Math 120 notes: Groups and rings

1. Overview of Groups: 9/24/12......Page 1 2. Meeting D2n and Sn: 9/26/12......Page 3 3. Homomorphisms and Isomorphisms: 9/28/12......Page 4 4. The Structure of Cyclic Groups: 10/1/12......Page 5 5. Quotient Groups: 10/3/12......Page 7 6. More Quotient Groups: 10/5/12......Page 8 7. Consequences of Lagrange's Theorem: 10/8/12......Page 9 8. The First Isomorphism Theorem: 10/10/12......Page 10 9. The Alternating Group: 10/12/12......Page 11 10. Proof That An is Simple when n5: 10/15/12......Page 13 11. Group Actions: 10/17/12......Page 14 12. Applications of Group Actions: 10/19/12......Page 15 13. Sylow's Theorems: 10/22/12......Page 16 14. More on Sylow's Theorems: 10/26/12......Page 17 15. Direct Products: 10/29/12......Page 18 16. Introduction to Rings: 10/31/12......Page 19 17. Ring Homomorphisms: 11/2/12......Page 20 18. The Chinese Remainder Theorem: 11/5/12......Page 22 19. Integral Domains and Maximal Ideals: 11/7/12......Page 23 20. PIDs and UFDs: 11/9/12......Page 24 21. Proof that PIDs are UFDs: 11/12/12......Page 25 23. Examples of Euclidean Domains: 11/16/12......Page 27 24. Factorization in the Gaussian Integers: 11/26/12......Page 28 25. Finite Fields: 11/28/12......Page 30 26. Existence of Finite Fields of Order pn: 11/30/12......Page 31 27. Uniqueness of Finite Fields of Order pn: 12/3/12......Page 32 28. Review of Group Theory: 12/5/12......Page 33 29. Review of Ring Theory: 12/7/12......Page 34