Edited by Bettye Anne Case and Anne M. Leggett

Complexities:
Women in Mathematics

Cloth | 2005 | ISBN: 0-691-11462-5
456 pp. | 6 x 9 | 15 line illus. 39 halftones. 7 tables.

Sophie Germain taught herself mathematics by candlelight, huddled in her bedclothes. Ada Byron Lovelace anticipated aspects of general-purpose digital computing by more than a century. Cora Ratto de Sadosky advanced messages of tolerance and equality while sharing her mathematical talents with generations of students.

This captivating book gives voice to women mathemeticians from the late eighteenth century through to the present day. It documents the complex nature of the conditions women around the world have faced--and continue to face--while pursuing their careers in mathematics. The stories of the three women above and those of many more appear here, each one enlightening and inspiring. The earlier parts of the book provide historical context and perspective, beginning with excursions into the lives of fifteen women born before 1920. Included are histories of collective efforts to improve women's opportunities in research mathematics. In addition, a photo essay puts a human face on the subject as it illustrates women's contributions in professional associations.

More than eighty women from academe, government, and the private sector provide a rich melange of insights and strategies for creating workable career paths while maintaining rewarding personal lives. The book discusses related social and cultural issues, and includes a summary of recent comparative data relating to women and men in mathematics and women from other sciences. First-person accounts provide explicit how-tos; many narratives demonstrate great determination and perseverance. Talented women vividly portray their pleasure in discovering new mathematics. The senior among them speak out candidly, interweaving their mathematics with autobiographical detail. At the beginning of a new century, women at all stages of their careers share their outlooks and experiences.

Clear, engaging, and meticulously researched, Complexities will inspire young women who are contemplating careers in mathematics and will speak to women in many fields of endeavor and walks of life.

Bettye Anne Case is Olga Larson Professor of Mathematics at Florida State University. Anne M. Leggett is Associate Professor of Mathematics at Loyola University, Chicago.

Endorsements:

"The talented and amazing women featured in this book will serve as inspirational role models for all generations that follow. Complexities carefully documents the importance of such role models in inspiring women to enter mathematics. It is a lesson that can be applied beyond this field to anywhere where women are underrepresented."--Linda Babcock, author, with Sara Laschever, of Women Don't Ask (Princeton).

"A provocative and informative inside view of what it is like to be both a mathematician and a woman. The belief that mathematics is solely a male preserve is fast disappearing, and Complexities will speed it on its way."--Ian Stewart, Mathematics Awareness Centre, University of Warwick

"This book contains a wealth of inspiration for women in the mathematical sciences, with real life advice on how to weather the tough times, find joy in the good times, and at the same time experience excitement and love for the subject. For young women seeking their paths in this field, the personal stories provide valuable mentorship. Even for those of us who have a parent as mentor, this collection provides essential insight into a variety of experiences and career paths."--Alison Marsden, Stanford University and Jerry Marsden, California Institute of Technology

"This astounding book provides a wealth of important information on women in mathematics over the ages, exploring how they entered the field, what excited them about it in their youth, what excites them now, and the many ways these women have advanced the frontiers of mathematics, or have used mathematics to the benefit of society. Although not a mathematician myself, I have known many of the women mathematicians in this book and have shared with them my experiences as a physicist. How wonderful that this is all gathered in one volume of easy reading."--Mildred Dresselhaus, MIT

Dennis S. Bernstein

Matrix Mathematics:
Theory, Facts, and Formulas with Application to Linear Systems Theory

Cloth | April 2005 | ISBN: 0-691-11802-7
752 pp. | 7 x 10 | 4 line illus.

Matrix Mathematics is a reference work for users of matrices in all branches of engineering, science, and applied mathematics. This book brings together a vast body of results on matrix theory for easy reference and immediate application.

Each chapter begins with the development of relevant background theory followed by a large collection of specialized results. Hundreds of identities, inequalities, and matrix facts are stated rigorously and clearly with cross references, citations to the literature, and illuminating remarks. Twelve chapters cover all of the major topics in matrix theory: preliminaries; basic matrix properties; matrix classes and transformations; matrix polynomials and rational transfer functions; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; norms; functions of matrices and their derivatives; the matrix exponential and stability theory; and linear systems and control theory.

A detailed list of symbols, a summary of notation and conventions, an extensive bibliography with author index, and an extensive reference list are provided for ease of use. The book will be useful for students at both the undergraduate and graduate levels, as well as for researchers and practitioners in all branches of engineering, science, and applied mathematics.

Dennis S. Bernstein is a Professor of Aerospace Engineering at the University of Michigan.

