Spirtes, P. /Glymour, C. /Scheines, R.

Causation, Prediction, and Search, 2nd ed.

(Adaptive Computation and Machine Learning, Series)
What assumptions and methods allow us to turn observations into causal knowledge, and how can even
incomplete causal knowledge be used in planning and prediction to influence and control our environment?
In this book Peter spirtes, Clark Glymour, and Richard Scheines address these questions us in the formalism
of Bayes networks, with results that have been applied in diverse areas of research in the social behavioral
and physical sciences. The authors show that although experimental and observational study designs may
not always permit the same inferences, they are subject to uniform principles. They axiomatize the connection
between causal structure and probabilistic independence, explore several varieties of causal indistinguishability,
formulate a theory of manipulation, and develop asymptotically reliable procedures for searching over equivalence
classes of causal models, including models of categorical data and structural equation models with and
without latent variables.
Aug. 2000 496 pp.
(M.I.T.) 0-262-19440-6

Berndt, R.

An Introduction to Symplectic Geometry.

(Graduate Studies in Mathematics, Vol. 26)
A Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology,
mathematical physics and representations of Lie groups. This book is a true introduction to symplectic
geometry, assuming only a general background in analysis and familiarity with linear algebra.
It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds
are defined and explored. In addition to the essential classic results, such as Darboux's theorem,
more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves.
These ideas have revolutionized the subject. The main examples of symplectic manifolds are given,
including the cotangent bundle, K?hler manifolds, and coadjoint orbits. Further principal ideas are
carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds.
Berndt describes some of the close connections between symplectic geometry and mathematical physics
in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old.
The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics.
This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of
the symplectic group.
2000 224 pp.
(A.M.S.) 0-8218-2056-7

Helgason, S.

Groups and Geometric Analysis
Integral Geometry, Invariant Differential Operators, and Spherical Functions.

(Published by Academic in 1984)
(Mathematical Surveys and Monographs, Series)
This volume, the second of Helgason's impressive three books on Lie groups and the geometry and analysis
of symmetric spaces, is an introduction to group-theoretic methods in analysis on spaces with a group action.
The first chapter deals with the three two-dimensional spaces of constant curvature, requiring only elementary methods and no Lie theory. It is remarkably accessible and would be suitable for a first-year graduate course.
The remainder of the book covers more advanced topics, including the work of Harish-Chandra and others,
but especially that of Helgason himself. Indeed, the exposition can be seen as an account of the author's
tremendous contributions to the subject.
Chapter I deals with modern integral geometry and Radon transforms.
The second chapter examines the interconnection between Lie groups and differential operators.
Chapter IV develops the theory of spherical functions on semisimple Lie groups with a certain degree of completeness, including a study of Harish-Chandra's c-function. The treatment of analysis on compact symmetric spaces (Chapter V) includes some finite-dimensional representation theory for compact Lie groups and Fourier analysis on compact groups.
Each chapter ends with exercises (with solutions given at the end of the book!) and historical notes.
2000 573 pp.
(A.M.S.) 0-8218-2673-5

Mcconnel, J. /Robson, J.

Noncomutative Noetherian Rings

(Published by John Wiley in 1987)
(Graduate Studies in Mathematics, Series)
From reviews of the first edition.... model of mathematical writing, as perfectly written a mathematics
book as I have seen ... It can be profitably read by non-experts... an almost perfectly conceiv-ed account
of major developments and general methods... will remain a basic reference for many years... ? ?
Bulletin of the AMS This is a reprinted edition of a work that was considered the definitive account in
the subject area upon its initial publication by J. Wiley & Sons in 1987. It presents, within a wider context,
a comprehensive account of noncommutative Noetherian rings. The author covers the major developments from the 1950s,
stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras,
PI rings, differential operators, and localization theory.
2000 616 pp.
(A.M.S.) 0-8218-2169-5

Tondeur, P. (ed. ):

Collected Papers of K. T. Chen.

(Contemporary Matheamticians, Series)
Kuo-Tsai Chen (1923-1987) is best known to the mathematics
community for his work on iterated integrals and power series
connections in conjunction with his research on the cohomology
of loop spaces. His work is intimately related to the theory of
minimal models as developed by Dennis Sullivan, whose own work
was in part inspired by the research of Chen.
The present volume is a comprehensive collection of Chen's
mathematical publications preceded by an article,
The Life and Work of K. T. Chen?, placing his work and research
interest into their proper context and demonstrating the power
and scope of his influence.
Oct. 2000 735 pp.
3-7643-4005-3 Birkhauser

Lang, S. /Jorgensen, J.:

Collected Papers, Vol. V : 1993- 1999

Serge Lang is one of the top mathematicians of our time.
He was honored with the Cole Prize by the American Mathematical Society
as well as with the Prix Carriere by the French Academy of Sciences.
In these five volumes many of his research papers are collected.

Sep. 2000 410 pp.
0-387-95030-3 13,960.
Springer