# Due Homework Topic
| 1 | Jan. 26
|
7.4 #8,10,(12,15) 7.6 # (5a) |
Properties of Ideals The Chinese Remainder Theorem |
| 2 | Feb. 2 | 8.1 #1a,2a,3, (8,one value for each part), 10, (11) 8.2 #1,(2),3 |
Euclidean Domains Principal Ideal Domains |
| 3 | Feb. 9 | 8.3 #5 with n odd,(6c) 9.1 #2,5,6,(7) 9.2 #1,2,5,(7),8 |
Unique Factorization Domains Basics of polynomial rings R[x] F[x] |
| 4 | (Holiday Feb. 16) Feb. 18 |
9.3 # (1), 2, 3, (4) 9.4 # 1,2, (3), first half of 5, 11, (19d), 20 |
Factorization in Polynomial Rings Irreducibility Criteria |
| 5 | (Take-home test due 2/23) Mar. 2 |
10.1 #1,2,5,(6),7,8a,(9,10),11,19 10.2 # (2),3,8,(12) |
Basics of Modules Quotients and Homomorphisms |
| 6 | (Break Mar. 9-13) Mar. 18 |
10.3 # (2),4,6,(7) 12.1 # 6 |
Free Modules Modules over PIDs |
| 7 | Mar. 23 | 11.1 # 8, (9) 11.2 # 8 See handout for other homework problems 11.4 # 5 |
Vector Space Basics Matrices Linear Transformations Determinants |
| 8 | (Take-home test due 3/ 30) April 6 |
12.2 # (9), (10) 12.3 # (6), (21) 13.1 #1,4, (6) |
Rational Canonical Form Jordan Canonical Form Field Extensions |
| 9 | April 13 |
13.2 #1,2,(4),5,(9),10,(11),12,13,16 |
Algebraic Extensions |
| 10 | April 20 |
13.3 # 4, 5 13.4 # 1 13.5 # 1, (6) 13.6 # 2, 10, (11) |
Constructibility Splitting Fields Separability Cyclotomic and Finite Fields |
| 11 | April 27 |
13.2 # (18) 14.1 # 4,(6),7,(8) 14.2 # 1,4 |
Elements of Galois Theory Galois Groups |
| 12 | May 4 (In my mailbox) |
14.2 # 3,5,6,15,(17) |
Fundamental Theorem of Galois Theory |