Jasbir S. Chahal
Professor of Mathematics, Brigham Young University.

A Brief Introduction to Algebraic Number Theory

2006. vi, 139 pp.

The author presents a concise introduction to algebraic number theory suitable for a beginning graduate course. The book is based on lectures given at the University of Salzburg and at Brigham Young University. Many exercises are incorporated into the text. As for prerequisites, the reader should be familiar with linear algebra, and some basic abstract algebra including Galois theory.

The methods used are classical, along the lines of the work of Dedekind and Hilbert. The Minkowski geometry of numbers is developed and used as a tool. The author takes pains to show how commutative algebra and algebraic geometry originate in the subject matter of algebraic number theory. Students who decide to specialize in algebraic number theory will find the suggestions for further reading helpful.

Algebraic number theory is one of the great accomplishments of pure mathematics. This was the view of David Hilbert and Hermann Weyl, for example. This brief introduction conveys the power and elegance of the subject, and tempts the reader to delve further into the literature.

Chapter 1: Basic Concepts. Chapter 2: Arithmetic in Relative Extensions. Chapter 3: Geometry of Numbers. Chapter 4: Analytic Methods. Chapter 5: Arithmetic in Galois Extensions. Chapter 6: Cyclotamic Fields. Chapter 7: The Kronecker-Weber Theorem. Chapter 8: Zeta Functions and Riemann Hypothesis.

Authors: Lev Klebanov (Charles University, Czech Republic), Tomasz J. Kozubowski (University of Nevada, USA) and Svetlozar T. Rachev (University of Karlsruhe, Germany)

Ill-Posed Problems in Probability and Stability of Random Sums Retail Price

Book Description:

This volume is concerned with the problems in probability and statistics. Ill-posed problems are usually understood as those results where small changes in the assumptions lead to arbitrarily large changes in the conclusions. Such results are not very useful for practical applications where the presumptions usually hold only approximately (because even a slightest departure from the assumed model may produce an uncontrollable shift in the outcome). Often, the ill-posedness of certain practical problems is due to the lack of their precise mathematical formulation. Consequently, one can deal with such problems by replacing a given ill-posed problem with another, well-posed problem, which in some sense is “close” to the original one.

The goal in this book is to show that ill-posed problems are not just a mere curiosity in the contemporary theory of mathematical statistics and probability. On the contrary, such problems are quite common, and majority of classical results fall into this class. The objective of this book is to identify problems of this type, and re-formulate them more correctly. Thus, alternative (more precise in the above sense) versions are proposed of numerous classical theorems in the theory of probability and mathematical statistics. In addition, some non-standard problems are considered from this point of view.

Binding: Hardcover
Pub. Date: 2006
ISBN: 1-60021-262-X

Graham Upton and Ian Cook

A Dictionary of Statistics, Second Edition

NEW EDITION
(Paperback)
ISBN-10: 0-19-861431-4
ISBN-13: 978-0-19-861431-9
Estimated publication date: August 2006
496 pages, 196x129 mm

Description

Jargon-free statistics dictionary, containing over 1,700 entries
Includes over 200 biographies of key figures in statistics
Wide ranging: areas covered include statistical journals and societies, terms used in computing, mathematics, operational research, and probability
Includes appendices of mathematical and statistical notation
Multi-disciplinary title: useful to students of many subjects, including statistics, politics, medicine and mathematics
Internet-linked: entries contain internet links where applicable. Also includes a new general appendix of useful statistics websites
Many illustrative examples, giving entries a practical context

New to this edition
Fully revised and updated with over 200 new entries
Over 30 new biographies
Internet-linked: entries contain internet links where applicable. Also includes a new general appendix of useful statistics websites
Many more illustrative examples, giving entries a practical context

This wide-ranging, jargon-free dictionary contains over 1,700 entries on all aspects of statistics including terms used in computing, mathematics, operational research, and probability, as well as biographical information on over 200 key figures in the field, and coverage of statistical journals and societies. It embraces the whole multi-disciplinary spectrum of this complex subject, and will be invaluable for students and professionals from a wide range of disciplines, including politics, market research, medicine, psychology, pharmaceuticals, and mathematics.

The entries are generously illustrated with useful figures and diagrams, and include worked examples where applicable, which place them in a practical context. Appendices include a historical calendar of important statistical events, and tables of statistical and mathematical notation. Fully updated for the second edition, the dictionary now boasts over 200 new entries including over 30 new biographies, as well as internet links which point to useful sites for further information, and many additional illustrative examples that clarify terms by showing them in use.

Concise and practical, this is an invaluable work of reference for students and professionals in fields related to statistics, and a clear introduction to the subject for the general reader.

Readership: Students of statistics and of disciplines featuring statistical material, such as politics, medicine, and mathematics. Also relevant to professionals in business, and industries such as market research and pharmaceuticals.

