Translated by Arturo Sangalli
With a foreword by Freeman Dyson
Cloth | May 2004 | ISBN: 0-691-09294-X
224 pp. | 5 x 8 | 39 line illus.
The twentieth century was a time of unprecedented
development in
mathematics, as well as in all sciences:
more theorems were
proved and results found in a hundred years
than in all of
previous history. In The Mathematical Century,
Piergiorgio
Odifreddi distills this unwieldy mass of
knowledge into a
fascinating and authoritative overview of
the subject. He
concentrates on thirty highlights of pure
and applied mathematics.
Each tells the story of an exciting problem,
from its historical
origins to its modern solution, in lively
prose free of technical
details.
Odifreddi opens by discussing the four main
philosophical
foundations of mathematics of the nineteenth
century and ends by
describing the four most important open mathematical
problems of
the twenty-first century. In presenting the
thirty problems at
the heart of the book he devotes equal attention
to pure and
applied mathematics, with applications ranging
from physics and
computer science to biology and economics.
Special attention is
dedicated to the famous "23 problems"
outlined by David
Hilbert in his address to the International
Congress of
Mathematicians in 1900 as a research program
for the new century,
and to the work of the winners of the Fields
Medal, the
equivalent of a Nobel prize in mathematics.
This eminently readable book will be treasured
not only by
students and their teachers but also by all
those who seek to
make sense of the elusive macrocosm of twentieth-century
mathematics.
Piergiorgio Odifreddi is Professor of Mathematical
Logic at the
University of Turin and has been a visiting
professor at Cornell
University for many years. He is the author
of the textbook
Classical Recursion Theory. He is also a
regular contributor to
the Italian daily La Repubblica. Freeman
Dyson, Professor
Emeritus of Physics at the Institute for
Advanced Study, is the
author of several books, including Disturbing
the Universe.
Endorsements:
"The Mathematical Century is both popular
and scholarly.
Piergiorgio Odifreddi clearly and accurately
covers many
important mathematical problems and the contributions
that
leading mathematicians have made to their
solutions. Offering a
personal but very balanced perspective, his
book is one that
amateur and professional alike can learn
from."--Sir Michael
Atiyah, Fields Medalist 1966, and former
President of the Royal
Society
"Piergiorgio Odifreddi has done a superb
job, telling the
story of twentieth-century mathematics in
one short and readable
volume."-- Freeman Dyson, Institute
for Advanced Study,
Princeton
With a new foreword by John Conway
Paper | May 2004 | ISBN: 0-691-11966-X
288 pp. | 5 x 8 | 31 line illus.
Reviews
A perennial bestseller by eminent mathematician
G. Polya, How to
Solve It will show anyone in any field how
to think straight.
In lucid and appealing prose, Polya reveals
how the mathematical
method of demonstrating a proof or finding
an unknown can be of
help in attacking any problem that can be
"reasoned"
out--from building a bridge to winning a
game of anagrams.
Generations of readers have relished Polya's
deft--indeed,
brilliant--instructions on stripping away
irrelevancies and going
straight to the heart of the problem.
Reviews:
"Every prospective teacher should read
it. In particular,
graduate students will find it invaluable.
The traditional
mathematics professor who reads a paper before
one of the
Mathematical Societies might also learn something
from the book:
'He writes a, he says b, he means c; but
it should be d.'--E. T.
Bell, Mathematical Monthly, December 1945
"[This] elementary textbook on heuristic
reasoning, shows
anew how keen its author is on questions
of method and the
formulation of methodological principles.
Exposition and
illustrative material are of a disarmingly
elementary character,
but very carefully thought out and selected."--Herman
Weyl,
Mathematical Review, October 1948
"I recommend it highly to any person
who is seriously
interested in finding out methods of solving
problems, and who
does not object to being entertained while
he does it."--Scientific
Monthly
"Any young person seeking a career in
the sciences would do
well to ponder this important contribution
to the teacher's art."--A.
C. Schaeffer, American Journal of Psychology,
April 1946
Cloth | June 2004 | ISBN: 0-691-11953-8
224 pp. | 6 x 9
Elliptic equations of critical Sobolev growth
have been the
target of investigation for decades because
they have proved to
be of great importance in analysis, geometry,
and physics. The
equations studied here are of the well-known
Yamabe type. They
involve Schrodinger operators on the left
hand side and a
critical nonlinearity on the right hand side.
