Abstract Algebra : An Inquiry Based Approach

✍ Scribed by Hodge, Jonathan K.; Schlicker, Steven; Sundstrom, Ted

• Publisher: CRC Press
• Year: 2013
• Tongue: English
• Leaves: 593
• Series: Textbooks in Mathematics
• Category: Library

✦ Synopsis

""This book arose from the authors' approach to teaching abstract algebra. They place an emphasis on active learning and on developing students' intuition through their investigation of examples. ... The text is organized in such a way that it is possible to begin with either rings or groups.""
-Florentina Chirteş, Zentralblatt MATH 1295

Abstract:

""This book arose from the authors' approach to teaching abstract algebra. They place an emphasis on active learning and on developing students' intuition through their investigation of examples. ... The text is organized in such a way that it is possible to begin with either rings or groups.""
-Florentina Chirteş, Zentralblatt MATH 1295

✦ Table of Contents

Content: Front Cover
Contents
Note to Students
Preface
I. The Integers
1. The Integers: An Introduction
2. Divisibility of Integers
3. Greatest Common Divisors
4. Prime Factorization
II. Other Number Systems
5. Equivalence Relations and Zn
6. Algebra in Other Number Systems
III. Rings
7. An Introduction to Rings
8. IntegerMultiples and Exponents
9. Subrings, Extensions, and Direct Sums
10. Isomorphism and Invariants
IV. Polynomial Rings
11. Polynomial Rings
12. Divisibility in Polynomial Rings
13. Roots, Factors, and Irreducible Polynomials
14. Irreducible Polynomials 15. Quotients of Polynomial RingsV. More Ring Theory
16. Ideals and Homomorphisms
17. Divisibility and Factorization in Integral Domains
18. From Z to C
VI. Groups
19. Symmetry
20. An Introduction to Groups
21. Integer Powers of Elements in a Group
22. Subgroups
23. Subgroups of Cyclic Groups
24. The Dihedral Groups
25. The Symmetric Groups
26. Cosets and Lagrange's Theorem
27. Normal Subgroups and Quotient Groups
28. Products of Groups
29. Group Isomorphisms and Invariants
30. Homomorphisms and Isomorphism Theorems
31. The Fundamental Theorem of Finite Abelian Groups 32. The First Sylow Theorem33. The Second and Third Sylow Theorems
VII. Special Topics
34. RSA Encryption
35. Check Digits
36. Games: NIM and the 15 Puzzle
37. Finite Fields, the Group of Units in Zn, and Splitting Fields
38. Groups of Order 8 and 12: Semidirect Products of Groups
A. Functions
B. Mathematical Induction and theWell-Ordering Principle

✦ Subjects

Algebra, Abstract -- Textbooks.