Elias M. Stein and Rami Shakarchi

Real Analysis:
Measure Theory, Integration, and Hilbert Spaces

Cloth | May 2005 | ISBN: 0-691-11386-6
392 pp. | 6 x 9 | 51 line illus.

Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science.

After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises.

As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels.

Also available, the first two volumes in the Princeton Lectures in Analysis:

Elias M. Stein is Professor of Mathematics at Princeton University. Rami Shakarchi received his Ph.D. in Mathematics from Princeton University in 2002.

Other Princeton books by Elias M. Stein:

Beijing Lectures in Harmonic Analysis. (AM-112).
Complex Analysis.
Fourier Analysis: An Introduction.
Hardy Spaces on Homogeneous Groups. (MN-28).
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43).
Introduction to Fourier Analysis on Euclidean Spaces (PMS-32).
Singular Integrals and Differentiability Properties of Functions (PMS-30).
Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63).

ed. O. Hirota

Quantum Information, Statistics, Probability
-celebration of Holevo's 60th birthday

224 pages, 9x6 inches
September 2004 Hardcover
ISBN 1-58949-041-X

Description:

This book is dedicated to Professor A.S.Holevo on the occasion of his60th birthday. Containing chapters by promising mathematicians, physicists, and information scientists, it offers new insights into the influence and importance of Holevo's achievement. Readers who are interested in either the foundations or applications of quantum information science will find this book to be of interest.

Contributions
O. Hirota:
Foreword
A. Arvind, P. Kurur, K. Parthasarathy:
Non-stabilizer quantum codes from Abelian subgroups of the error group
A.Barchielli, G.Lupieri:
Instrumental processes, entropies, information in quantum continual measurement
S. Barnett:
Optical demonstrations of statistical decision theory for quantum systems
C. Bennett:
A resource-based view of quantum information
C.A. Fuchs:
On the quantumness of a Hilbert space
A. Fujiwara:
Statistical estimation of a quantum operation
V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. Shapiro, H. Yuen:
Classical capacity of free-space optical communication
C.King, M.Ruskai:
Comments on multiplicativity of maximal p-norms when p=2
L. Lanz, B. Vacchini, O. Melsheimer:
On consistency of quantum theory and macroscopic objectivity
M. Sasaki:
Towards implementation of coding for quantum sources and channels
P. Shor:
The classical capacity achievable by a quantum channel assisted by limited entanglement
R. Werner:
The uncertainty relation for joint measurement of position and moment
A. Winter:
Quantum and classical message identification via quantum channels


John C. Strikwerda

Finite Difference Schemes and Partial Differential Equations, Second Edition

This book provides a unified and accessible introduction to the basic theory of finite difference schemes applied to the numerical solution of partial differential equations. Originally published in 1989, its objective remains to clearly present the basic methods necessary to perform finite difference schemes and to understand the theory underlying the schemes.

Finite Difference Schemes and Partial Differential Equations, Second Edition is one of the few texts in the field to not only present the theory of stability in a rigorous and clear manner but also to discuss the theory of initial-boundary value problems in relation to finite difference schemes. Fourier analysis is used throughout the book to give a unified treatment of many of the important ideas found in the first eleven chapters. The material on elliptic partial differential equations found in the later chapters provides an introduction that will enable students to progress to more advanced texts and to knowledgeably implement the basic methods.

This updated edition includes several important modifications. The notion of a stability domain is now included in the definition of stability and is more prevalent throughout the book. The author has added many new figures and tables to clarify important concepts and illustrate the properties of finite difference schemes.

Audience

Finite Difference Schemes and Partial Differential Equations, Second Edition is intended for first-year graduate students in scientific and engineering computation. Researchers in numerical analysis also will find it a useful reference for studying stability theory for finite difference schemes applied to linear partial differential equations.

Contents

Preface to the Second Edition; Preface to the First Edition; Chapter 1: Hyperbolic Partial Differential Equations; Chapter 2: Analysis of Finite Difference Schemes; Chapter 3: Order of Accuracy of Finite Difference Schemes; Chapter 4:Stability for Multistep Schemes; Chapter 5: Dissipation and Dispersion; Chapter 6:Parabolic Partial Differential Equations; Chapter 7: Systems of Partial Differential Equations in Higher Dimensions; Chapter 8: Second-Order Equations; Chapter 9: Analysis of Well-Posed and Stable Problems; Chapter 10: Convergence Estimates for Initial Value Problems; Chapter 11: Well-Posed and Stable Initial-Boundary Value Problems; Chapter 12: Elliptic Partial Differential Equations and Difference Schemes; Chapter 13: Linear Iterative Methods; Chapter 14: The Method of Steepest Descent and the Conjugate Gradient Method; Appendix A: Matrix and Vector Analysis; Appendix B: A Survey of Real Analysis; Appendix C: A Survey of Results from Complex Anaylsis; References; Index.

