Kategoria BISAC: Mathematics >> Algebra - General

This book presents a self-contained introduction to H.M. Stark s remarkable conjectures about the leading term of the Taylor expansion of Artin s L-functions at s=0. These conjectures can be viewed as a vast generalization of Dirichlet s class number formula and Kronecker s limit formula. They provide an unexpected contribution to Hilbert s 12th problem on the generalization of class fields by the values of transcendental functions. This volume belongs on the shelf of every mathematics library."

* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples.

* Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications.

* Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.

First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world. English reading students now have the opportunity to enjoy this lively presentation, from elementary ideas to cartoons to funny examples, and to follow the mind of an imaginative and creative mathematician into a world of enduring mathematical creations.

Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed.

Features and Topics:

* The mathematical foundations of geometric algebra are explored

* Applications in...

Hundreds of novel and innovative computer algebra "recipes" will enable readers starting at the second year undergraduate level to easily and rapidly solve and explore most problems they encounter in their classical mechanics studies. While the aim is not to try and teach the fundamentals of the subject, the recipes are organized to correlate with topics found in standard classical mechanics texts.

Using the powerful computer algebra system MAPLE (Release 8) --- no prior knowledge of MAPLE is presumed --- the relevant command structures are explained on a need-to-know basis as the...

* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory

* The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry

* Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry

* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed

*Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices

* Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography

* Covers filtered algebras, the associated...

This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.

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. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a...

Focuses on the interaction between algebra and algebraic geometry, including high-level research papers and surveys contributed by over 40 top specialists representing more than 15 countries worldwide. Describes abelian groups and lattices, algebras and binomial ideals, cones and fans, affine and projective algebraic varieties, simplicial and cellular complexes, polytopes, and arithmetics.