The following is a tentative syllabus for the course. Practice exercises are from the text and are not to be graded. It is good to choose a few practice problems from each set to check your understanding.
Week | Lectures | Sections in Text | Brief Description | Practice Exercises |
---|---|---|---|---|
1 | 9/16 | Ch 1, 2 | Introduction, Operations | Chapter 2: A, B |
9/18 | Ch 3, 4 | Groups | Chapter 3: A, B, D Chapter 4: C, D |
|
9/19 | (x-hour) | Proof techniques (Practice) (Solutions) | ||
9/20 | Ch 5 | Subgroups | Chapter 5: A.1,4,6, B.1-3, C.1,4, E | |
2 | 9/23 | Ch 6, 7 | Functions, permutations | Chapter 6: B.1-3, D.2, E.3,5 Chapter 7: B, D, F.2 |
9/25 | Ch 7, 8 | Permutations of a finite set | Chapter 8: A.5,6, B.4,5, C.1, D.1-3 | |
9/27 | Ch 9 | Isomorphisms | Chapter 9: B.3, E.2,6 | |
3 | 9/30 | Ch 9,10 | More on isomorphisms, order of group elements | Chapter 10: B, C, F |
10/2 | Ch 11 | Cyclic groups | Chapter 11: A, B, E | |
10/3 | (x-hour) | Problem session (Practice) (Solutions) | ||
10/4 | No class today. | |||
4 | 10/7 | Ch 12 | Partitions and equivalence relations | Chapter 12: A.1-2, B.1-4, C.1-6 |
10/9 | Exam 1 in-class portion | Material through Ch 11. Take-home portion due 10/11. | ||
10/11 | Ch 13 | Cosets and Lagrange's Theorem | Chapter 13: A.1-2, B.3-5, C.4, E.1-3 | |
5 | 10/14 | Ch 14 | Homomorphisms and normal subgroups | Chapter 14: A.2,4, B.6, C.1-3, D.1-4 |
10/16 | Ch 15 | Quotient groups | Chapter 15: A.1,5,6, B.1-3, C.1 | |
10/18 | Ch 16 | Fundamental homomorphism theorem | Chapter 16: A.1,4,5, C.1-3 | |
6 | 10/21 | Ch 16 | More on FHT | |
10/23 | Ch 17 | Rings | Chapter 17: A.1-7, C.1-3, H.1-3, I.1-4 | |
10/24 | (x-hour) | Problem session (Practice) (Solutions) | ||
10/25 | Ch 18 | Ideals and homomorphisms | Chapter 18: A.3,6, B.1-4, C.1,3,4, E.1,3,4, G.5 | |
7 | 10/28 | Ch 19 | Quotient rings | B.1,3,4, C.1,2, E.2,6, F.1-4 |
10/30 | Exam 2 in-class portion | Material through Ch 18. Take-home portion due 11/1. | ||
11/1 | Ch 20 | Integral domains | Chapter 20: A.1,3,5, B.1, C.1, E.7 | |
8 | 11/4 | Ch 20 | Finite fields | Chapter 20: D.1-7, F.1-3 |
11/6 | Ch 24 | Polynomial rings | Chaper 24: A.1,2,5, B.4, C.2,3 | 11/7 | (x-hour) | Special topic: elliptic curves | Note: Not covered on the final exam. |
11/8 | Ch 25 | Factoring polynomials | Chapter 25: A.3, B.1-7, C.1 | |
9 | 11/11 | Ch 25 | Factoring polynomials | Chapter 25: D.3, F.1-4 |
11/13 | Ch 26 | Substitution in polynomials | Chapter 26: A.1-4, C.1-4,7 | |
11/15 | Ch 26 | Eisenstein's irreducibility criterian | Chapter 26: B.1,5, E.1-4 | |
10 | 11/18 | Wrap-up | Final Exam Study Guide (Practice) (Solutions) |