Bruno Poizat, Universite Claude Bernard, Villeurbanne, France
Stable Groups
Expected publication date is June 15, 2001
From a review of the French edition:
"This is a beautiful book in which almost everything known about stable groups appears."
-- Zentralblatt fur Mathematik
Description
This is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemporary mathematical logic to the model-theoretic study of groups, i.e., into
what can be said about groups, and for that matter, about all the traditional algebraic objects.
The author introduces the groups of finite Morley rank (those satisfying the most restrictive assumptions from the point of view of logic), and highlights their resemblance to algebraic groups, of which they are the prototypes. (All the necessary prerequisites from algebraic geometry are included in the book.) Then,
whenever possible, generalizations of properties of groups of finite Morley type to broader classes of superstables and stable groups are described.
The exposition in the first four chapters can be understood by mathematicians who have some knowledge of logic (model theory). The last three chapters are intended for specialists in mathematical logic.
Contents
A couple of words about groups
Introduction
Chain
Structure
Fields
Geometry
Generics
Rank
Weight
Bibliography
Index
Postscript: Thirteen years later
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Mathematical Surveys and Monographs, Volume: 87
Publication Year: 2001
ISBN: 0-8218-2685-9
Paging: approximately 132 pp.
Binding: Hardcover
Edited by: Alfred G. Noel, University of Massachusetts, Boston, MA,
Earl Barnes, Georgia Institute of Technology, Atlanta, GA,
and Sonya A. F. Stephens, Florida A & M University, Tallahassee, FL
Council for African American Researchers in the Mathematical Sciences: Volume III
Expected publication date is June 7, 2001
Description
This volume presents research and expository papers presented at the third and fifth meetings of the Council for African American Researchers in the Mathematical Sciences (CAARMS). The CAARMS is a group dedicated to organizing an annual conference that showcases the current research primarily, but not exclusively, of African Americans in the mathematical sciences, including mathematics, operations research, statistics, and computer science. Held annually since 1995, significant numbers of researchers have presented their current work in hour-long technical presentations, and graduate students have presented their work in organized poster sessions. The events create an ideal forum for mentoring and networking where attendees can meet researchers and graduate students interested in the same fields.
For volumes based on previous CAARMS proceedings, see African Americans in Mathematics II (Volume 252 in the AMS series, Contemporary Mathematics), and African Americans in Mathematics (Volume 34 in the AMS series, DIMACS).
Contents
Research and expository papers
E. R. Barnes -- A lower bound for the chromatic number of a graph
M. R. Currie and E. H. Goins -- The fractional parts of $\frac NK$
D. E. Davenport -- Ultrafilters and Ramsey theory
E. H. Goins -- Artins' conjecture and elliptic curves
C. Graham -- Chaoticity results for "join the shortest queue"
J. S. Ivy and S. M. Pollock -- Maintenance of deteriorating machines with probabilistic monitoring and silent failures
B. V. Saunders -- The application of numerical grid generation to problems in computational fluid dynamics
D. Stephens and G. Howell -- The elementary residual method
M. Y. Stephens and Z. Liu -- The response of the upper ocean to surface buoyancy forcing: A characteristic solution to wave propagation
S. A. F. Stephens and V. Lakshmikantham -- An overview of integro-differential equations and variational Lyapunov method
Papers on philosophy of mathematics
J. P. King -- The art of mathematics
W. A. Massey -- Mathematics is four dimensional
Tutorials
S. W. Williams -- Compact! A tutorial
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, Volume: 275
Publication Year: 2001
ISBN: 0-8218-2141-5
Paging: approximately 184 pp.
Binding: Softcover
Dmitri Burago, Pennsylvania State University, University Park, PA, and Yuri Burago
and Sergei Ivanov, Steklov Institute of Mathematics, St. Petersburg, Russia
A Course in Metric Geometry
Expected publication date is July 7, 2001
Description
"Metric geometry" is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations.
The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and
Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with "easy-to-touch"
mathematical objects using "easy-to-visualize" methods.
The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of exposition.
Contents
Metric Spaces
Length Spaces
Constructions
Spaces of Bounded Curvature
Smooth Length Structures
Curvature of Riemannian Metrics
Space of Metric Spaces
Large-scale Geometry
Spaces of Curvature Bounded Above
Spaces of Curvature Bounded Below
Bibliography
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Graduate Studies in Mathematics,
Publication Year: 2001
ISBN: 0-8218-2129-6
Paging: 417 pp.
Binding: Hardcover
Sigurdur Helgason, Massachusetts Institute of Technology, Cambridge, MA
Differential Geometry, Lie Groups, and Symmetric Spaces
Expected publication date is July 15, 2001
From reviews for the First Edition:
"A great book ... a necessary item in any mathematical library."
-- S. S. Chern, University of California
"Written with unmatched lucidity, systematically, carefully, beautifully."
-- S. Bochner, Princeton University
"Helgason's monograph is a beautifully done piece of work and should be extremely useful for several years to come, both in teaching and in research."
-- D. Spencer, Princeton University
"A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics."
-- Barrett O'Neill, University of California
"Renders a great service in permitting the non-specialist, with a minimum knowledge of differential geometry and Lie groups, an initiation to the theory of symmetrical
spaces."
-- H. Cartan, Secretariat Mathematique, Paris
"The mathematical community has long been in need of a book on symmetric spaces. S. Helgason has admirably satisfied this need with his book, DifferentialGeometry and Symmetric Spaces. It is a remarkably well-written book ... a masterpiece of concise, lucid mathematical exposition ... it might be used as a textbook
for "how to write mathematics"."
-- Louis Auslander
"[The author] will earn the gratitude of many generations of mathematicians for this skillful, tasteful, and highly efficient presentation. It will surely become a classic."
-- G. D. Mostow, Yale University
Description
The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis
either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material.
Helgason begins with a concise, self-contained introduction to differential geometry. He then introduces Lie groups and Lie algebras, including important results on their structure. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the
classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbf{C}$ and Cartan's classification of simple Lie algebras over $\mathbf{R}$.
The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All the problems have either solutions or substantial hints, found at the back of the book.
For this latest edition, Helgason has made corrections and added helpful notes and useful references. The sequels to the present book are published in the AMS's Mathematical Surveys and Monographs Series: Groups and Geometric Analysis, Volume 83, and Geometric Analysis on Symmetric Spaces, Volume 39.
Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.
Contents
Elementary differential geometry
Lie groups and Lie algebras
Structure of semisimple Lie algebras
Symmetric spaces
Decomposition of symmetric spaces
Symmetric spaces of the noncompact type
Symmetric spaces of the compact type
Hermitian symmetric spaces
Structure of semisimple Lie groups
The classification of simple Lie algebras and of symmetric spaces
Solutions to exercises
Some details
Bibliography
List of notational conventions
Symbols frequently used
Index
Reviews for the first edition
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Graduate Studies in Mathematics,
Publication Year: 2001
ISBN: 0-8218-2848-7
Paging: 641 pp.
Binding: Hardcover