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A First Course in Abstract Algebra: International edition(7th,2003)  무료배송

 
지은이 : John B. Fraleigh
출판사 : Addison-Wesley
판수 : seventh edition
페이지수 : 520
ISBN : 0321156080
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 품절
     

 

Considered a classic by many, A First Course in Abstract Algebra, Seventh Edition쟧s an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.



Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gr�bner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra



For all readers interested in abstract algebra.

0. Sets and Relations.
I. GROUPS AND SUBGROUPS.
1. Introduction and Examples.
2. Binary Operations.
3. Isomorphic Binary Structures.
4. Groups.
5. Subgroups.
6. Cyclic Groups.
7. Generators and Cayley Digraphs.
II. PERMUTATIONS, COSETS, AND DIRECT PRODUCTS.
8. Groups of Permutations.
9. Orbits, Cycles, and the Alternating Groups.
10. Cosets and the Theorem of Lagrange.
11. Direct Products and Finitely Generated Abelian Groups.
12. *Plane Isometries.
III. HOMOMORPHISMS AND FACTOR GROUPS.
13. Homomorphisms.
14. Factor Groups.
15. Factor-Group Computations and Simple Groups.
16. **Group Action on a Set.
17. *Applications of G-Sets to Counting.
IV. RINGS AND FIELDS.
18. Rings and Fields.
19. Integral Domains.
20. Fermat's and Euler's Theorems.
21. The Field of Quotients of an Integral Domain.
22. Rings of Polynomials.
23. Factorization of Polynomials over a Field.
24. *Noncommutative Examples.
25. *Ordered Rings and Fields.
V. IDEALS AND FACTOR RINGS.
26. Homomorphisms and Factor Rings.
27. Prime and Maximal Ideas.
28. *Gr�bner Bases for Ideals.
VI. EXTENSION FIELDS.
29. Introduction to Extension Fields.
30. Vector Spaces.
31. Algebraic Extensions.
32. *Geometric Constructions.
33. Finite Fields.
VII. ADVANCED GROUP THEORY.
34. Isomorphism Theorems.
35. Series of Groups.
36. Sylow Theorems.
37. Applications of the Sylow Theory.
38. Free Abelian Groups.
39. Free Groups.
40. Group Presentations.
VIII. *GROUPS IN TOPOLOGY.
41. Simplicial Complexes and Homology Groups.
42. Computations of Homology Groups.
43. More Homology Computations and Applications.
44. Homological Algebra.
IX. Factorization.
45. Unique Factorization Domains.
46. Euclidean Domains.
47. Gaussian Integers and Multiplicative Norms.
X. AUTOMORPHISMS AND GALOIS THEORY.
48. Automorphisms of Fields.
49. The Isomorphism Extension Theorem.
50. Splitting Fields.
51. Separable Extensions.
52. *Totally Inseparable Extensions.
53. Galois Theory.
54. Illustrations of Galois Theory.
55. Cyclotomic Extensions.
56. Insolvability of the Quintic.
Appendix: Matrix Algebra.
Notations.
Answers to odd-numbered exercises not asking for definitions or proofs.
Index.

"I am a mathematics professor at a small liberal arts university in Canada, and I use Fraleigh's book to teach a 300-level full-year introductory course in abstract algebra. I find it excellent. It is clear to me that Fraleigh has been teaching a course very similar to mine, to students very similar to mine, for probably three decades. He has figured out almost exactly the right way to introduce a difficult subject. He makes my job easy.

The book is broken into many small chapters, each of which can be easily translated into one or two hours of high-quality lecture. Thus, I can structure my lectures to closely follow the book, which has two advantages: (1) less preparation time for me (important when you have a heavy teaching load but still want to do a good job) and (2) The students have effectively a preprinted copy of the classroom lecture notes (so they can spend less time writing notes and more time paying attention and learning).

Fraleigh avoids the countless pitfalls which bedevil the naive algebra instructor (and many other textbook writers). He keeps things simple without making them stupid. Math students at my university have a wide range of background and skills. Some are highly talented and motivated, and I want to adequately prepare these students for graduate school. Others students are `future highschool teachers' (may God help our children) who apparently chose to study math because they thought it would resemble the polynomial arithmetic which they enjoyed in highschool, and who are often quite upset to discover otherwise. For these people, math is `supposed' to be computation, and any kind of logic or abstraction is anathema.

There are some abstract algebra texts (such as Bloch) which are designed to appeal to the `computational' crowd. Abstract algebra is one of the most beautiful and important parts of mathematics, and I describe these books as `algebra murdered and come back rotting from the grave'. There are also algebra books (such as Dummit & Foote, or Michael Artin) which are designed for `future graduate students'. Although I love these books, they are too sophisticated for most of my students. Also, their long chapters and sometimes poor organization means that preparing a decent lecture is often a lot of work.

Fraleigh finds an excellent compromise between these extremes. He develops some quite sophisticated material (including Galois theory and homology), but always finds a way to explain things simply and clearly. He provides exactly the right amount of information (e.g. the right number of examples and corollaries) to allow the instructor to move through the material efficiently (so you can actually finish the syllabus), while still explaining everything clearly. The exposition is lucid, and the books tightly organized. There are plenty of exercises which are challenging, but not too challenging, which is a boon when you are designing homework assignments.

I have a few small issues. For example, I don't think it's a good idea to develop group theory in terms of `abstract binary operations; one should develop it in terms of concrete symmetry groups. Also, I found that the section on the structure theory of finitely generated abelian groups and the chapter on homology theory were both a bit weak and needed to be supplemented. However, these are both very minor complaints compared to the overall quality of the book.

Teaching an advanced pure math course with a poorly designed textbook is a nightmare (and I should know). Teaching algebra using Fraleigh was a snap."


"This book was my introduction to algebra, and I can say that with me it hit its target - I not only learned and understood abstract algebra, but I grew to love it and be thrilled by it. If you are outside of mathematics and looking for the way in, I don't think you can do much better than Fraleigh. You'll outgrow it - almost as soon as you put it down. But that's just testament to how far it can take you in just a dozen or so chapters.

I would recommend, if you can afford it, also buying a copy of a zippier book like Hungerford or Dummit & Foote (ask around) and using it together with Fraleigh. Fraleigh won't let you down in terms of giving you the space you sometimes need to grasp things (for example, he gives Tons of examples, and there are plenty of easy exercises that allow you to soak in patterns in the structures for yourself) and an advanced book will give you increased perspective and power."
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