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The Białowieża workshops on Geometric Methods in Physics, taking
place in the unique environment of the Białowieża natural forest in
Poland, are among the important meetings in the field. Every year
some 80 to 100 participants both from mathematics and physics join
to discuss new developments and to interchange ideas. The current
volume was produced on the occasion of the XXXI meeting in 2012.
For the first time the workshop was followed by a... more...

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... more...

This textbook is distinguished from other texts on the subject by
the depth of the presentation and the discussion of the calculus
of moving surfaces, which is an extension of tensor calculus to
deforming manifolds.
Designed for advanced undergraduate and graduate students, this
text invites its audience to take a fresh look at previously
learned material through the prism of tensor calculus. Once the
framework is... more...

This book is about dynamical aspects of ordinary differential
equations and the relations between dynamical systems and certain
fields outside pure mathematics. A prominent role is played by the
structure theory of linear operators on finite-dimensional vector
spaces; the authors have included a self-contained treatment of
that subject.

This text uses the concepts usually taught in the first
semester of a modern abstract algebra course to illuminate
classical number theory: theorems on primitive roots, quadratic
Diophantine equations, and the Fermat conjecture for exponents
three and four. The text contains abundant numerical examples
and a particularly helpful collection of exercises.

Ausgehend von einer grundlegenden Einführung in Begriffe und
Methoden der Algebra werden im Buch die wesentlichen Ergebnisse
dargestellt und ein Einblick in viele Entwicklungen innerhalb der
Algebra gegeben, die mit anderen Gebieten der Mathematik stark
verflochten sind.
Beginnend mit Begriffsbildungen wie Gruppe und Ring führt das
Buch hin zu den Körpererweiterungen und der Galoistheorie. Danach
werden zentrale Teile der Theorie... more...

Presents up-to-date Banach space results.
* Features an extensive bibliography for outside reading.
* Provides detailed exercises that elucidate more introductory
material.

This book consists of three parts, rather different in level and
purpose. The first part was originally written for quantum
chemists. It describes the correspondence, due to Frobenius,
between linear representations and characters. The second part is
a course given in 1966 to second-year students of l’Ecole
Normale. It completes in a certain sense the first part. The
third part is an introduction to Brauer Theory.

Since they first arose in the 1970s and early 1980s, quantum groups
have proved to be of great interest to mathematicians and
theoretical physicists. This book gives a comprehensive view of
quantum groups and their applications. The authors build on a
self-contained account of the foundations of the subject and go on
to treat the more advanced aspects concisely and with detailed
references to the literature. Researchers in mathematics and
theoretical... more...