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lgli/fra.pdf
A First Course in Abstract Algebra [Seventh 7th Edition] 🔍
John B. Fraleigh, Neal E. Brand Pearson Books, 8, 2021
英语 [en] · PDF · 48.1MB · 2021 · 📘 非小说类图书 · 🚀/lgli/lgrs · Save
描述
"This is an introduction to abstract algebra. It is anticipated that the students have studied calculus and probably linear algebra. However, these are primarily mathematical maturity prerequisites; subject matter from calculus and linear algebra appears mostly in illustrative examples and exercises. As in previous editions of the text, my aim remains to teach students as much about groups, rings, and fields as I can in a first course. For many students, abstract algebra is their first extended exposure to an axiomatic treatment of mathematics. Recognizing this, I have included extensive explanations concerning what we are trying to accomplish, how we are trying to do it, and why we choose these methods. Mastery of this text constitutes a firm foundation for more specialized work in algebra, and also provides valuable experience for any further axiomatic study of mathematics"-- Provided by publisher
备用文件名
lgrsnf/fra.pdf
备选作者
John B. Fraleigh, Victor J. Katz
备用出版商
Globe Fearon Educational Publishing
备用出版商
Hachette jeunesse - Disney
备用出版商
Larry Michael Limited
备用出版商
Hachette collections
备用出版商
Longman Publishing
备用出版商
Cengage Gale
备用出版商
Pluriel
备用版本
World student series, Eighth edition, Hoboken, New Jersey, 2021
备用版本
United States, United States of America
备用版本
Nigeria, Nigeria
备用版本
France, France
备用版本
2020
元数据中的注释
Lossy compression of https://libgen.rs/book/index.php?md5=7E41E44E10591C00E79177F9EF8A47F1 to get to a reasonable file size; still too large
备用描述
Title
Contents
Instructor's Preface
Student’s Preface
0. Sets and Relations
I. Groups and Subgroups
1. Binary Operations
2. Groups
3. Abelian Examples
4. Nonabelian Examples
5. Subgroups
6. Cyclic Groups
7. Generating Sets and Cayley Digraphs
II. Structure of Groups
8. Groups of Permutations
9. Finitely Generated Abelian Groups
10. Cosets and the Theorem of Lagrange
11. Plane Isometries
III. Homomorphisms and Factor Groups
12. Factor Groups
13. Factor-Group Computations and Simple Groups
14. Group Action on a Set
15. Applications of G-Sets to Counting
IV. Advanced Group Theory
16. Isomorphism Theorems
17. Sylow Theorems
18. Series of Groups
19. Free Abelian Groups
20. Free Groups
21. Group Presentations
V. Rings and Fields
22. Rings and Fields
23. Integral Domains
24. Fermat’s and Euler’s Theorems
25. Encryption
VI. Constructing Rings and Fields
26. The Field of Quotients of an Integral Domain
27. Rings of Polynomials
28. Factorization of Polynomials over a Field
29. Algebraic Coding Theory
30. Homomorphisms and Factor Rings
31. Prime and Maximal Ideals
32. Noncommutative Examples
VII. Commutative Algebra
33. Vector Spaces
34. Unique Factorization Domains
35. Euclidean Domains
36. Number Theory
37. Algebraic Geometry
38. Gröbner Bases for Ideals
VIII. Extension Fields
39. Introduction to Extension Fields
40. Algebraic Extensions
41. Geometric Constructions
42. Finite Fields
IX. Galois Theory
43. Introduction to Galois Theory
44. Splitting Fields
45. Separable Extensions
46. Galois Theory
47. Illustrations of Galois Theory
48. Cyclotomic Extensions
49. Insolvability of the Quintic
Appendix: Matrix Algebra
Bibliography
Notations
Answers to Odd-Numbered Exercises Not Asking for Definitions or Proofs
Index
开源日期
2022-05-09
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