Contents

Preface

A-Z Dictionary of Statistics

Appendices

Statistical Notation
Mathematical Notation
Greek Letters
Cumulative Probabilities for the Bionomial Distribution
Cumulative Probabilities for the Poisson Distribution
Upper-Tail Percentage Points for the Standard Normal Distribution
The Standard Normal Distribution Function
Percentage Points for the t-Distribution
Percentage Points for the F-Distribution
Percentage Points for the Chi-Squared Distribution
Critical Values for Spearman's Rank Correlation Coefficient
Critical Values for Kendall
Critical Values for the Product-Moment Correlation Coefficient, r
Pseudo-Random Numbers
Selected Landmarks in the Development of Statistics
Further Reference
Useful websites

Edited by
Diana Kormos Buchwald, Tilman Sauer, Ze'ev Rosenkranz, Josef Illy & Virginia Iris Holmes

The Collected Papers of Albert Einstein, Volume 10:
The Berlin Years: Correspondence, May-December 1920, and Supplementary Correspondence, 1909-1920. (English translation of selected texts)

Paper | August 2006 | ISBN: 0-691-12826-X
Cloth | August 2006 | ISBN: 0-691-12825-1

384 pp. | 7 1/2 x 10

In this latest volume, Einstein is embroiled in public attacks on his recently confirmed theory of general relativity. He considers leaving Berlin, thus depriving Germany of its most famous scientist. Colleagues, friends, and unknown admirers offer support, while Einstein worries about the care of his two sons and ex-wife in Switzerland, and his new family in Berlin. This volume also contains a substantial body of previously unavailable material from the 1909-1920 period.

The intensity of this period, during which anti-Semitism and nationalistic sentiment seeped into scientific debate, is reflected in numerous letters. Einstein continues research and promotes general relativity. He travels to Leyden as a visiting professor and is deeply involved with issues at the forefront of physics. He visits Oslo and Copenhagen--where he meets with Niels Bohr--and receives invitations to America. Correspondence with Moritz Schlick, Hans Reichenbach, and others attests to Einstein's central role in the lively intellectual atmosphere of the Weimar Republic.

At the California Institute of Technology, Diana Kormos Buchwald is Professor of History; Tilman Sauer is a Senior Research Associate in History; and Ze'ev Rosenkranz, Jozsef Illy, and Virginia Iris Holmes are research staff in History.

Table of Contents:

PUBLISHER'S FOREWORD ix
LIST OF TEXTS xi
SELECTED TEXTS
Supplementary Correspondence, 1909-1920 3
Correspondence, May-December 1920 149
INDEX 349

Wassim M. Haddad, VijaySekhar Chellaboina & Sergey G. Nersesov

Impulsive and Hybrid Dynamical Systems:
Stability, Dissipativity, and Control

Cloth | July 2006 | ISBN: 0-691-12715-8
520 pp. | 6 x 9 | 61 line illus. 1 table.

This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Such a framework is imperative for modern complex engineering systems that involve interacting continuous-time and discrete-time dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of increasing complexity--whether advanced high-performance tactical fighter aircraft and space vehicles, variable-cycle gas turbine engines, or air and ground transportation systems.

Impulsive and Hybrid Dynamical Systems goes beyond similar treatments by developing invariant set stability theorems, partial stability, Lagrange stability, boundedness, ultimate boundedness, dissipativity theory, vector dissipativity theory, energy-based hybrid control, optimal control, disturbance rejection control, and robust control for nonlinear impulsive and hybrid dynamical systems. A major contribution to mathematical system theory and control system theory, this book is written from a system-theoretic point of view with the highest standards of exposition and rigor. It is intended for graduate students, researchers, and practitioners of engineering and applied mathematics as well as computer scientists, physicists, and other scientists who seek a fundamental understanding of the rich dynamical behavior of impulsive and hybrid dynamical systems.

Wassim M. Haddad is Professor of Aerospace Engineering at the Georgia Institute of Technology. VijaySekhar Chellaboina is Associate Professor of Mechanical, Aerospace, and Biomedical Engineering at the University of Tennessee. Sergey G. Nersesov is Assistant Professor of Mechanical Engineering at Villanova University. Haddad, Chellaboina, and Nersesov previously coauthored Thermodynamics: A Dynamical Systems Approach (Princeton).

Endorsements:

"This book is a significant and timely contribution to the field. Interest in the study of hybrid systems has been growing exponentially in recent years, and the investigation of impulsive differential equations has also drawn much attention. In combining these two important areas, Impulsive and Hybrid Dynamical Systems captures the rich behavior of both in a manner applicable to many applied, technical, and real-world problems. It provides all the necessary tools for the benefit of users."--V. Lakshmikantham, Florida Institute of Technology

"This carefully written book fills a void in the literature on hybrid and impulsive systems. No book in print has the depth and breadth of this one. The authors present their material in a rigorous and mathematically sound manner."--Anthony Michel, University of Notre Dame