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Joseph A. Gallian - Contemporary Abstract Algebra (Textbooks in Mathematics)

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Joseph A. Gallian Contemporary Abstract Algebra (Textbooks in Mathematics)
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Contemporary Abstract Algebra, Tenth EditionFor more than three decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.The author presents the concepts and methodologies of contemporary abstract algebra as used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop but rarely do. Applications are included to illustrate the utility of the abstract concepts.Examples and exercises are the heart of the book. Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The exercises often foreshadow definitions, concepts, and theorems to come.Changes for the tenth edition include new exercises, new examples, new quotes, and a freshening of the discussion portions. The hallmark features of previous editions of the book are enhanced in this edition. These include: A good mixture of approximately 1900 computational and theoretical exercises, including computer exercises, that synthesize concepts from multiple chapters Approximately 300 worked-out examples from routine computations to the challenging Many applications from scientific and computing fields and everyday life Historical notes and biographies that spotlight people and events Motivational and humorous quotations Numerous connections to number theory and geometryWhile many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructors Solutions Manual written by the author has comprehensive solutions for all exercises and some alternative solutions to develop a critical thought and deeper understanding. It is available from CRC Press only. The Student Solution Manual has comprehensive solutions for all odd-numbered exercises and many even-numbered exercises.

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Contemporary Abstract Algebra Textbooks in Mathematics Series editors Al - photo 1
Contemporary Abstract Algebra
Textbooks in Mathematics

Series editors:

Al Boggess, Kenneth H. Rosen

Mathematical Modeling in the Age of the Pandemic

William P. Fox

Linear Algebra

James R. Kirkwood, Bessie H. Kirkwood

Real Analysis

With Proof Strategies

Daniel W. Cunningham

Train Your Brain

Challenging Yet Elementary Mathematics

Bogumil Kaminski, Pawel Pralat

Contemporary Abstract Algebra, Tenth Edition

Joseph A. Gallian

Geometry and Its Applications

Walter J. Meyer

Linear Algebra

What You Need to Know

Hugo J. Woerdeman

Introduction to Real Analysis, 3rd Edition

Manfred Stoll

Discovering Dynamical Systems Through Experiment and Inquiry

Thomas LoFaro, Jeff Ford

Functional Linear Algebra

Hannah Robbins

Introduction to Financial Mathematics

With Computer Applications

Donald R. Chambers, Qin Lu

Linear Algebra

An Inquiry-based Approach

Jeff Suzuki

Cover image by John Stembridge

2-dimensional representation of E8 Lie group

First edition published 1986 D. C. Heath and Company

6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press

2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN

10th edition c 2021 Taylor & Francis Group, LLC

CRC Press is an imprint of Taylor & Francis Group, LLC

Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use.

The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint.

Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers.

For permission to photocopy or use material electronically from this work, access

Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.

Library of Congress Cataloging.in.Publication Data

ISBN: 978-0-367-65178-7 (hbk)

ISBN: 978-1-003-14233-1 (ebk)

Typeset in Computer Modern font

by KnowledgeWorks Global Ltd.

To Char, Krissy, and Joey

Contents

SET THEORY

iISi

intersection of sets Si,iI

iISi

union of sets Si,iI

[ a]

{xS|x~a}, equivalence class of Scontaining a, 16

|s|

number of elements in the set of S

SPECIAL SETS

Z

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