Abstract Algebra an Introduction to Groups Rings and Fields 2nd Edition

Abstract Algebra  an Introduction to Groups  Rings and Fields  2nd Edition

This second edition covers essentially the same topics as the first.

Author: Clive Reis

Publisher: World Scientific Publishing Company

ISBN: 9814730548

Category: Mathematics

Page: 555

View: 924

This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata. This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book 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, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless. In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
Categories: Mathematics

Abstract Algebra

Abstract Algebra

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 ...

Author: Clive Reis

Publisher: World Scientific

ISBN: 9789814335645

Category: Mathematics

Page: 509

View: 553

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.
Categories: Mathematics

Introduction To Abstract Algebra An Sets Groups Rings And Fields

Introduction To Abstract Algebra  An  Sets  Groups  Rings  And Fields

This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including ...

Author: Steven Howard Weintraub

Publisher: World Scientific

ISBN: 9789811246685

Category: Mathematics

Page: 438

View: 589

This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.
Categories: Mathematics

Rings Fields and Groups

Rings  Fields and Groups

This book provides a stimulating and unusiual introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses in universities and polytechnics.

Author: R. B. J. T. Allenby

Publisher: Hodder Education

ISBN: UCSC:32106016516962

Category: Algebra, Abstract

Page: 422

View: 251

This book provides a stimulating and unusiual introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses in universities and polytechnics. The mixture of informal and formal presentation generates the enthusiasm of the reader without neglecting the axiomatic approach necessary for the serious study.
Categories: Algebra, Abstract

Introduction to Modern Algebra and Its Applications

Introduction to Modern Algebra and Its Applications

The book provides an introduction to modern abstract algebra and its applications.

Author: Nadiya Gubareni

Publisher: CRC Press

ISBN: 9781000209532

Category: Mathematics

Page: 394

View: 302

The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger’s algorithm which is one of the important algorithms for constructing Gröbner basis. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.
Categories: Mathematics

Introduction to Abstract Algebra

Introduction to Abstract Algebra

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 ...

Author: W. Keith Nicholson

Publisher: John Wiley & Sons

ISBN: 9781118135358

Category: Mathematics

Page: 560

View: 714

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.
Categories: Mathematics

Abstract Algebra

Abstract Algebra

This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and the information and physical sciences.

Author: Derek J.S. Robinson

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110691214

Category: Mathematics

Page: 456

View: 206

This is the third edition of the book. In addition to introducing the main concepts of modern algebra, new topic are added: categories and functors; an introduction to representations of finite groups; projective and injective modules; an introduction to noetherian rings and modules and to Hilbert’s Nullstellensatz. There is ample material for a two semester course in abstract algebra.
Categories: Mathematics

Introduction to MATLAB with Applications for Chemical and Mechanical Engineers

Introduction to MATLAB with Applications for Chemical and Mechanical Engineers

It also offers instruction on the use of the MATLAB® optimization toolbox. With a CD-ROM of MATLAB programs, this text is essential for chemical engineers, mechanical engineers, applied mathematicians, and students.

Author: Daniel G. Coronell

Publisher: CRC Press

ISBN: 9781584885153

Category: Science

Page: 693

View: 620

Introduction to MATLAB with Applications for Chemical and Mechanical Engineers provides applications from chemical engineering and biotechnology, such as thermodynamics, heat transfer, fluid mechanics, and mass transfer. The book features a section on input, output, and storage of data as well as a section on data analysis and parameter estimation that contains statistical analysis, curve fitting optimization, and error analysis. Many applied case studies are included from the engineering disciplines. It also offers instruction on the use of the MATLAB® optimization toolbox. With a CD-ROM of MATLAB programs, this text is essential for chemical engineers, mechanical engineers, applied mathematicians, and students.
Categories: Science

Abstract Algebra

Abstract Algebra

The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students.

Author: Gregory T. Lee

Publisher: Springer

ISBN: 9783319776491

Category: Mathematics

Page: 301

View: 622

This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.
Categories: Mathematics

A First Course in Abstract Algebra

A First Course in Abstract Algebra

Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.

Author: John B. Fraleigh

Publisher: Pearson

ISBN: STANFORD:36105111947490

Category: Mathematics

Page: 544

View: 287

Considered a classic by many, A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.
Categories: Mathematics