Math 120 Notes

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