Böcker utgivna av American Mathematical Society

Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. This book presents an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. It is suitable for a year-long graduate course.

Focuses on the fundamentals of a theory, which is an analog of affine algebraic geometry for partial differential equations. This work describes applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants and variational calculus.

Treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. This book covers a wide range of topics of modern coordinate-free differential geometry.

An introduction to stochastic processes studying certain elementary continuous-time processes. It includes a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps.

Deals with the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics.

Mathematicians are expected to publish their work: in journals, conference proceedings, and books. It is vital to advancing their careers. This is a guidebook to publishing mathematics. It describes both the general setting of mathematical publishing and the specifics about the various publishing situations mathematicians may encounter.

The Ausdehnungslehre of 1862 is Grassmann's mature presentation of his extension theory. The work captured his mathematical achievements. This book includes development of the inner product and its relation to the concept of angle, the 'theory of functions' from the point of view of extension theory, and his contribution to the Pfaff problem.

Presents research on understanding, teaching, and learning mathematics at the post-secondary level. This book offers some preliminary results on student learning using technology when lessons are delivered via the Internet.

Based on courses given by the author at MIT and at Rome University in spring 1997, this book presents an introduction to algebraic aspects of conformal field theory. It includes material on the foundations of a rapidly growing area of algebraic conformal theory.

Presents the basics of linear algebra, with an emphasis on nonstandard and interesting proofs. This book features about 230 problems with solutions. It is suitable as a supplementary text for an undergraduate or graduate algebra course.

Includes a treatment of exponential, logarithmic, and trigonometric functions, progressions, and induction method, as well as an extensive introduction to differential and integral calculus.

Suitable for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum. This book contains vast theoretical and problem material in main areas of what authors consider to be 'extracurricular mathematics'.

A guide to the qualitative theory of foliations. It features topics including: analysis on foliated spaces, characteristic classes of foliations and foliated manifolds. It is suitable as a supplementary text for a topics course at the advanced graduate level.

Presents the translation from the Japanese textbook for the grade 10 course, 'Basic Mathematics'. This book covers algebra (including quadratic functions, equations, and inequalities), trigonometric functions, and plane coordinate geometry.

Covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.

Presents an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide an account of the introductory portions of this important and technically difficult subject.

Presents modern algebra. This book includes such topics as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. It is suitable for independent study for advanced undergraduates and graduate students.

Probability theory has become a convenient language and a useful tool in many areas of modern analysis. This book intends to explore part of this connection concerning the relations between Brownian motion on a manifold and analytical aspects of differential geometry. It begins with a review of stochastic differential equations on Euclidean space.

Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. This book presents a comprehensive monograph on mirror symmetry, covering the original observations by the physicists.

Offers a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. This book predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space.

In May 1974, the American Mathematical Society sponsored a special symposium on the mathematical consequences of the Hilbert problems, held at Northern Illinois University, DeKalb, Illinois. This title contains the proceedings of that symposium and includes papers corresponding to the invited addresses with one exception.

Produced under the auspices of the International Mathematical Union (IMU), this volume was born as part of the activities observing the World Mathematical Year 2000. It consists of 30 articles that also offer reflections about the amazing mathematical progress we have witnessed in this century.