Expected publication date is July 17, 2005
Description
This three-volume set addresses the interplay between topology,
functions, geometry, and algebra. Bringing the beauty and fun of
mathematics to the classroom, the authors offer serious
mathematics in a lively, reader-friendly style. Included are
exercises and many figures illustrating the main concepts. It is
suitable for advanced high-school students, graduate students,
and researchers.
Contents
Part I
Invitation to topology (Viewing figures globally)
Introduction
The Euler characteristic
Vortices created by winds and the Euler characteristic
Curvature of a surface and the Euler characteristic
The story of dimension
Introduction
Learning to appreciate dimension
What is dimension?
Three-dimensional figures
Physics and dimension
Part II
The legacy of trigonometric functions
Introduction
Trigonometric functions and infinite series
Elliptic functions
Intersection of geometry and algebra
Introduction
The Poncelet closure theorem
The Poncelet theorem for circles
The Poncelet theorem in the world of complex numbers
Proof of the Poncelet theorem using plane geometry
Conclusion
Part III
The story of the birth of manifolds
The prelude to the birth of manifolds
The birth of manifolds
The story of area and volume from everyday notions to
mathematical concepts
Transition from the notion of "size" to the concept of
"area"
Scissors-congruent polygons
Scissors-congruent polyhedra
Details:
Series: Mathematical World,
Publication Year: 2005
ISBN: 0-8218-3859-8
Paging: 392 pp.
Binding: Softcover
Expected publication date is August 21, 2005
"The role of minority and women mathematicians in developing
our American mathematical community is an important but
previously under-told story. Pat Kenschaft, in her highly
readable and entertaining style, fills this knowledge gap. This
valuable book should be in your personal library!"
-- Donald G. Saari, University of California, Irvine
"Kenschaft reveals the passions that motivated past and
present mathematicians and the obstacles they overcame to achieve
their dreams. Through research and in-depth personal interviews,
she has explored the sensitive issues of racism and sexism,
rejoicing in positive changes and alerting us to issues that
still need our attention."
-- Claudia Zaslavsky, the author of "Africa Counts" and
other books on equity issues in mathematics education
Description
Based on dozens of interviews and extensive historical research,
and spiced with interesting photographs, this entertaining book
relates stories about mathematicians who have defied stereotypes.
There are five chapters about women that provide insight into the
nineteenth and the mid-twentieth century, the early 1970s, the
early 1990s, and 2004. Activists in many fields will take heart
at the progress made during that time. The author documents the
rudimentary struggles to become professionals, being married
without entirely giving up a career, organizing to eliminate
flagrant discrimination, improving the daily treatment of women
in the professional community, and the widespread efforts toward
true equality.
The stories of African Americans in mathematics include the
efforts of Benjamin Banneker, an eighteenth century American who
had three grandparents born in Africa. He helped design
Washington, DC, and made the computations for almanacs that
succeeded Benjamin Franklin's. There are stories about African
American mathematicians who were students and faculty in late
nineteenth century colleges and accounts of several efforts to
integrate the mathematical community in the mid-twentieth century.
These stories indicate that though some efforts were more
successful than others, all of them were difficult.
The book concludes with a happier chapter about five black
mathematicians in the early twenty-first century. The book also
includes five interviews with leading Latin American
mathematicians, along with the results of a survey of Latino
research mathematicians in the Southwest.
The author is a skilled story-teller with good stories to tell.
This book is a page-turner that all mathematicians--as well as
others concerned with equality--should read. It is a work of
great interest and an enjoyable read.
Contents
Introduction
With the help of good white men
Women and mathematics in the nineteenth century
The Twentieth century: Mathematics and marriage
African American mathematicians from the eighteenth through the
twentieth century
Latino mathematicians
Reawakening: The Association for Women in Mathematics
Skits tell what's happening around 1990
Women in mathematics now (2004)
Minorities in mathematics now (2004)
Conclusions
Appendix (to Chapter 5): What were the careers of 75 African
American mathematicians of New Jersey in mid-1985?
Details:
Publication Year: 2005
ISBN: 0-8218-3748-6
Paging: approximately 212 pp.
Binding: Softcover
Expected publication date is August 31, 2005
Description
A conference, Coding Theory and Quantum Computing, was held in
Charlottesville, VA, to provide an opportunity for computer
scientists, mathematicians, and physicists to interact about
subjects of common interest. This proceedings volume grew out of
that meeting.
It is divided into two parts: "Coding Theory" and
"Quantum Computing". In the first part, Harold Ward
gives an introduction to coding theory. Other papers survey
recent important work, such as coding theory applications of
Grobner bases, methods of computing parameters of codes
corresponding to algebraic curves, and problems in the theory of
designs. The second part of the book covers a wide variety of
directions in quantum information with an emphasis on
understanding entanglement.
The material presented is suitable for graduate students and
researchers interested in coding theory and in quantum computing.