A significant development in the study of
such equations occurred
in the 1980s. It was discovered that the
sequence splits into a
solution of the limit equation--a finite
sum of bubbles--and a
rest that converges strongly to zero in the
Sobolev space
consisting of square integrable functions
whose gradient is also
square integrable. This splitting is known
as the integral theory
for blow-up. In this book, the authors develop
the pointwise
theory for blow-up. They introduce new ideas
and methods that
lead to sharp pointwise estimates. These
estimates have important
applications when dealing with sharp constant
problems (a case
where the energy is minimal) and compactness
results (a case
where the energy is arbitrarily large). The
authors carefully and
thoroughly describe pointwise behavior when
the energy is
arbitrary.
Intended to be as self-contained as possible,
this accessible
book will interest graduate students and
researchers in a range
of mathematical fields.
Olivier Druet is Researcher at CNRS, Ecole
Normale Superieure de
Lyon. Emmanuel Hebey is Professor at Universite
de Cergy-Pontoise.
Frederic Robert is Associate Professor at
Universite de Nice
Sophia-Antipolis.
Endorsement:
"This is an important and original work.
It develops
critical new ideas and methods for the analysis
of elliptic PDEs
on compact manifolds, especially in the framework
of the Yamabe
equation, critical Sobolev embedding, and
blow-up techniques.
This volume will have an important influence
on current research."--William
Beckner, University of Texas at Austin
Series: Mathematical Notes
With a new introduction by Harold Kuhn and
an afterword by
Ariel Rubinstein
60th Anniversary Edition
Cloth | June 2004 | ISBN: 0-691-11993-7
704 pp. | 6 x 9
This is the classic work upon which modern-day
game theory is
based. What began more than sixty years ago
as a modest proposal
that a mathematician and an economist write
a short paper
together blossomed, in 1944, when Princeton
University Press
published Theory of Games and Economic Behavior.
In it, John von
Neumann and Oskar Morgenstern conceived a
groundbreaking
mathematical theory of economic and social
organization, based on
a theory of games of strategy. Not only would
this revolutionize
economics, but the entirely new field of
scientific inquiry it
yielded--game theory--has since been widely
used to analyze a
host of real-world phenomena from arms races
to optimal policy
choices of presidential candidates, from
vaccination policy to
major league baseball salary negotiations.
And it is today
established throughout both the social sciences
and a wide range
of other sciences.
This sixtieth anniversary edition includes
not only the original
text but also an introduction by Harold Kuhn,
an afterword by
Ariel Rubinstein, and reviews and articles
on the book that
appeared at the time of its original publication
in the New York
Times, the Journal of Economic Perspectives,
and a variety of
other publications. Together, these writings
provide readers a
matchless opportunity to more fully appreciate
a work whose
influence will yet resound for generations
to come.
John von Neumann (1903-1957) was one of the
greatest
mathematicians of the twentieth century and
a pioneering figure
in computer science. A native of Hungary
who held professorships
in Germany, he was appointed Professor of
Mathematics at the
Institute for Advanced Study (IAS) in 1933.
Later he worked on
the Manhattan Project, helped develop the
IAS computer, and was a
consultant to IBM. An important influence
on many fields of
mathematics, he is the author of Continuous
Geometry, Functional
Operators (two volumes), and Mathematical
Foundations of Quantum
Mechanics (all Princeton). Oskar Morgenstern
(1902-1977) taught
at the University of Vienna and directed
the Austrian Institute
of Business Cycle Research before settling
in the United States
in 1938. There he joined the faculty of Princeton
University,
eventually becoming a professor and from
1948 directing its
econometric research program. He advised
the United States
government on a wide variety of subjects.
Though most famous for
the book he co-authored with von Neumann,
Morgenstern was also
widely known for his skepticism about economic
measurement, as
reflected in one of his many other books,
On the Accuracy of
Economic Observations (Princeton). Harold
Kuhn is Professor
Emeritus of Mathematical Economics at Princeton
University. Ariel
Rubinstein is Professor of Economics at Tel
Aviv University and
at New York University.
Reviews:
"Posterity may regard this book as one
of the major
scientific achievements of the first half
of the twentieth
century. This will undoubtedly be the case
if the authors have
succeeded in establishing a new exact science--the
science of
economics. The foundation which they have
laid is extremely
promising."--The Bulletin of the American
Mathematical
Society
"One cannot but admire the audacity
of vision, the
perseverance in details, and the depth of
thought displayed in
almost every page of the book. . . . The
appearance of a book of
[this] calibre . . . is indeed a rare event."--The
American
Economic Review
"The main achievement of the book lies,
more than in its
concrete results, in its having introduced
into economics the
tools of modern logic and in using them with
an astounding power
of generalization."--The Journal of
Political Economy