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.

This work is based on the notes from the graduate course given by the author at Rutgers University in the fall of 1994 and the spring of 1995. The main goal of the book is to acquaint the reader with various perspectives of the theory of automorphic forms. In addition to detailed and often nonstandard exposition of familiar topics of the theory, particular attention is paid to such subjects as theta-functions and representations by quadratic forms.

Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills. The mathematics involved in modern finance springs from the heart of probability and analysis, for example: the It calculus, stochastic control, differential equations, and martingales. The authors give rigorous treatments of these topics, while always keeping the applications in...

This is an English edition of Dixmier's book, which is the first systematic exposition of the algebraic approach to representations of Lie groups via representations of (or modules over) the corresponding universal enveloping algebras, turned out to be so well written that even today it remains one of the main textbooks and reference books on the subject. In 1992, Dixmier was awarded the Leroy P. Steele prize for expository writing in mathematics. The Committee's citation described this as one of Dixmier's extraordinary books. Written with unique precision and elegance, the book provides the...

Although the theory and applications of secondary cohomology operations are an important part of an advanced graduate-level algebraic topology course, there are few books on the subject. The AMS aims to fill that gap with the publication of this volume. The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among many applications considered are the Hopf invariant one theorem (for all primes $p$, including $p = 2$), Browder's theorem...

Explores the algebraic decidability of local classification problems, and rigidity of holomorphic foliations. This work also discusses topics such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles

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.

Probability theory has become a convenient language and a useful tool in many areas of modern analysis. The main purpose of this book is to explore part of this connection concerning the relations between Brownian motion on a manifold and analytical aspects of differential geometry. A dominant theme of the book is the probabilistic interpretation of the curvature of a manifold.

Since the first edition of this book, the Gelfand-Kirillov dimension had emerged as a useful and powerful tool for investigating non-commutative algebras. For this edition, the authors have incorporated the original text with only minor modifications. Errors have been corrected, items have been rephrased, and more mathematical expressions have been displayed for the purpose of clarity. An additional chapter provides broad overviews of the developments since the first edition, with references to the literature for details. The bibliography has been updated and accordingly, and is almost double...

This text is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups. It considers both the general theory and representation of specific groups. Representation theory is discussed on the following types of groups: finite groups of rotations, permutation groups, and classical compact semisimple Lie groups. Along the way, the structure theory of the compact semisimple Lie groups is exposed. This is aimed at research mathematicians and graduate students studying group theory.