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First Course in Abstract Algebra, A

Onbekend Engels 2020 9780321390363
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For courses in Abstract Algebra.

A comprehensive approach to abstract algebra, in a powerful eText format

A First Course in Abstract Algebra, 8th Edition retains its hallmark goal of covering all the topics needed for an in-depth introduction to abstract algebra, and is designed to be relevant to future graduate students, future high school teachers, and students who intend to work in industry. New co-author Neal Brand has revised this classic text carefully and thoughtfully, drawing on years of experience teaching the course with this text to produce a meaningful and worthwhile update. This in-depth introduction gives students a firm foundation for more specialized work in algebra by including extensive explanations of the what, the how, and the why behind each method the authors choose. This revision also includes applied topics such as RSA encryption and coding theory, as well as examples of applying Gröbner bases. Key to the 8th Edition has been transforming from a print-based learning tool to a digital learning tool. The eText is packed with content and tools, such as mini-lecture videos and interactive figures, that bring course content to life for students in new ways and enhance instruction. A low-cost, loose-leaf version of the text is also available for purchase within the Pearson eText.

Extend learning beyond the classroom
Pearson eText is an easy-to-use digital textbook that students can purchase on their own or you can assign for your course. It lets students read, highlight, and take notes all in one place. The mobile app lets students learn on the go, offline or online. Creating a course allows you to schedule readings, view reading analytics, and share your own notes with students, motivating them to keep reading, and keep learning. Learn more about Pearson eText.

Specificaties

ISBN13:9780321390363
Taal:Engels
Bindwijze:onbekend

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Inhoudsopgave

<h2>Brief Table of Contents</h2> <div class="c-section-headers-non-traditional-number-list_container"> <ul> <li>Instructor's Preface</li> <li>Dependence Chart</li> <li>Student's Preface</li> </ul> <ol start="0"> <li>Sets and Relations</li> </ol> <h3>I. GROUPS AND SUBGROUPS</h3> <ol> <li>Binary Operations</li> <li>Groups</li> <li>Abelian Groups</li> <li>Nonabelian Examples</li> <li>Subgroups</li> <li>Cyclic Groups</li> <li>Generating Sets and Cayley Digraphs</li> </ol> <h3>II. STRUCTURE OF GROUPS</h3> <ol start="8"> <li>Groups and Permutations</li> <li>Finitely Generated Abelian Groups</li> <li>Cosets and the Theorem of Lagrange</li> <li>Plane Isometries</li> </ol> <h3>III. HOMOMORPHISMS AND FACTOR GROUPS</h3> <ol start="12"> <li>Factor Groups</li> <li>Factor-Group Computations and Simple Groups</li> <li>Groups Actions on a Set</li> <li>Applications of G -Sets to Counting</li> </ol> <h3>IV. ADVANCED GROUP THEORY</h3> <ol start="16"> <li>Isomorphism Theorems</li> <li>Sylow Theorems</li> <li>Series of Groups</li> <li>Free Abelian Groups</li> <li>Free Groups</li> <li>Group Presentations</li> </ol> <h3>V. RINGS AND FIELDS </h3> <ol start="22"> <li>Rings and Fields</li> <li>Integral Domains</li> <li>Fermat's and Euler's Theorems</li> <li>Encryption</li> </ol> <h3>VI. CONSTRUCTING RINGS AND FIELDS</h3> <ol start="26"> <li>The Field of Quotients of an Integral Domain</li> <li>Rings and Polynomials</li> <li>Factorization of Polynomials over Fields</li> <li>Algebraic Coding Theory</li> <li>Homomorphisms and Factor Rings</li> <li>Prime and Maximal Ideals</li> <li>Noncommutative Examples</li> </ol> <h3>VII. COMMUTATIVE ALGEBRA</h3> <ol start="33"> <li>Vector Spaces</li> <li>Unique Factorization Domains</li> <li>Euclidean Domains</li> <li>Number Theory</li> <li>Algebraic Geometry</li> <li>Gröbner Basis for Ideals</li> </ol> <h3>VIII. EXTENSION FIELDS</h3> <ol start="39"> <li>Introduction to Extension Fields</li> <li>Algebraic Extensions</li> <li>Geometric Constructions</li> <li>Finite Fields</li> </ol> <h3>IX. Galois Theory</h3> <ol start="43"> <li>Introduction to Galois Theory</li> <li>Splitting Fields</li> <li>Separable Extensions</li> <li>Galois Theory</li> <li>Illustrations of Galois Theory</li> <li>Cyclotomic Extensions</li> <li>Insolvability of the Quintic</li> </ol> </div>

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        First Course in Abstract Algebra, A