The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to s...
This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.
Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.
Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
ELEMENTS OF MODERN ALGEBRA is intended for an introductory course in abstract algebra taken by Math and Math for Secondary Education majors. Helping to make the study of abstract algebra more accessible, this text gradually introduces and develops concepts through helpful features that provide guidance on the techniques of proof construction and logic analysis. The text develops mathematical maturity for students by presenting the material in a theorem-proof format, with definitions and major results easily located through a user-friendly format. The treatment is rigorous and self-contained, in keeping with the objectives of training the student in the techniques of algebra and of providing a bridge to higher-level mathematical courses. The text has a flexible organization, with section dependencies clearly mapped out and optional topics that instructors can cover or skip based on their course needs. Additionally, problem sets are carefully arranged in order of difficulty to cater assignments to varying student ability levels. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
This Book Is Meant To Provide A Text For The Graduate And Post-Graduate Classes On Modern Algebra At All Indian Universities And At The Institutes Of Technology, But Is Also Intended To Be Useful For All Competitive Examinations Such As I.A.S., Net Etc.This Book Presents Basic And More Important Results In Group Theory, Ring Theory, Linear Algebra And Field Theory. It Is A Self-Contained Book And Also Provides An Understanding Of Basic Mathematical Concepts To Science, Engineering And Social Science Students.There Is Always A Danger Of Introducing The Abstract Concepts Too Suddenly And Without Sufficient Base Of Examples. In Order To Mitigate It The Concepts Have Been Motivated Beforehand. The Topics Have Been Presented In A Simple, Clear And Coherent Style With A Number Of Examples And Exercises. Exercises Of Various Levels Of Difficulty Are Given At The End Each Section.