Kategoria BISAC: Mathematics >> Algebra - Abstract

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole, presenting the subject matter in a forward-looking way that takes into account its historical development.

Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group...

Written for students taking a second or third year undergraduate course in mathematics or computer science, this book is the ideal companion to a course in enumeration. Enumeration is a branch of combinatorics where the fundamental subject matter is numerous methods of pattern formation and counting. Introduction to Enumeration provides a comprehensive and practical introduction to this subject giving a clear account of fundamental results and a thorough grounding in the use of powerful techniques and tools.

Two major themes run in parallel through the book, generating functions...

Originally published in 1985, this classic textbook is an English translation of Einfuhrung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhauser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience.

Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and--a closely...

In the 1970's, James developped a characterictic-free'' approach to the representation theory of the symmetric group on n letters, where Specht modules and certain bilinear forms on them play a crucial role. In this framework, we obtain a natural parametrization of the irreducible representations, but it is a major open problem to find explicit formulae for their dimensions when the ground field has positive characteristic.

In a wider context, this problem is a special case of the problem of determining the irreducible representations of Iwahori--Hecke algebras at roots of...

Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject.

The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into...