Math 462 (Abstract Algebra) Syllabus
Spring 2003

Homework: There are 10 problem sets. Each problem set is worth 10 points. They are due at the lecture indicated by HW#N. 

HW#1: pp. 260-263: 2, 3, 6, 7, 8, 12, 17, 18, 31, 40, 44. 

1
Rings and Fields
5.1
2
" " "
5.1
3
Integral Domains
5.2 
4
HW#1 Fermat's and Euler's Thms.
5.3

HW#2: pp. 268-269: 3, 5, 6, 10, 13, 14, 21; p. 276: 4, 12. 

5
Field of Quotients of a Domain
5.4
6
Rings of Polynomials
5.5 
7
HW#2 " " "
5.5 

HW#3: p. 284: 2; pp. 295-297:1, 5, 12, 13, 20, 22, 24, 29. 

8
Division Algorithm in F [x]
5.6 
9
 " " "
5.6
10
HW#3 Irreducible Polynomials
5.6

HW#4: pp. 306-308: 1, 7, 9, 10, 13, 16, 32, 33

11
" " " Cylotomic Polynomials
5.6 
12
Factorization in F [x]
5.6
13
 HW#4 Homomorphisms and Factor Rings
6.1
14
" " "
6.1

HW#5: pp. 331- 334: 1, 4, 11, 12, 13, 20, 24, 26, 37, 39

15
Ideals
6.1
16
R e v i e w
 
17
--------- Exam 1 -------- 
 
18
Fundamental Homomorphism  Theorem
6.1
19
HW#5 Prime and Maximal Ideals
6.2

HW#6: pp. 390 - 392: 2, 3, 6, 29, 30, 34, 35, 36

20
" " "
6.2
21
Introduction to Extension Fields
8.1
22
Algebraic and Transcendental Elements; Simple Extensions
8.1

HW#7: pp. 411 - 412: 3, 4, 6, 10, 25, 26, 28

23
HW#6 Vector Spaces
8.2
24
Finite Extensions
8.3
25
HW#7 R e v i e w
 
26
--------- Exam 2 --------
 
27
Finite Extensions
8.3

HW#8: p. 418: 3, 4; pp. 423 - 4 24: 2, 5, 10, 15

28 
Geometric Constructions
8.4
29
 " " "
8.4
30
Finite Fields
8.5
31
" " "
8.5
32
HW#8  Automorphisms of Fields
9.1

HW#9: pp. 438 - 441: 6, 9, 11, 30, 32, 33

33
" " "
9.1
34
 " " "
9.1
35
Splitting Fields
9.3
36
" " "
9.3
37
HW#9 R e v i e w
 

HW#10: pp. 472 - 473: 1, 2, 3, 4; p. 480: 1, 4, 7

38
--------- Exam 3 --------
 
39
Introduction to Galois Theory
9.6
40
 " " "
9.6
41
" " "
9.6
42
Examples
9.7
43
HW#10 Cyclotomic Extensions
9.8
44
" " "
9.8
 
45
Insolvability of the Quintic
9.9
 
46
R e v i e w
9.9
 

Final Exam