August 2004 | Hardback | 400 pages 163 line diagrams 65 half-tones
6 tables 110 figures | ISBN: 0-88385-546-1
Covering a span of almost 4000 years, from the ancient
Babylonians to the eighteenth century, this collection chronicles
the enormous changes in mathematical thinking over this time, as
viewed by distinguished historians of mathematics from the past
and the present. Each of the four sections of the book (Ancient
Mathematics, Medieval and Renaissance Mathematics, The
Seventeenth Century, The Eighteenth Century) is preceded by a
Foreword, in which the articles are put into historical context,
and followed by an Afterword, in which they are reviewed in the
light of current historical scholarship. In more than one case,
two articles on the same topic are included, to show how
knowledge and views about the topic changed over the years. This
book will be enjoyed by anyone interested in mathematics and its
history - and in particular by mathematics teachers at secondary,
college, and university levels.
August 2004 | Hardback | 280 pages 60 line diagrams 85 half-tones
46 exercises 30 figures | ISBN: 0-88385-73-67
Where did maths come from? Who thought up all those algebra
symbols, and why? What's the story behind … negative numbers?
… the metric system? … quadratic equations? … sine and
cosine? The 25 independent sketches in Math through the Ages
answer these questions and many others in an informal, easygoing
style that's accessible to teachers, students, and anyone who is
curious about the history of mathematical ideas. Each sketch
contains Questions and Projects to help you learn more about its
topic and to see how its main ideas fit into the bigger picture
of history. The 25 short stories are preceded by a 56-page bird's-eye
overview of the entire panorama of mathematical history, a
whirlwind tour of the most important people, events, and trends
that shaped the mathematics we know today. Reading suggestions
after each sketch provide starting points for readers who want to
pursue a topic further.
Reviews
‘This is a beautiful and important book, a pleasure to read, in
which the history recounted fully illuminates the mathematical
ideas, and the ideas themselves are superbly explained: a
wonderful accomplishment.’ Barry Mazur, Harvard University
August 2004 | Paperback | 150 pages 60 line diagrams 37 tables
119 exercises 26 worked examples | ISBN: 0-88385-734-0
Contains supplementary exercises and projects designed to
facilitate students・understanding of the fundamental concepts
in real analysis, a subject notoriously hard for beginners. The
exercises can be used in a number of ways: to motivate a lecture;
to serve as a basis for in-class activities; in lab sessions
where students work in small groups and submit reports of their
investigations. For the last of these, programs in Maple are
supplied with further ancillary material available via from http://www.saintmarys.edu/~jsnow/maplets.html.
August 2004 | Paperback | 240 pages 64 line diagrams 59 tables
48 figures | ISBN: 0-88385-037-0
This book traces a remarkable path of mathematical connections
through seemingly disparate topics. Frustrations with a 1940’s
electro-mechanical computer at a premier research laboratory
begin this story. Subsequent mathematical methods of encoding
messages to ensure correctness when transmitted over noisy
channels led to discoveries of extremely efficient lattice
packings of equal-radius balls, especially in 24-dimensional
space. In turn, this highly symmetric lattice, with each point
neighbouring exactly 196,560 other points, suggested the possible
presence of new simple groups as groups of symmetries. Indeed,
new groups were found and are now part of the ‘Enormous Theorem’
- the classification of all simple groups whose entire proof runs
to some 10,000+ pages. And these connections, along with the
fascinating history and the proof of the simplicity of one of
those ‘sporadic’ simple groups, are presented at an
undergraduate mathematical level.
Reviews
‘Thompson provides an excellent example of the constant
interaction between applied and theoretical mathematics. Thompson’s
work is first-rate historical research and good clear writing. As
a mathematics teacher, he has gone to great pains to make the
material understandable to anyone with even a casual acquaintance
with vector spaces and groups.’ Annals of the History of
Computing
August 2004 | Hardback | 200 pages 40 exercises | ISBN: 0-88385-036-2
The foundations of mathematics include mathematical logic, set
theory, recursion theory, model theory, and Godel’s
incompleteness theorems. Professor Wolf provides here a guide
that any interested reader with some post-calculus experience in
mathematics can read, enjoy, and learn from. It could also serve
as a textbook for courses in the foundations of mathematics, at
the undergraduate or graduate level. The book is deliberately
less structured and more user-friendly than standard texts on
foundations, so will also be attractive to those outside the
classroom environment wanting to learn about the subject.
(Hardback)
0-19-853099-4
Publication date: September 2004
500 pages, 246mm x 189mm
Collection of works from Professor Sir Michael Atiyah, one of the
eminent mathematicians of the 20th century, Fields Medallist and
winner of the Abel Prize 2004
Includes key papers from 1987 to 2003
Description
This is volume six in the series of collected works from
Professor Sir Michael Atiyah, one of the eminent mathematicians
of the 20th century and Fields Medallist. It contains a selection
of his publications since 1987, including his work on skyrmions,
"Atiyah's axioms" for topological quantum field
theories, monopoles, knots, K-theory, equivariant problems, point
particles, and M-theory.
Readership: Research and graduate mathematicians and theoretical
physicists
(Hardback)
0-19-853068-4
Publication date: September 2004
200 pages, 234mm x 156mm
Series: Oxford Lecture Series in Mathematics and Its Applications
First text in exciting and developing field of mathematics
Etingof is an internationally recognized leader in this field
Description
The text is based on an established graduate course given at MIT
that provides an introduction to the theory of the dynamical Yang-Baxter
equation and its applications, which is an important area in
representation theory and quantum groups. The book, which
contains many detailed proofs and explicit calculations, will be
accessible to graduate students of mathematics, who are familiar
with the basics of representation theory of semisimple Lie
algebras.
Readership: Graduate students and researchers in related
representation theory, theory of special functions, algebra,
integrable systems, and quantum field theory.
Contents/contributors
0 Preface
1 Introduction
2 Background material
3 Intertwiners, fusion and exchange operators for Lie algebras
4 Quantum groups
5 Intertwiners, fusion and exchange operators for U q (g)
6 Dynamical R-matrices and integrable systems
7 Traces of intertwiners for U q (g)
8 Traces of intertwiners and Macdonald polynomials
9 Dynamical Weyl group