Contents
Coding theory
J. B. Farr and S. Gao -- Grobner bases, Pade approximation, and
decoding of linear codes
G. L. Matthews -- Some computational tools for estimating the
parameters of algebraic geometry codes
H. N. Ward -- An introduction to algebraic coding theory
Q. Xiang -- Recent results on $p$-ranks and Smith normal forms of
some $2-(v,k,\lambda)$ designs
Quantum computing
E. Feldman and M. Hillery -- Quantum walks on graphs and quantum
scattering theory
S. J. Lomonaco, Jr. and L. H. Kauffman -- A continuous variable
Shor algorithm
S. J. van Enk -- Entangled states of light
L. Viola, H. Barnum, E. Knill, G. Ortiz, and R. Somma --
Entanglement beyond subsystems
A. Yimsiriwattana and S. J. Lomonaco, Jr. -- Generalized GHZ
states and distributed quantum computing
Series: Contemporary Mathematics, Volume: 381
Publication Year: 2005
ISBN: 0-8218-3600-5
Paging: 147 pp.
Binding: Softcover
Expected publication date is September 9, 2005
Description
This book introduces mathematicians to the fascinating
mathematical interplay between ideas from stochastics and
information theory and practical issues in studying complex
multiscale nonlinear systems. It emphasizes the serendipity
between modern applied mathematics and applications where
rigorous analysis, the development of qualitative and/or
asymptotic models, and numerical modeling all interact to explain
complex phenomena.
After a brief introduction to the emerging issues in multiscale
modeling, the book has three main chapters. The first chapter is
an introduction to information theory with novel applications to
statistical mechanics, predictability, and Jupiter's Red Spot for
geophysical flows. The second chapter discusses new mathematical
issues regarding fluctuation-dissipation theorems for complex
nonlinear systems including information flow, various
approximations, and illustrates applications to various
mathematical models. The third chapter discusses stochastic
modeling of complex nonlinear systems. After a general
discussion, a new elementary model, motivated by issues in
climate dynamics, is utilized to develop a self-contained example
of stochastic mode reduction.
Based on A. Majda's Aisenstadt lectures at the University of
Montreal, the book is appropriate for both pure and applied
mathematics graduate students, postdocs and faculty, as well as
interested researchers in other scientific disciplines. No
background in geophysical flows is required.
About the authors: Andrew Majda is a member of the National
Academy of Sciences and has received numerous honors and awards,
including the National Academy of Science Prize in Applied
Mathematics, the John von Neumann Prize of the Society of
Industrial and Applied Mathematics, the Gibbs Prize of the
American Mathematical Society, and the Medal of the College de
France. In the past several years at the Courant Institute, Majda
and a multi-disciplinary faculty have created the Center for
Atmosphere Ocean Science to promote cross-disciplinary research
with modern applied mathematics in climate modeling and
prediction. R.V. Abramov is a young researcher; he received his
PhD in 2002. M. J. Grote received his Ph.D. under Joseph B.
Keller at Stanford University in 1995.
Contents
Overview on multiscale modeling in complex nonlinear systems
Information theory, predictability, Jupiter's great red spot, and
equilibrium statistical mechanics
The fluctuation-dissipation theorem for complex nonlinear systems
Mathematical strategies for stochastic mode reduction in climate
Details:
Series: CRM Monograph Series, Volume: 25
Publication Year: 2005
ISBN: 0-8218-3843-1
Paging: approximately 144 pp.
Binding: Hardcover
Expected publication date is September 8, 2005
Description
Computer-Aided Design and Manufacturing (CAD/CAM) is concerned
with all aspects of the process of designing, prototyping,
manufacturing, inspecting, and maintaining complex geometric
objects under computer control. The DIMACS Center (Piscataway, NJ)
sponsored a workshop to further promote the interaction between
these two fields. Attendees from academia, research laboratories,
and industry took part in the invited talks, contributed
presentations, and informal discussions. This volume is an
outgrowth of that meeting.
Topics covered in this volume include geometric modeling,
computational topology, computational metrology, geometric
constraint solving, part immobilization, geometric aspects of
machining, layered manufacturing, and algebraic methods.
The book is suitable for graduate students and researchers
interested in geometric and algorithmic aspects of computer-aided
design and manufacturing.
Contents
I. Boier-Martin, D. Zorin, and F. Bernardini -- A survey of
subdivision-based tools for surface modeling
T. K. Dey -- Sample based geometric modeling
D. Blackmore, Y. Mileyko, M. C. Leu, W. C. Regli, and W. Sun --
Computational topology and swept volumes
V. Srinivasan -- Elements of computational metrology
M. Sitharam -- Combinatorial approaches to geometric constraint
solving: Problems, progress and directions
A. F. van der Stappen -- Immobilization: Analysis, existence, and
output-sensitive synthesis
R. Janardan and M. Smid -- Geometric algorithms for layered
manufacturing
P. Singh and D. Dutta -- A process planning framework for multi-direction
layered deposition
T. Kim and S. E. Sarma -- Machinability: Geometric reasoning for
cutting
D. Misra, V. Sundararajan, and P. K. Wright -- Zig-zag tool path
generation for sculptured surface finishing
I. Z. Emiris and I. S. Kotsireas -- Implicitization exploiting
sparseness
J. Keyser, K. Ouchi, and J. M. Rojas -- The exact rational
univariate representation for detecting degeneracies
W. R. Franklin -- Mass properties of the union of millions of
identical cubes
Details:
Series: DIMACS: Series in Discrete Mathematics and Theoretical
Computer Science, Volume: 67
Publication Year: 2005
ISBN: 0-8218-3628-5
Paging: approximately 352 pp.