A Friendly Introduction To Abstract Algebra

Author : Ryota Matsuura
Publisher : American Mathematical Society
Page : 404 pages
File Size : 50,9 Mb
Release : 2022-07-06
Category : Mathematics
ISBN : 9781470468811

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A Friendly Introduction to Abstract Algebra by Ryota Matsuura Pdf

A Friendly Introduction to Abstract Algebra offers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics. The author's pedagogical philosophy is that when students abstract from a wide range of examples, they are better equipped to conjecture, formalize, and prove new ideas in abstract algebra. Thus, students thoroughly explore all concepts through illuminating examples before formal definitions are introduced. The instruction in proof writing is similarly grounded in student exploration and experience. Throughout the book, the author carefully explains where the ideas in a given proof come from, along with hints and tips on how students can derive those proofs on their own. Readers of this text are not just consumers of mathematical knowledge. Rather, they are learning mathematics by creating mathematics. The author's gentle, helpful writing voice makes this text a particularly appealing choice for instructors and students alike. The book's website has companion materials that support the active-learning approaches in the book, including in-class modules designed to facilitate student exploration.

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 53,8 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9780486474175

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A Book of Abstract Algebra by Charles C Pinter Pdf

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.

Author : Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 51,9 Mb
Release : 2014-11-17
Category : Mathematics
ISBN : 9781118497753

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An Introduction to Essential Algebraic Structures by Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin Pdf

A reader-friendly introduction to modern algebra with important examples from various areas of mathematics Featuring a clear and concise approach, An Introduction to Essential Algebraic Structures presents an integrated approach to basic concepts of modern algebra and highlights topics that play a central role in various branches of mathematics. The authors discuss key topics of abstract and modern algebra including sets, number systems, groups, rings, and fields. The book begins with an exposition of the elements of set theory and moves on to cover the main ideas and branches of abstract algebra. In addition, the book includes: Numerous examples throughout to deepen readers’ knowledge of the presented material An exercise set after each chapter section in an effort to build a deeper understanding of the subject and improve knowledge retention Hints and answers to select exercises at the end of the book A supplementary website with an Instructors Solutions manual An Introduction to Essential Algebraic Structures is an excellent textbook for introductory courses in abstract algebra as well as an ideal reference for anyone who would like to be more familiar with the basic topics of abstract algebra.

Author : I. N. Herstein
Publisher : Macmillan College
Page : 322 pages
File Size : 44,5 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015049346839

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Abstract Algebra by I. N. Herstein Pdf

Author : David Nash
Publisher : Unknown
Page : 158 pages
File Size : 53,9 Mb
Release : 2016-08-17
Category : Electronic
ISBN : 1517100453

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A Friendly Introduction to Group Theory by David Nash Pdf

This book is an attempt at creating a friendlier, more colloquial textbook for a one-semester course in Abstract Algebra in a liberal arts setting. The textbook covers introductory group theory -- starting with basic notions and examples and moving through subgroups, quotient groups, group homomorphisms, and isomorphisms.

Author : John W. Lawrence,Frank A. Zorzitto
Publisher : Cambridge University Press
Page : 639 pages
File Size : 46,8 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9781108836654

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An Introduction to Abstract Algebra by John W. Lawrence,Frank A. Zorzitto Pdf

A lucid guide to abstract algebra, this comprehensive textbook provides in depth coverage for upper undergraduate students.

Author : T.A. Whitelaw
Publisher : CRC Press
Page : 260 pages
File Size : 44,5 Mb
Release : 1995-05-15
Category : Mathematics
ISBN : 0751401471

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Introduction to Abstract Algebra, Third Edition by T.A. Whitelaw Pdf

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.

Author : Jonathan D. H. Smith
Publisher : CRC Press
Page : 330 pages
File Size : 52,9 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781420063721

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Introduction to Abstract Algebra by Jonathan D. H. Smith Pdf

Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.

Author : Steven Howard Weintraub
Publisher : World Scientific
Page : 438 pages
File Size : 52,7 Mb
Release : 2022-05-25
Category : Mathematics
ISBN : 9789811246685

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Introduction To Abstract Algebra, An: Sets, Groups, Rings, And Fields by Steven Howard Weintraub Pdf

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.

Author : Gary L. Mullen,James A. Sellers
Publisher : CRC Press
Page : 204 pages
File Size : 54,5 Mb
Release : 2016-12-19
Category : Mathematics
ISBN : 9781482250077

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Abstract Algebra by Gary L. Mullen,James A. Sellers Pdf

Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors who need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic. Features Groups before rings approach Interesting modern applications Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers. Numerous exercises at the end of each section Chapter "Hint and Partial Solutions" offers built in solutions manual

Author : Derek J.S. Robinson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 456 pages
File Size : 48,9 Mb
Release : 2022-02-07
Category : Mathematics
ISBN : 9783110691160

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Abstract Algebra by Derek J.S. Robinson Pdf

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.

Author : Jonathan D. H. Smith
Publisher : CRC Press
Page : 324 pages
File Size : 43,5 Mb
Release : 2015-10-23
Category : Mathematics
ISBN : 9781498731812

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Introduction to Abstract Algebra by Jonathan D. H. Smith Pdf

Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups.This new edition of a widely adopted textbook covers

Author : Audrey Terras
Publisher : Cambridge University Press
Page : 331 pages
File Size : 47,6 Mb
Release : 2018-12-20
Category : Mathematics
ISBN : 9781107164079

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Abstract Algebra with Applications by Audrey Terras Pdf

This text offers a friendly and concise introduction to abstract algebra, emphasizing its uses in the modern world.

Author : W. Keith Nicholson
Publisher : John Wiley & Sons
Page : 560 pages
File Size : 45,8 Mb
Release : 2012-03-20
Category : Mathematics
ISBN : 9781118135358

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Introduction to Abstract Algebra by W. Keith Nicholson Pdf

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.

Author : Derek J.S. Robinson
Publisher : Walter de Gruyter
Page : 293 pages
File Size : 50,7 Mb
Release : 2008-08-22
Category : Electronic
ISBN : 9783110198164

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An Introduction to Abstract Algebra by Derek J.S. Robinson Pdf

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.