This eminently readable book focuses on the
people of
mathematics and draws the reader into their
fascinating world. In
a monumental address, given to the International
Congress of
Mathematicians in Paris in 1900, David Hilbert,
perhaps the most
respected mathematician of his time, developed
a blueprint for
mathematical research in the new century.
Jokingly called a
natural introduction to thesis writing with
examples, this
collection of problems has indeed become
a guiding inspiration to
many mathematicians, and those who succeeded
in solving or
advancing their solutions form an Honors
Class among research
mathematicians of this century.
In a remarkable labor of love and with the
support of many of the
major players in the field, Ben Yandell has
written a fascinating
account of the achievements of this Honors
Class, covering
mathematical substance and biographical aspects.
Year: 2003 ISBN: 1-56881-216-7
486 pages. Paperback.
Expected publication date is January 15,
2004
Description
The formative years of the American Mathematical
Society
coincided with a time of remarkable development
in mathematics.
During this period, the Bulletin of the American
Mathematical
Society and its predecessor, The Bulletin
of the New York
Mathematical Society, served as a primary
vehicle for reporting
mathematics to American mathematicians. As
a result, some of the
most important and fundamental work of early
twentieth-century
mathematics found its way into the Bulletin.
Milestone articles
include Hilbert's problems presented at the
1900 Paris
International Congress of Mathematicians
(ICM), Poincare's 1904
lecture on the future of mathematical physics
(with commentary
suggesting that he was tantalizingly close
to capturing the
notion of relativity), and Klein's Erlangen
program; all of these
articles received added publicity when the
first English
translation was published in the Bulletin.
This book reproduces these and other well-written
articles from
the early Bulletin, offering readers the
best way to experience a
slice of that time. Other articles in the
book include, in
particular, a report to American mathematicians
about what
happened at that important 1900 ICM meeting
and three articles
from the scientific portion of the 1904 centennial
celebration of
the Louisiana Purchase: Darboux describing
the development of
geometry, Pierpont focusing on nineteenth-century
mathematics,
and Poincare emphasizing the significance
of mathematical physics.
Accompanying the transition from the nineteenth
to twentieth
century was that new important thing called
"mathematical
rigor". Included is an article by Klein
reflecting the
beliefs of the time with his promotion of
rigor.
These are just some of the many topics characterizing
the early
days of the developing American mathematical
community. The book
offers a captivating review of mathematics
through the early
years of the Bulletin.
Contents
D. G. Saari -- Introduction
D. G. Saari -- Spirit of the time
J. Pierpont -- The history of mathematics
in the nineteenth
century
F. Cajori -- Evolution of criteria of convergence
C. A. Scott -- The International Congress
of Mathematicians in
Paris
M. G. Darboux -- A survey of the development
of geometric methods
D. G. Saari -- Fifth degree polynomials
J. Pierpont -- Lagrange's place in the theory
of substitutions
J. Pierpont -- On the Ruffini-Abelian theorem
J. Pierpont -- Early history of Galois' theory
of equations
D. G. Saari -- Henri Poincare
E. W. Brown -- Poincare's mecanique celeste
H. Poincare -- The relations of analysis
and mathematical physics
H. Poincare -- The present and the future
of mathematical physics
D. G. Saari -- Felix Klein
F. Klein -- A comparative review of recent
researches in geometry
F. Klein -- The arithmetizing of mathematics
F. Klein -- Riemann and his significance
for the development of
modern mathematics
D. G. Saari -- David Hilbert
H. Poincare -- Review of Hilbert's "Foundations
of geometry"
D. Hilbert -- Mathematical problems
Details:
Publication Year: 2003
ISBN: 0-8218-2672-7
Paging: 326 pp.
Binding: Softcover
Expected publication date is February 27,
2004
Description
"[In the book] we are dealing with a
theme which cuts across
the mathematics courses classically taught
in the first four
years of college. Thus it offers the reader
the opportunity to
learn, review and give long-term thought
to the concepts covered
in these programmes by following the guiding
thread of this
favoured number."
--from the Preface
This is a clever, beautiful book. The authors
trace the thread of
$\pi$ through the long history of mathematics.
In so doing, they
touch upon many major subjects in mathematics:
geometry (of
course), number theory, Galois theory, probability,
transcendental numbers, analysis, and, as
their crown jewel, the
theory of elliptic functions, which connects
many of the other
subjects.
By this device, the authors provide a tour
through mathematics,
one that mathematicians of all levels, amateur
or professional,
may appreciate. In many cases, the tour visits
well-known topics
from particular special interest groups.
Remarkably, $\pi$ is
often found at the places of deepest beauty.
The volume includes many exercises with detailed
solutions.
Anyone from undergraduate mathematics majors
through university
professors will find many things to enjoy
in this book.
Contents
Measurement of the circle
Wallis's formula and some others
Euler, Euler again, always Euler
Squaring the circle
$\pi$ and elliptic integrals
Solutions to the exercises
Bibliography
Index
Details:
Publication Year: 2004
ISBN: 0-8218-3246-8
Paging: approximately 322 pp.
Binding: Softcover
Expected publication date is March 11, 2004
Description
This book brings the beauty and fun of mathematics
to the
classroom. It offers serious mathematics
in a lively, reader-friendly
style. Included are exercises and many figures
illustrating the
main concepts.
The first chapter talks about the theory
of trigonometric and
elliptic functions. It includes subjects
such as power series
expansions, addition and multiple-angle formulas,
and arithmetic-geometric
means. The second chapter discusses various
aspects of the
Poncelet Closure Theorem. This discussion
illustrates to the
reader the idea of algebraic geometry as
a method of studying
geometric properties of figures using algebra
as a tool.
This is the second of three volumes originating
from a series of
lectures given by the authors at Kyoto University
(Japan). It is
suitable for classroom use for high school
mathematics teachers
and for undergraduate mathematics courses
in the sciences and
liberal arts. The first volume is available
as Volume 19 in the
AMS series, Mathematical World. A third volume
is forthcoming.
Contents
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
Details:
Series: Mathematical World, Volume: 20
Publication Year: 2004
ISBN: 0-8218-3283-2
Paging: approximately 131 pp.
Binding: Softcover
Expected publication date is March 6, 2004
Description
Over the last ten years, the theory of Bergman
spaces has
undergone a remarkable metamorphosis. In
a series of major
advances, central problems once considered
intractable were
solved, and a rich theory emerged. Although
progress continues,
the time seems ripe for a full and unified
account of the
subject, weaving the old and new results
together. This thorough
exposition provides just that.
The subject of Bergman spaces is a masterful
blend of complex
function theory with functional analysis
and operator theory. It
has much in common with Hardy spaces, but
involves new elements
such as hyperbolic geometry, reproducing
kernels, and biharmonic
Green functions.
In this book, the authors develop background
material and provide
a self-contained introduction to a broad
range of topics,
including recent advances on interpolation
and sampling,
contractive zero-divisors, and invariant
subspaces. The book is
accessible to researchers and advanced graduate
students who have
studied basic complex function theory, measure
theory, and
functional analysis.
Contents
Overview
The Bergman kernel function
Linear space properties
Analytic properties
Zero-sets
Contractive zero-divisors
Sampling and interpolation
Proofs of sampling and interpolation theorems
Invariant subspaces
Structure of invariant subspaces
References
Index
Details:
Series: Mathematical Surveys and Monographs,Volume:
100
Publication Year: 2004
ISBN: 0-8218-0810-9
Paging: approximately 328 pp.
Binding: Hardcover