Date

Chapter

Topic

Homework

1/14

10.110.3

Review of Modules and Direct Products^{}


1/16

10.3, 10.4

Free Modules and Extension of Modules using Tensor Products

10.2: 6, 9, 10, 11, 12, 1310.3: 2, 7, 9, 11

1/18

10.4

Tensor Products


1/23

10.4

Tensor Products

10.4: 2, 3, 6, 7, 10, 12, 16, 19, 25due on 2/4

1/25

10.5

Exact Sequences


1/28

10.5

Projective Modules


1/30

10.5

Injective Modules

10.5: 1, 2, 3, 6, 7
due on 2/8

2/1

10.5

Injective Zmodules


2/4

10.5

Flat Modules


2/6

11.111.4

Linear Algebra Review and Dual Vector Spaces

10.5: 15, 16, 21, 25, 28
11.3: 1, 4

2/8

11.5

Tensor Algebras


2/11

11.5

Symmetric Algebras


2/13

11.5

Exterior Algebras

11.5: 4, 6, 8, 13
12.2: 8, 10, 14
Due 2/25

2/15


Review


2/18


Midterm I


2/20

12.2

Rational Canonical Form


2/22

12.2, 12.3

Rational Canonical Form, Jordan Canonical Form


2/25

12.3, 13.1

Jordan Canonical Form, Field Extensions


2/27

13.1

Field Extensions

12.3: 5, 9, 18, 22, 37
13.1: 2, 3, 6

3/1

13.2

Algebraic Extensions


3/4

13.2

Algebraic Extensions


3/6

13.4

Splitting Fields

13.2 4, 8, 9, 12, 14, 16, 1813.4 2, 4

3/8

13.4

Algebraic Closures


3/18


No Class


3/20

13.5

Separability

13.5 1, 2, 4, 5, 8

3/22

13.6

Cyclotomic Fields


3/25

14.1

Fixed Fields

13.6 1, 3, 4, 6, 8
14.1 1, 8, 9

3/27

14.1

Galois Extensions


3/29

14.1

Galois Extensions


4/1


Take Home Midterm II


4/3

14.2

The Galois Correspondence


4/5

14.2

The Galois Correspondence


4/8

14.4

Joins and Intersections of Galois Extensions


4/10

14.5

Abelian Extensions

14.2: 5, 6, 8, 9, 13, 23, 29
14.4: 4, 6

4/12

14.5

Abelian Extensions


4/15

14.6

Galois Groups of Polynomials


4/17

14.6

Galois Groups of Polynomials

14.5: 1, 7, 8
14.6: 2(a,b), 7, 11, 13, 14

4/19

14.7

Solvability by radicals


4/22

14.7

Insolvability by the quintic


4/24

14.9

Transcendental Extensions

14.7: 4, 7, 9, 12, 19
14.9: 6, 7, 9,

4/26

14.9

Transcendental Extensions


4/29


Review


5/1


Review


5/3


Review


5/10


Final exam

7:30 am
Take home problems 14.6 15 and 48
