Empires of Time
by Peter Galison
0-393-02001-0 256pp. 46 illustrations 2003/5 cloth
膨大な理論的突破口となった相対性理論にとって欠くべからざる現実世界のバックグランドになったものは19世紀後半の幾つかの難題：時計と列車、電信と植民地の支配であろう。
近代科学の基礎にあった二人の巨人は、一歩一歩とその回答に向かってそれぞれに歩みを進めていた。一人は若く無名のドイツ物理学者アルバート・アインシュタインで、電信ネットワークを使うことと、汽車の停留場にある時計の時間調整をとおして時を計測する実験を行っていた。もう一人は、高名な数学者にしてフランスロンジチュード局長であるポワンカレーで、大陸を跨いで時を調整する地図をつくっていた。
そして、両者ともに新しい地球的世界を理解するには、ピュアなとき（純粋な時）というのが存在するのか否か、そのピュアなときの同時性は絶対的なものであるのか、それとも”時“というのは相対的なものであるのかを決する必要があると発見していた。
高名な科学史家ピーター・ギャリソンは滅多に目にふれることのない多数の写真。忘れ去られらパテント、これまで手のついていないアーカイブなどから新しい情報を拾いだし二人の魅力的な科学者が具体的で、専門的な興味に嵌って“時の帝国”を征服する理論へと静かなレースを進めるさまを語ってくれます。
著者は大学のHistory of Science and Physicsの
Mallinckrodt教授である。MacArthur Fellowshipと Max Planck
賞の受賞者。また、科学史で最も優れた書に送られるPfizer
賞をImage and Logic で受賞している。
Series : Lecture Notes in Mathematics, Vol. 1848
2004, IX, 219 p., Softcover
ISBN: 3-540-22358-4
About this book
The geometry of real submanifolds in complex manifolds and the
analysis of their mappings belong to the most advanced streams of
contemporary Mathematics. In this area converge the techniques of
various and sophisticated mathematical fields such as P.D.E.s,
boundary value problems, induced equations, analytic discs in
symplectic spaces, complex dynamics. For the variety of themes
and the surprisingly good interplaying of different research
tools, these problems attracted the attention of some among the
best mathematicians of these latest two decades. They also
entered as a refined content of an advanced education. In this
sense the five lectures of this volume provide an excellent
cultural background while giving very deep insights of current
research activity.
Table of contents
Preface.- M. Abate: Angular Derivatives in Several Complex
Variables.- J.E. Fornaess: Real Methods in Complex Dynamics.- X.
Huang: Local Equivalence Problems for Real Submanifolds in
Complex Spaces.- J.-P. Rosay: Introduction to a General Theory of
Boundary Values.- A. Tumanov: Extremal Discs and the Geometry of
CR Manifolds.
Series : Lecture Notes in Mathematics , Vol. 1849
2004, X, 517 p., Softcover
ISBN: 3-540-22290-1
About this book
Heegner points on both modular curves and elliptic curves over
global fields of any characteristic form the topic of this
research monograph. The Heegner module of an elliptic curve is an
original concept introduced in this text. The computation of the
cohomology of the Heegner module is the main technical result and
is applied to prove the Tate conjecture for a class of elliptic
surfaces over finite fields, this conjecture is equivalent to the
Birch and Swinnerton-Dyer conjecture for the corresponding
elliptic curves over global fields.
Table of contents
Preface.- Introduction.- Preliminaries.- Bruhat-Tits trees with
complex multiplication.- Heegner sheaves.- The Heegner module.-
Cohomology of the Heegner module.- Finiteness of the Tate-Shafarevich
groups.- Appendix A.: Rigid analytic modular forms.- Appendix B.:
Automorphic forms and elliptic curves over function fields.-
References.- Index.
Series : Lecture Notes in Mathematics , Vol. 1850
2004, X, 301 p., Softcover
ISBN: 3-540-22360-6
About this book
The Israeli GAFA seminar (on Geometric Aspect of Functional
Analysis) during the years 2002-2003 follows the long tradition
of the previous volumes. It reflects the general trends of the
theory. Most of the papers deal with different aspects of the
Asymptotic Geometric Analysis. In addition the volume contains
papers on related aspects of Probability, classical Convexity and
also Partial Differential Equations and Banach Algebras. There
are also two expository papers on topics which proved to be very
much related to the main topic of the seminar. One is Statistical
Learning Theory and the other is Models of Statistical Physics.
