General

...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had...

This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to...

Contemporary Abstract Algebra, Tenth EditionFor more than three decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics...

This step-by-step approach helps you learn algebra quickly and easily!For many students-whether they're kids in middle school or adults returning to college-algebra is a difficult subject that only gets tougher as more concepts are learned. That's why...

This is the second of two volumes which will provide an introduction to modern developments in the representation theory of finite groups and associative algebras. The subject is viewed from the perspective of homological algebra and the theory of...

This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built...

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume...

Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics in matrix theory not included in the previous volume, but with important applications and of special mathematical interest. As with the...

This book is an introduction to the theory of quiver representations and quiver varieties, starting with basic definitions and ending with Nakajima's work on quiver varieties and the geometric realization of Kac-Moody Lie algebras.The first part of the...

In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates...

Everyone knows what braids are, whether they be made of hair, knitting wool, or electrical cables. However, it is not so evident that we can construct a theory about them, i.e. to elaborate a coherent and mathematically interesting corpus of results...

Homological algebra has found a large number of applications in many fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In the new edition of this broad introduction to the...

Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory,...

Ideal for courses that require the use of a graphing calculator, ALGEBRA AND TRIGONOMETRY: REAL MATHEMATICS, REAL PEOPLE, 6th Edition, features quality exercises, interesting applications, and innovative resources to help you succeed. Retaining the...

Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an...

Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph.D. in mathematics at Princeton in 1974. He spent the year 1974 -75 and the spring semester 1978 in Moscow, where he did research in p -adic analysis and also translated Yu. I...

With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research...

This book develops thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring". Almost rings are the commutative unitary...

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms,...

This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of...

Problem-solving is an art central to understanding and ability in mathematics. With this series of books, the authors have provided a selection of worked examples, problems with complete solutions and test papers designed to be used with or instead of...

In addition to the standard topics, this volume contains many topics not often found in an algebra book, such as inequalities, and the elements of substitution theory. Especially extensive is Chrystal's treatment of the infinite series, infinite...

Winner of the 2015 Prose Award for Best Mathematics Book!In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe,...

The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local...

This is the first textbook treatment of work leading to the landmark 1979 Kazhdan- Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra g over C. The setting is the module category O introduced by...

This is the second of three volumes that, together, give an exposition of the mathematics of grades 9-12 that is simultaneously mathematically correct and grade-level appropriate. The volumes are consistent with CCSSM (Common Core State Standards for...

Finally, a Clear Introduction to Algebra -- Courtesy of Dr. Math ? ! You've made it through pre-algebra, but now things are getting harder in algebra class. Never fear! Dr. Math?-the popular online math resource-is here to help you figure out even the...

This book helps readers bridge the gap between school-level mathematical skills and the quantitative and analytical skills required at the professional level. It presents basic mathematical concepts in an everyday context, enabling readers to pick up...

One of the landmarks in the history of mathematics is the proof of the nonex- tence of algorithms based solely on radicals and elementary arithmetic operations (addition, subtraction, multiplication, and division) for solutions of general al- braic...

The original version of this book, handed out to my students in weekly in stallments, had a certain rugged charm. Now that it is dressed up as a Springer UTM volume, I feel very much like Alfred Dolittle at Eliza's wedding. I hope the reader will still...

During the last 40 years the theory of finite groups has developed dramatically. The finite simple groups have been classified and are becoming better understood. Tools exist to reduce many questions about arbitrary finite groups to similar questions...

The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of...

Textbook writing must be one of the cruelest of self-inflicted tortures. - Carl Faith Math Reviews 54: 5281 So why didn't I heed the warning of a wise colleague, especially one who is a great expert in the subject of modules and rings? The answer is...

This book represents a complete course in abstract algebra, providing instructors with flexibility in the selection of topics to be taught in individual classes. All the topics presented are discussed in a direct and detailed manner. Throughout the text,...

Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. In Lie Groups: An Approach through Invariants and Representations, the author's masterful approach gives the reader a comprehensive treatment of the...

This book is a readable introduction to linear algebra, starting at an elementary level. It is intended to be useful both for students of pure mathematics who may subsequently pursue more advanced study in this area and for students who require linear...

In the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay...

The Representation Theory of the Symmetric Group provides an account of both the ordinary and modular representation theory of the symmetric groups. The range of applications of this theory is vast, varying from theoretical physics, through combinatories...

Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of...

Dessins d'Enfants are combinatorial objects, namely drawings with vertices and edges on topological surfaces. Their interest lies in their relation with the set of algebraic curves defined over the closure of the rationals, and the corresponding action...