Elements of Abstract Algebra

Author: Allan Clark

Publisher: Courier Corporation

ISBN: 0486140350

Category: Mathematics

Page: 224

View: 2582

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 with Applications

Volume 1: Vector Spaces and Groups

Author: Karlheinz Spindler

Publisher: CRC Press

ISBN: 9780824791445

Category: Mathematics

Page: 776

View: 3600

A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

A History of Abstract Algebra

Author: Israel Kleiner

Publisher: Springer Science & Business Media

ISBN: 081764685X

Category: Mathematics

Page: 168

View: 662

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.

Abstract Algebra

Applications to Galois Theory, Algebraic Geometry, and Cryptography

Author: Celine Carstensen,Benjamin Fine,Gerhard Rosenberger

Publisher: Walter de Gruyter

ISBN: 311025008X

Category: Mathematics

Page: 366

View: 3172

A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations; also contains topics that cannot be found elsewhere, and also offers a chapter on cryptography. End of chapter problems help readers with accessing the subjects. This work is co-published with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics."

A Concrete Approach to Abstract Algebra

From the Integers to the Insolvability of the Quintic

Author: Jeffrey Bergen

Publisher: Academic Press

ISBN: 9780080958620

Category: Mathematics

Page: 720

View: 7406

A Concrete Approach to Abstract Algebra presents a solid and highly accessible introduction to abstract algebra by providing details on the building blocks of abstract algebra. It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study. This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus. Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices

ABSTRACT ALGEBRA

Author: DIPAK CHATTERJEE

Publisher: PHI Learning Pvt. Ltd.

ISBN: 9788120328709

Category: Mathematics

Page: 372

View: 2459

Appropriate for undergraduate courses, this second edition has a new chapter on lattice theory, many revisions, new solved problems and additional exercises in the chapters on group theory, boolean algebra and matrix theory. The text offers a systematic, well-planned, and elegant treatment of the main themes in abstract algebra. It begins with the fundamentals of set theory, basic algebraic structures such as groups and rings, and special classes of rings and domains, and then progresses to extension theory, vector space theory and finally the matrix theory. The boolean algebra by virtue of its relation to abstract algebra also finds a proper place in the development of the text. The students develop an understanding of all the essential results such as the Cayley's theorem, the Lagrange's theorem, and the Isomorphism theorem, in a rigorous and precise manner. Sufficient numbers of examples have been worked out in each chapter so that the students can grasp the concepts, the ideas, and the results of structure of algebraic objects in a comprehensive way. The chapter-end exercises are designed to enhance the student's ability to further explore and inter-connect various essential notions.

Abstract Algebra

A First Course, Second Edition

Author: Dan Saracino

Publisher: Waveland Press

ISBN: 1478610131

Category: Mathematics

Page: 313

View: 6630

The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.

Applied Abstract Algebra

Author: Rudolf Lidl,Günter Pilz

Publisher: Springer Science & Business Media

ISBN: 1475729413

Category: Mathematics

Page: 488

View: 5032

Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.

Introduction to Abstract Algebra

Author: W. Keith Nicholson

Publisher: John Wiley & Sons

ISBN: 1118135350

Category: Mathematics

Page: 535

View: 3205

Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.

Abstract Algebra

An Introduction to Groups, Rings and Fields

Author: Clive Reis

Publisher: World Scientific

ISBN: 9814335649

Category: Mathematics

Page: 491

View: 8103

Suitable for second to fourth year undergraduates, this title contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space.

An Introduction to Abstract Algebra

Author: Derek J.S. Robinson

Publisher: Walter de Gruyter

ISBN: 3110198169

Category: Mathematics

Page: 292

View: 5949

This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader's skill and progress. The book should be suitable for students in the third or fourth year of study at a North American university or in the second or third year at a university in Europe.

ABSTRACT ALGEBRA, THIRD EDITION

Author: CHATTERJEE, DIPAK

Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120351495

Category: Mathematics

Page: 408

View: 3637

Appropriate for undergraduate courses, this third edition has new chapters on Galois Theory and Module Theory, new solved problems and additional exercises in the chapters on group theory, boolean algebra and matrix theory. The text offers a systematic, well-planned, and elegant treatment of the main themes in abstract algebra. It begins with the fundamentals of set theory, basic algebraic structures such as groups and rings, and special classes of rings and domains, and then progresses to extension theory, vector space theory and finally the matrix theory. The boolean algebra by virtue of its relation to abstract algebra also finds a proper place in the development of the text. The students develop an understanding of all the essential results such as the Cayley’s theorem, the Lagrange’s theorem, and the Isomorphism theorem, in a rigorous and precise manner. Sufficient numbers of examples have been worked out in each chapter so that the students can grasp the concepts, the ideas, and the results of structure of algebraic objects in a comprehensive way. The chapter-end exercises are designed to enhance the student’s ability to further explore and interconnect various essential notions. Besides undergraduate students of mathematics, this text is equally useful for the postgraduate students of mathematics.

A First Graduate Course in Abstract Algebra

Author: William Jennings Wickless

Publisher: CRC Press

ISBN: 0824757181

Category: Mathematics

Page: 234

View: 9827

Realizing the specific needs of first-year graduate students, this reference allows readers to grasp and master fundamental concepts in abstract algebra-establishing a clear understanding of basic linear algebra and number, group, and commutative ring theory and progressing to sophisticated discussions on Galois and Sylow theory, the structure of abelian groups, the Jordan canonical form, and linear transformations and their matrix representations.

A Course on Abstract Algebra

Author: Minking Eie,Shou-Te Chang

Publisher: World Scientific

ISBN: 981427190X

Category: Mathematics

Page: 359

View: 3627

This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the author's lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions. This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.

Abstract Algebra and Solution by Radicals

Author: John Edward Maxfield,Margaret W. Maxfield

Publisher: Courier Corporation

ISBN: 9780486671215

Category: Mathematics

Page: 209

View: 1847

Easily accessible undergraduate-level text covers groups, polynomials, Galois theory, radicals, much more. Features many examples, illustrations and commentaries as well as 13 appendices. 1971 edition.

Abstract Algebra

Author: Pierre Antoine Grillet

Publisher: Springer Science & Business Media

ISBN: 0387715681

Category: Mathematics

Page: 674

View: 9659

A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theories.

Abstract Algebra: An Introduction

Author: Thomas W. Hungerford

Publisher: Cengage Learning

ISBN: 1285414977

Category: Mathematics

Page: 616

View: 7088

Abstract Algebra: An Introduction is set apart by its thematic development and organization. The chapters are organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups. This enables students to see where many abstract concepts come from, why they are important, and how they relate to one another. New to this edition is a groups first option that enables those who prefer to cover groups before rings to do so easily. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Introduction to Abstract Algebra, Third Edition

Author: T.A. Whitelaw

Publisher: CRC Press

ISBN: 9780751401479

Category: Mathematics

Page: 256

View: 8441

The first and second editions of this successful textbook have been highly praised for their lucid and detailed coverage of abstract algebra. In this third edition, the author has carefully revised and extended his treatment, particularly the material on rings and fields, to provide an even more satisfying first course in abstract algebra.

Abstract algebra

a computational approach

Author: Charles C. Sims

Publisher: John Wiley & Sons

ISBN: 9780471098461

Category: Mathematics

Page: 491

View: 1671