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frontmatter.xml
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<?xml version="1.0" encoding="UTF-8" ?>
<!--********************************************************************
Copyright 2015 Robert A. Beezer
This file is part of MathBook XML.
MathBook XML is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 or version 3 of the
License (at your option).
MathBook XML is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with MathBook XML. If not, see <http://www.gnu.org/licenses/>.
*********************************************************************-->
<!-- This file was originally part of the book -->
<!-- (as copied on 2015/07/12) -->
<!-- -->
<!-- Abstract Algebra: Theory and Applications -->
<!-- -->
<!-- Copyright (C) 1997-2014 Thomas W. Judson -->
<frontmatter xml:id="index" xmlns:xi="http://www.w3.org/2001/XInclude">
<titlepage>
<author>
<personname>Robin Cruz</personname>
<department>Department of Mathematics and Physical Sciences</department>
<institution>The College of Idaho</institution>
<email>rcruz@collegeofidaho.edu</email>
</author>
<author>
<personname>Lynda Danielson</personname>
<department>Department of Mathematics and Physical Sciences</department>
<institution>The College of Idaho</institution>
<email>ldanielson@collegeofidaho.edu</email>
</author>
<credit>
<title>Beginning and Intermediate Algebra</title>
<author>
<personname>Tyler Wallace</personname>
<department>Department of Mathematics and Computer Science</department>
<institution>http://wallace.ccfaculty.org/book/book.html</institution>
</author>
</credit>
<date><today /></date>
</titlepage>
<colophon>
<copyright>
<year>2016</year>
<holder>Robin Cruz, Lynda Danielson</holder>
<minilicense>GFDL License</minilicense>
<shortlicense>Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the appendix entitled <q>GNU Free Documentation License.</q> All trademarks<trademark /> are the registered<registered /> marks of their respective owners.</shortlicense>
</copyright>
</colophon>
<!-- A section of its own in HTML, migrates to copyright-page in LaTeX (sans a title)-->
<biography>
<p>Robin Cruz and Lynda Danielson presently teach at the College of Idaho.</p>
<p>Stuff.</p>
</biography>
<!-- The following items must be placed in the desired/required order -->
<!-- This will be checked by a Document Type Definition eventually -->
<!-- Order: dedication, acknowledgements, forewords, prefaces -->
<!-- Each paragraph gets centered and has some vertical separatation -->
<!-- A line break may be used here to aid with intended formatting -->
<dedication>
<p>To students of algebra everywhere<ndash />they are the reason</p>
<p>And to those who teach them</p>
</dedication>
<acknowledgement>
<p>I would like to acknowledge the following reviewers for their helpful comments and suggestions. </p>
<ul>
<li><p>David Anderson, University of Tennessee, Knoxville</p></li>
<li><p>Robert Beezer, University of Puget Sound</p></li>
<li><p>Myron Hood, California Polytechnic State University</p></li>
<li><p>Herbert Kasube, Bradley University</p></li>
<li><p>John Kurtzke, University of Portland</p></li>
<li><p>Inessa Levi, University of Louisville</p></li>
<li><p>Geoffrey Mason, University of California, Santa Cruz</p></li>
<li><p>Bruce Mericle, Mankato State University</p></li>
<li><p>Kimmo Rosenthal, Union College</p></li>
<li><p>Mark Teply, University of Wisconsin</p></li>
</ul>
<p>I would also like to thank Steve Quigley, Marnie Pommett, Cathie Griffin, Kelle Karshick, and the rest of the staff at PWS Publishing for their guidance throughout this project. It has been a pleasure to work with them.</p>
<!-- Added NSF support statement. TWJ 8/9/2012 -->
<p>Robert Beezer encouraged me to make <em>Abstract Algebra: Theory and Applications</em> available as an open source textbook, a decision that I have never regretted. With his assistance, the book has been rewritten in MathBook XML (<url href="http://mathbook.pugetsound.edu">http://mathbook.pugetsound.edu</url>), making it possible to quickly output print, web, PDF versions and more from the same source. The open source version of this book has received support from the National Science Foundation (Award <hash />DUE-1020957).</p>
</acknowledgement>
<preface>
<p>This text is intended for a one or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.</p>
<p>Until recently most abstract algebra texts included few if any applications. However, one of the major problems in teaching an abstract algebra course is that for many students it is their first encounter with an environment that requires them to do rigorous proofs. Such students often find it hard to see the use of learning to prove theorems and propositions; applied examples help the instructor provide motivation.</p>
