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Author: Ryota Matsuura
Publisher: American Mathematical Society
ISBN: 1470468816
Category : Mathematics
Languages : en
Pages : 404
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Book Description
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: Ryota Matsuura
Publisher: American Mathematical Society
ISBN: 1470468816
Category : Mathematics
Languages : en
Pages : 404
Get Book Here
Book Description
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
ISBN: 0486474178
Category : Mathematics
Languages : en
Pages : 402
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Book Description
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: I. N. Herstein
Publisher: Macmillan College
ISBN:
Category : Mathematics
Languages : en
Pages : 322
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Book Description
Author: Jonathan D. H. Smith
Publisher: CRC Press
ISBN: 1498731627
Category : Mathematics
Languages : en
Pages : 353
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Book Description
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: Joseph H. Silverman
Publisher: Pearson
ISBN: 9781292027098
Category :
Languages : en
Pages : 472
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Book Description
For one-semester undergraduate courses in Elementary Number Theory. A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet-number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.
Author: Benjamin Fine
Publisher: JHU Press
ISBN: 1421411776
Category : Mathematics
Languages : en
Pages : 583
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Book Description
A new approach to abstract algebra that eases student anxieties by building on fundamentals. Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic
Author: David Nash
Publisher:
ISBN: 9781517100452
Category :
Languages : en
Pages : 158
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Book Description
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: Laura L. Dos Reis
Publisher: Createspace Independent Publishing Platform
ISBN: 9781539436072
Category : Algebra, Abstract
Languages : en
Pages : 364
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Book Description
"Learning abstract algebra is not hard. It is not like getting to know the deep forest - its trails, streams, lakes, flora, and fauna. It takes time, effort, and a willingness to venture into new territory, It is a task that cannot be done overnight. But with a good guide (this book!), it should be an exciting excursion with, perhaps, only a few bumps along the way. Students - even students who have done very well in calculus - often have trouble with abstract algebra. Our objective in writing this book is to make abstract algebra as accessible as elementary calculus and, we hope, a real joy to study. Our textbook has three advantages over the standard abstract algebra textbook. First, it covers all the foundational concepts needed for abstract algebra (the only prerequisite for this book is high school algebra). Second, it is easier to read and understand (so it is ideal for self-learners). Third, it gets the reader to think mathematically and to do mathematics - to experiment, make conjectures, and prove theorems - while reading the book. The result is not only a better learning experience but also a more enjoyable one" -- from back cover.
Author: Derek J.S. Robinson
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110340879
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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, and should ease the transition to (post)graduate studies.
Author: W. E. Deskins
Publisher: Courier Corporation
ISBN: 0486158462
Category : Mathematics
Languages : en
Pages : 656
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Book Description
Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problems.