All the papers of this collection are original research papers.
Series : Undergraduate Texts in Mathematics
2004, XVI, 360 p. 55 illus.
ISBN: 0-387-21375-9, Hardcover
ISBN: 0-387-21364-3, Softcover
About this textbook
The Mathematics of Finance has become a hot topic ever since the
discovery of the Black-Scholes option pricing formulas in 1973.
Unfortunately, there are very few undergraduate textbooks in this
area. This book is specifically written for advanced
undergraduate or beginning graduate students in mathematics,
finance or economics. With the exception of an optional chapter
on the Capital Asset Pricing Model, the book concentrates on
discrete derivative pricing models, culminating in a careful and
complete derivation of the Black-Scholes option pricing formulas
as a limiting case of the Cox-Ross-Rubinstein discrete model. The
final chapter is devoted to American options. The mathematics is
not watered down but is appropriate for the intended audience. No
measure theory is used and only a small amount of linear algebra
is required. All necessary probability theory is developed
throughout the book on a "need-to-know" basis. No
background in finance is required, since the book also contains a
chapter on options.
Written for:
Advanced undergraduate or beginning graduate students in
Mathematics, Finance or Economics
Table of contents
Preface.- Introduction.- Probability I: Introduction to Discrete
Probability.- Portfolio Management and the Capital Asset Pricing
Model.- Background on Options.- An Aperitif on Arbitrage.-
Probability II: More Discrete Probability.- Discrete-Time Pricing
Models.- The Cox-Ross-Rubinstein Model.- Probability III:
Continuous Probability.- The Black-Scholes Option Pricing Formula.-
Optimal Stopping and American Options.- Appendix: Convexity and
Separation.
Series : Lecture Notes in Mathematics , Vol. 1846
2004, IX, 238 p., Softcover
ISBN: 3-540-22483-1
About this book
This is the first book to provide a systematic exposition of
promising techniques for the reconstruction of small
inhomogeneities from boundary measurements. In particular,
theoretical results and numerical procedures for the inverse
problems for the conductivity equation, the Lame system, as well
as the Helmholtz equation are discussed in a readable and
informative manner. The general approach developed in this book
is based on layer potential techniques and modern asymptotic
analysis of partial differential equations. The book is
particularly suitable for graduate students in mathematics.
Series : Universitext
2004, XII, 301 p., Softcover
ISBN: 3-540-21290-6
About this textbook
Complex geometry studies (compact) complex manifolds. It
discusses algebraic as well as metric aspects. The subject is on
the crossroad of algebraic and differential geometry. Recent
developments in string theory have made it an highly attractive
area, both for mathematicians and theoretical physicists. The
author’s goal is to provide an easily accessible introduction
to the subject. The book contains detailed accounts of the basic
concepts and the many exercises illustrate the theory. Appendices
to various chapters allow an outlook to recent research
directions. Daniel Huybrechts is currently Professor of
Mathematics at the University Denis Diderot in Paris.
Table of contents
Series : Undergraduate Texts in Mathematics
2004, Approx. 215 p. 13 illus., Hardcover
ISBN: 0-387-21428-3
About this textbook
This unique textbook focuses on the structure of fields and is
intended for a second course in abstract algebra. Besides
providing proofs of the transcendence of pi and e, the book
includes material on differential Galois groups and a proof of
Hilbert's irreducibility theorem. The reader will hear about
equations, both polynomial and differential, and about the
algebraic structure of their solutions. In explaining these
concepts, the author also provides comments on their historical
development and leads the reader along many interesting paths. In
addition, there are theorems from analysis: as stated before, the
transcendence of the numbers pi and e, the fact that the complex
numbers form an algebraically closed field, and also Puiseux's
theorem that shows how one can parametrize the roots of
polynomial equations, the coefficients of which are allowed to
vary. There are exercises at the end of each chapter, varying in
degree from easy to difficult. To make the book more lively, the
author has incorporated pictures from the history of mathematics,
including scans of mathematical stamps and pictures of
mathematicians. Antoine Chambert-Loir taught this book when he
was Professor at Ecole Polytechnique, Palaiseau, France. He is
now Professor at Universite de Rennes 1.
Table of contents
Field Extensions.- Roots.- Galois Theory.- A Bit of Group Theory.-
Applications.- Algebraic Theory of Differential Equations.-
Examination Problems.- References.- Index.