2004 | Approx. xii + 434 | Hardcover | ISBN 0-89871-567-9

J. L. Hodges, Jr. and E. L. Lehmann

Basic Concepts of Probability and Statistics, Second Edition

Basic Concepts of Probability and Statistics provides a mathematically rigorous introduction to the fundamental ideas of modern statistics for readers without a calculus background. It is the only book at this level to introduce readers to modern concepts of hypothesis testing and estimation, covering basic concepts of finite, discrete models of probability and elementary statistical methods. Although published in 1970, it maintains a modern outlook, especially in its emphasis on models and model building and also by its coverage of topics such as simple random and stratified survey sampling, experimental design, and nonparametric tests and its discussion of power.

The book covers a wide range of applications in manufacturing, biology, and social science, including demographics, political science, and sociology. Each section offers extensive problem sets, with selected answers provided at the back of the book. Among the topics covered that readers may not expect in an elementary text are optimal design and a statement and proof of the fundamental (Neyman–Pearson) lemma for hypothesis testing.

Audience

Basic Concepts of Probability and Statistics is intended for high school and undergraduate students as well as others who want a mathematically rigorous introduction to probability and statistics that does not require calculus. It is well suited to supplement high school and college courses on discrete mathematics and will appeal especially to instructors teaching statistics courses within mathematics departments.

Contents

Preface to the Classics Edition; Preface to the Second Edition; Preface to the First Edition; Part I: Probability. Chapter 1: Probability Models; Chapter 2: Sampling; Chapter 3: Product Models; Chapter 4: Conditional Probability; Chapter 5: Random Variables; Chapter 6: Special Distributions; Chapter 7: Multivariate Distributions; Part II: Statistics. Introduction to Statistics; Chapter 8: Estimation; Chapter 9: Estimation in Measurement and Sampling Models; Chapter 10: Optimum Methods of Estimation; Chapter 11: Tests of Significance; Chapter 12: Tests for Comparative Experiments; Chapter 13: Concept of Power;
Tables; Selected answers to problems; Index; Example Index.

Available December 2004 / Approx. xiv + 441 pages / Softcover / ISBN 0-89871-575-X

Jenny Baglivo

Mathematica Laboratories for Mathematical Statistics:
Emphasizing Simulation and Computer Intensive Methods

Integrating computers into mathematical statistics courses allows students to simulate experiments and visualize their results, handle larger data sets, analyze data more quickly, and compare the results of classical methods of data analysis with those using alternative techniques. This text presents a concise introduction to the concepts of probability theory and mathematical statistics. The accompanying in-class and take-home computer laboratory activities reinforce the techniques introduced in the text and are accessible to students with little or no experience with Mathematica. These laboratory materials present applications in a variety of real-world settings, with data from epidemiology, environmental sciences, medicine, social sciences, physical sciences, manufacturing, engineering, marketing, and sports.

Mathematica Laboratories for Mathematical Statistics: Emphasizing Simulation and Computer Intensive Methods includes parametric, nonparametric, permutation, bootstrap and diagnostic methods. Chapters on permutation and bootstrap techniques follow the formal inference chapters and precede the chapters on intermediate-level topics. Permutation and bootstrap methods are discussed side by side with classical methods in the later chapters.

Audience

This book is written with both the instructor and the student in mind. The order of topics and the level of presentation are similar to those of other mathematical statistics books. Thus, instructors will find it easy to incorporate this approach in their classroom. The accompanying student CD of laboratory activities, written as Mathematica notebooks, contains text, data, computations, and graphics. Mathematica notebooks are particularly well-suited for presenting concepts and problems, and for writing solutions. Over half of the 238 laboratory problems use real-world data, many from recent research reports or on-going research. Prerequisites include multivariable calculus and familiarity with the basics of set theory, vectors, matrices, and problem-solving using a computer.

Contents

Preface: Chapter 1: Introductory Probability Concepts; Chapter 2: Discrete Probability Distributions; Chapter 3: Continuous Probability Distributions; Chapter 4: Mathematical Expectation; Chapter 5: Limit Theorems; Chapter 6: Transition to Statistics; Chapter 7: Estimation Theory; Chapter 8: Hypothesis Testing Theory; Chapter 9: Order Statistics and Quantiles; Chapter 10: Two Sample Analysis; Chapter 11: Permutation Analysis; Chapter 12: Bootstrap Analysis; Chapter 13: Multiple Sample Analysis; Chapter 14: Linear Least Squares Analysis; Chapter 15: Contingency Table Analysis; Bibliography; Index

Available December 2004 / xx + 260 pages / Softcover / ISBN 0-89871-566-0