<p>This text contains more material than can possibly be covered in a single semester. Certainly there is adequate material for a two-semester course, and perhaps more; however, for a one-semester course it would be quite easy to omit selected chapters and still have a useful text. The order of presentation of topics is standard: groups, then rings, and finally fields. Emphasis can be placed either on theory or on applications. A typical one-semester course might cover groups and rings while briefly touching on field theory, using Chapters<nbsp />1 through 6, 9, 10, 11, 13 (the first part), 16, 17, 18 (the first part), 20, and 21. Parts of these chapters could be deleted and applications substituted according to the interests of the students and the instructor. A two-semester course emphasizing theory might cover Chapters<nbsp />1 through 6, 9, 10, 11, 13 through 18, 20, 21, 22 (the first part), and 23. On the other hand, if applications are to be emphasized, the course might cover Chapters 1 through 14, and 16 through 22. In an applied course, some of the more theoretical results could be assumed or omitted. A chapter dependency chart appears below. (A broken line indicates a partial dependency.)</p>
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<p>Though there are no specific prerequisites for a course in abstract algebra, students who have had other higher-level courses in mathematics will generally be more prepared than those who have not, because they will possess a bit more mathematical sophistication. Occasionally, we shall assume some basic linear algebra; that is, we shall take for granted an elementary knowledge of matrices and determinants. This should present no great problem, since most students taking a course in abstract algebra have been introduced to matrices and determinants elsewhere in their career, if they have not already taken a sophomore or junior-level course in linear algebra.</p>
<p>Exercise sections are the heart of any mathematics text. An exercise set appears at the end of each chapter. The nature of the exercises ranges over several categories; computational, conceptual, and theoretical problems are included. A section presenting hints and solutions to many of the exercises appears at the end of the text. Often in the solutions a proof is only sketched, and it is up to the student to provide the details. The exercises range in difficulty from very easy to very challenging. Many of the more substantial problems require careful thought, so the student should not be discouraged if the solution is not forthcoming after a few minutes of work.</p>
<!-- Removed reference to the solutions manual. TWJ 8/19/2010 -->
<!-- A complete solutions manual is available for the instructor's use. -->
<p>There are additional exercises or computer projects at the ends of many of the chapters. The computer projects usually require a knowledge of programming. All of these exercises and projects are more substantial in nature and allow the exploration of new results and theory.</p>
<!-- % Added Sage blurb, RAB 2011/07/28 -->
<p>Sage (<url href="http://sagemath.org">sagemath.org</url>) is a free, open source, software system for advanced mathematics, which is ideal for assisting with a study of abstract algebra. Sage can be used either on your own computer, a local server, or on SageMathCloud (<url href="https://cloud.sagemath.com">https://cloud.sagemath.com</url>). Robert Beezer has written a comprehensive introduction to Sage and a selection of relevant exercises that appear at the end of each chapter, including live Sage cells in the web version of the book.</p>
<!-- RAB 2014/08/18 Should move flush right with some vertical spacing -->
<attribution>Thomas W. Judson <br />Nacogdoches, Texas 2015</attribution>
</preface>
<preface>
<title>Contributors to the 4<m>^\mathrm{th}</m> Edition</title>
<contributors>
<contributor xml:id="tjudson">
<personname>Thomas Judson</personname>
<department>Department of Mathematics and Statistics</department>
<institution>Stephen F. Austin State University</institution>
<email>judsontw@sfasu.edu</email>
</contributor>
<contributor xml:id="dfarmer">
<personname>David Farmer</personname>
<institution>American Institute of Mathematics</institution>
<email>farmer@aimath.org</email>
</contributor>
<contributor xml:id="rbeezer">
<personname>Robert Beezer</personname>
<department>Department of Mathematics and Computer Science</department>
<institution>University of Puget Sound</institution>
<email>beezer@pugetsound.edu</email>
</contributor>
<contributor xml:id="ajordan">
<personname>Alex Jordan</personname>
<department>Department of Mathematics</department>
<institution>Portland Community College</institution>
<email>alex.jordan@pcc.edu</email>
</contributor>
</contributors>
</preface>
</frontmatter>