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
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.
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).
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
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
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
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