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A Friendly Introduction To Abstract Algebra
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Book Synopsis A Friendly Introduction to Abstract Algebra by : Ryota Matsuura
Download or read book A Friendly Introduction to Abstract Algebra written by Ryota Matsuura and published by American Mathematical Society. This book was released on 2022-07-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Friendly Introduction to Group Theory by : David Nash
Download or read book A Friendly Introduction to Group Theory written by David Nash and published by . This book was released on 2016-08-17 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Essential Algebraic Structures by : Martyn R. Dixon
Download or read book An Introduction to Essential Algebraic Structures written by Martyn R. Dixon and published by John Wiley & Sons. This book was released on 2014-11-17 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Abstract Algebra by : Jonathan D. H. Smith
Download or read book Introduction to Abstract Algebra written by Jonathan D. H. Smith and published by CRC Press. This book was released on 2016-04-19 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Abstract Algebra by : Gary L. Mullen
Download or read book Abstract Algebra written by Gary L. Mullen and published by CRC Press. This book was released on 2016-12-19 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Introduction to Abstract Algebra, Third Edition by : T.A. Whitelaw
Download or read book Introduction to Abstract Algebra, Third Edition written by T.A. Whitelaw and published by CRC Press. This book was released on 1995-05-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Abstract Algebra by : Derek J.S. Robinson
Download or read book An Introduction to Abstract Algebra written by Derek J.S. Robinson and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Abstract Algebra with Applications by : Audrey Terras
Download or read book Abstract Algebra with Applications written by Audrey Terras and published by Cambridge University Press. This book was released on 2018-12-20 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers a friendly and concise introduction to abstract algebra, emphasizing its uses in the modern world.
Book Synopsis Abstract Algebra by : Derek J.S. Robinson
Download or read book Abstract Algebra written by Derek J.S. Robinson and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-02-07 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Friendly Introduction to Group Theory by : David Nash
Download or read book A Friendly Introduction to Group Theory written by David Nash and published by . This book was released on 2017-09 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a friendlier, more colloquial textbook for a one-semester course in Abstract Algebra in a liberal arts setting. It would also provide a nice supplement for a more advanced course or an excellent resource for an independent learner hoping to become familiar with group theory. The textbook covers introductory group theory with an overarching goal of classifying small finite groups. It starts with a chapter of preliminary background material (set theory, basic number theory, induction, etc.) before introducing groups. The rest of the second edition builds up the basic notions and creates a bank of nice examples before proceeding on to more advanced topics. Those topics include: subgroups, quotient groups, decompositions of groups, group homomorphisms, isomorphisms, automorphism groups, p-groups, the Fundamental Theorem of Finite Abelian Groups, group actions, conjugation, Sylow subgroups and the Sylow theorems.The second edition adds over 75 pages of new material with an entirely new chapter, several new sections, and additional examples and exposition throughout. There are also almost 200 new exercises and an index to help you find what you are looking for.
Book Synopsis Introduction To Abstract Algebra, An: Sets, Groups, Rings, And Fields by : Steven Howard Weintraub
Download or read book Introduction To Abstract Algebra, An: Sets, Groups, Rings, And Fields written by Steven Howard Weintraub and published by World Scientific. This book was released on 2022-05-25 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Abstract Algebra, Third Edition by : T.A. Whitelaw
Download or read book Introduction to Abstract Algebra, Third Edition written by T.A. Whitelaw and published by Routledge. This book was released on 2020-04-14 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Abstract Algebra by : F. M. Hall
Download or read book An Introduction to Abstract Algebra written by F. M. Hall and published by Cambridge University Press. This book was released on 1972-04-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume course on abstract algebra provides a broad introduction to the subject for those with no previous knowledge of it but who are well grounded in ordinary algebraic techniques. It starts from the beginning, leading up to fresh ideas gradually and in a fairly elementary manner, and moving from discussion of particular (concrete) cases to abstract ideas and methods. It thus avoids the common practice of presenting the reader with a mass of ideas at the beginning, which he is only later able to relate to his previous mathematical experience. The work contains many concrete examples of algebraic structures. Each chapter contains a few worked examples for the student - these are divided into straightforward and more advanced categories. Answers are provided. From general sets, Volume 1 leads on to discuss special sets of the integers, other number sets, residues, polynomials and vectors. A chapter on mappings is followed by a detailed study of the fundamental laws of algebra, and an account of the theory of groups which takes the idea of subgroups as far as Langrange's theorem. Some improvements in exposition found desirable by users of the book have been incorporated into the second edition and the opportunity has also been taken to correct a number of errors.
Book Synopsis Thinking Algebraically: An Introduction to Abstract Algebra by : Thomas Q. Sibley
Download or read book Thinking Algebraically: An Introduction to Abstract Algebra written by Thomas Q. Sibley and published by American Mathematical Soc.. This book was released on 2021-06-08 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. After an historical overview, the first chapter studies familiar examples and elementary properties of groups and rings simultaneously to motivate the modern understanding of algebra. The text builds intuition for abstract algebra starting from high school algebra. In addition to the standard number systems, polynomials, vectors, and matrices, the first chapter introduces modular arithmetic and dihedral groups. The second chapter builds on these basic examples and properties, enabling students to learn structural ideas common to rings and groups: isomorphism, homomorphism, and direct product. The third chapter investigates introductory group theory. Later chapters delve more deeply into groups, rings, and fields, including Galois theory, and they also introduce other topics, such as lattices. The exposition is clear and conversational throughout. The book has numerous exercises in each section as well as supplemental exercises and projects for each chapter. Many examples and well over 100 figures provide support for learning. Short biographies introduce the mathematicians who proved many of the results. The book presents a pathway to algebraic thinking in a semester- or year-long algebra course.
Book Synopsis An Introduction to Abstract Algebra by : John W. Lawrence
Download or read book An Introduction to Abstract Algebra written by John W. Lawrence and published by Cambridge University Press. This book was released on 2021-04-15 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lucid guide to abstract algebra, this comprehensive textbook provides in depth coverage for upper undergraduate students.
Book Synopsis Introduction to Abstract Algebra by : W. Keith Nicholson
Download or read book Introduction to Abstract Algebra written by W. Keith Nicholson and published by John Wiley & Sons. This book was released on 2012-03-20 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Abstract Algebra by : J. Strother Moore
Download or read book Introduction to Abstract Algebra written by J. Strother Moore and published by Academic Press. This book was released on 2014-06-28 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Abstract Algebra provides insight into the methods of abstract algebra. This book provides information pertinent to the fundamental concepts of abstract algebra. Organized into five chapters, this book begins with an overview of the study of natural numbers that are used historically for the purpose of counting the objects in different assemblages. This text then examines the concepts of set and elements of a set. Other chapters contain an intuitive survey of the different kinds of real numbers, with the inclusion of many very important results on integers. This book presents as well a brief survey of algebraic systems from the trivial sets to the more highly structures groups, with emphasis on the elementary properties of groups. The final chapter deals with the simple development of complex numbers. This book is intended to be suitable for students in abstract algebra.
