introduction; Part I: Indifference Zone Formulation. Chapter 2. Ranking of Normal Populations; Chapter 3: Some Optimum Properties of Fixed Subset Size Selection Rules; Chapter 4: Ranking and Selection Problems for Discrete Distributions; Chapter 5: Selection from Univariate Populations, Optimum Sampling, and Estimation of Probability of Correct Selection; Chapter 6: Sequential Selection Procedures; Chapter 7: Selection from Multivariate Populations; Chapter 8: Nonparametric Selection Procedures; Chapter 9: Fixed-Size Subset Selection: A Generalized Goal and Other Modifications; Chapter 10: Bayesian Selection and Ranking Procedures; Part II: Subset Selection Formulation. Chapter 11: Subset Selection: General Theory; Chapter 12: Selection from Univariate Continuous Populations; Chapter 13: Selection from Discrete Populations; Chapter 14: Selection from Multivariate Normal Populations; Chapter 15: Nonparametric Procedures; Chapter 16: Selection from Restricted Families of Probability Distributions; Chapter 17: Sequential Procedures; Chapter 18: Bayes, Empirical Bayes, and ?-Minimax Procedures; Chapter 19: Some Modified Formulations and Other Related Problems; Part III: Comparison with a Control, Estimation, and Related Topics. Chapter 20: Comparison of Several Populations with a Standard or a Control; Chapter 21: Estimation of Ordered Parameters; Chapter 22: General Theory of Some Multiple-Decision Problems and Some Miscellaneous Topics; Chapter 23: Guide to Tables; Chapter 24: Illustrative Examples; Bibliography; Related References; Monographs, Books and Special Issues of Journals Devoted Fully or Partially to Ranking and Selection Problems; Author Index; Subject Index.

2002 / xxxii + 573 pages / Softcover / ISBN 0-89871-532-6

M. Vidyasagar

Nonlinear Systems Analysis, Second Edition

Classics in Applied Mathematiacs 42

When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature.

The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. In addition, it includes valuable reference material in these chapters that is unavailable elsewhere. The text also features a large number of problems that allow readers to test their understanding of the subject matter and self-contained sections and chapters that allow readers to focus easily on a particular topic.

Audience

This text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers. The subject of nonlinear systems continues to interest not only theorists but also practitioners working in areas such as robotics, spacecraft control, motor control, and power systems. This book is sure to enlighten readers on this timeless and ever-fascinating subject.

Contents

Preface to the Classics Edition; Preface; Note to the Reader; Chapter 1: Introduction; Chapter 2: Nonlinear Differential Equations; Chapter 3: Second-Order Systems; Chapter 4: Approximate Analysis Methods; Chapter 5: Lyapunov Stability; Chapter 6: Input-Output Stability; Chapter 7: Differential Geometric Methods; Appendix A: Prevalence of Differential Equations with Unique Solutions; Appendix B: Proof of the Kalman-Yacubovitch Lemma; Appendix C: Proof of the Frobenius Theorem; References; Index.

2002 / xviii + 498 pages / Softcover / ISBN 0-89871-526-1

Daniel Barbara and Chandrika Kamath, Editors

Proceedings of the Third SIAM International Conference on Data Mining

Conference held May 2003, San Francisco, California.

The Third SIAM International Conference on Data Mining continued the tradition of providing an open forum for the presentation, discussion, and development of innovative algorithms, software, and theories for data mining applications and data intensive computation. This year's invited speakers highlighted new trends in algorithm development, discussed new trends and challenges for data mining from an industrial perspective, revealed important issues in both the monitoring and mining of network data streams, and exposed important mathematical and computational problems that arise in protecting privacy during transactional database mining and analysis. A workshop on counter-terrorism and security was held for the first time.

This proceedings includes 21 research papers; 14 were accepted as poster presentations, and seven were accepted as student papers from the conference.

2003 / xiv + 347 pages / Softcover / ISBN 0-89871-545-8