Contemporary Abstract Algebra
Chapman & Hall/CRC (Verlag)
978-1-032-77891-4 (ISBN)
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CONTEMPORARY ABSTRACT ALGEBRA, ELEVENTH EDITION is intended for a course whose main purpose is to enable students to do computations and write proofs. This text stresses the importance of obtaining a solid introduction to the traditional topics, while at the same time presenting abstract algebra as a contemporary and very much active subject which is currently being used by working physicists, chemists, and computer scientists.
For 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 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.
This new edition is streamlined. The 10th edition had 26 new examples, 330 new exercises, a few new theorems, and a substantial, number of minor modifications to the explanatory material, discussion text, and proofs. We have omitted suggested readings, references, biographies, etc that tally to 56 pages less. A number of corrections were also made for this edition.
Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The hallmark features of previous editions of the book are enhanced in this edition. These include:
A good mixture of approximately 1900 exercises.
Approximately 300 worked-out examples
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 geometry.
While many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructor’s Solutions Manual offers solutions for all the exercises. The Student Solution Manual has comprehensive solutions for all odd-numbered exercises and many even-numbered exercises and is well-loved for alternative solutions as well.
Joseph A. Gallian earned his Ph.D. from Notre Dame. In addition to receiving numerous national awards for his teaching and exposition, he has served terms as the Second Vice President, and the President of the MAA. He has served on 40 national committees, chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in national news outlets, including the New York Times, the Washington Post, the Boston Globe, and Newsweek, among many others.
1 Introduction to Groups
2 Groups
3 Finite Groups; Subgroups
4 Cyclic Groups
5 Permutation Groups
6 Ismorphisms
7 Cosets and Lagrange's Theorem
8 External Direct Products
9 Normal Subgroups and Factor Groups
10 Group Homomorphisms
11 Fundamental Theorem of Finite Abelian Groups
12 Introduction to Rings
13 Integral Domains
14 Ideals and Factor Rings
15 Ring Homomorphisms
16 Polynomial Rings
17 Factorization of Polynomials
18 Divisibilty in Integral Domains
19 Extension Fields
20 Algebraic Extensions
21 Finite Fields
22 Geometric Constructions
23 Sylow Theorems
24 Finite Simple Groups
25 Generators and Relations
26 Symmetry Groups
27 Symmetry and Counting
28 Cayley Digraphs of Groups
29 Introduction to Algebraic Coding Theory
30 An Introduction to Galois Theory
31 Cyclotomic Extensions
| Erscheint lt. Verlag | 10.2.2025 |
|---|---|
| Reihe/Serie | Textbooks in Mathematics |
| Zusatzinfo | 59 Line drawings, black and white; 13 Halftones, black and white; 72 Illustrations, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-032-77891-1 / 1032778911 |
| ISBN-13 | 978-1-032-77891-4 / 9781032778914 |
| Zustand | Neuware |
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