First Course in Abstract Algebra, A
Pearson (Hersteller)
978-0-321-39036-3 (ISBN)
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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.
For courses in Abstract Algebra.
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Neil Brand is the Departmental Chair and Professor of Mathematics at the University of North Texas in Denton, Texas, where he has taught since 1983. Before teaching at UNT, he taught at Ohio State University and Loyola University of Chicago, and he was employed as a scientist at McDonnell-Douglass Corporation. He received his BS in Mathematics from Purdue University in 1975, and his MS and PhD in Mathematics from Stanford University in 1976 and 1978 respectively. He has authored or co-authored 26 refereed articles that have appeared in the mathematical literature. Dr. Brand is a member of the Mathematical Association of America and the American Mathematical Society. Outside of mathematics, his interests include woodworking and carpentry. He is a founding board member and current board president of Habitat for Humanity of Denton County. He lives in Denton, Texas with his wife Shari. He also has two grown daughters.
Brief Table of Contents
Instructor's Preface
Dependence Chart
Student's Preface
Sets and Relations
I. GROUPS AND SUBGROUPS
Binary Operations
Groups
Abelian Groups
Nonabelian Examples
Subgroups
Cyclic Groups
Generating Sets and Cayley Digraphs
II. STRUCTURE OF GROUPS
Groups and Permutations
Finitely Generated Abelian Groups
Cosets and the Theorem of Lagrange
Plane Isometries
III. HOMOMORPHISMS AND FACTOR GROUPS
Factor Groups
Factor-Group Computations and Simple Groups
Groups Actions on a Set
Applications of G -Sets to Counting
IV. ADVANCED GROUP THEORY
Isomorphism Theorems
Sylow Theorems
Series of Groups
Free Abelian Groups
Free Groups
Group Presentations
V. RINGS AND FIELDS
Rings and Fields
Integral Domains
Fermat's and Euler's Theorems
Encryption
VI. CONSTRUCTING RINGS AND FIELDS
The Field of Quotients of an Integral Domain
Rings and Polynomials
Factorization of Polynomials over Fields
Algebraic Coding Theory
Homomorphisms and Factor Rings
Prime and Maximal Ideals
Noncommutative Examples
VII. COMMUTATIVE ALGEBRA
Vector Spaces
Unique Factorization Domains
Euclidean Domains
Number Theory
Algebraic Geometry
Gröbner Basis for Ideals
VIII. EXTENSION FIELDS
Introduction to Extension Fields
Algebraic Extensions
Geometric Constructions
Finite Fields
IX. Galois Theory
Introduction to Galois Theory
Splitting Fields
Separable Extensions
Galois Theory
Illustrations of Galois Theory
Cyclotomic Extensions
Insolvability of the Quintic
| Erscheint lt. Verlag | 18.9.2020 |
|---|---|
| Sprache | englisch |
| Maße | 10 x 10 mm |
| Gewicht | 1000 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-321-39036-9 / 0321390369 |
| ISBN-13 | 978-0-321-39036-3 / 9780321390363 |
| Zustand | Neuware |
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