Date

Chapter

Topic

Homework

1/12

10.1,10.2

Modules and Module Homomorphisms
^{}


1/14

10.3

Direct Sums and Free Modules

10.1 5, 8, 9, 10; 10.2 4, 6, 8, 9, 10

1/16

10.4

Tensor Products


1/21

10.4

Tensor Products

10.3 9, 12, 13; 10.4 2, 3, 5, 7, 12, 16, 19

1/23

10.5

Exact Sequences and Projective Modules


1/26

10.5

Injective Modules


1/28

10.5

Injective Modules

10.5 1, 2, 3, 7, 10, 12, 15, 16

1/30

10.5

Flat Modules


2/2

11.111.2

Linear Algebra Review


2/4

11.3

Dual Vector Spaces

10.5 5, 9, 20, 22 and 11.3 4, 5

2/6

11.5

Tensor Algebras


2/9

11.5

Tensor Algebras continued


2/11

12.1

Modules over PIDs


2/13

12.2

Rational Canonical Form

11.5 1, 5, 13 and 12.2 9, 10, 11, 14

2/16

12.2

Rational Canonical Form


2/18

12.3

Jordan Canonical Form


2/20


Review


2/23


Midterm 1


2/25

13.1

Field Extensions

12.3 3, 5, 21, 24, 31; 13.1 1, 3 and 13.2 2, 4, 7

2/27

13.2

Algebraic Extensions


3/2

13.3

Ruler and Compass Constructions


3/4

13.4

Splitting Fields

13.2 9, 12, 14, 18; 13.3 4, 5; 13.4 4, 6

3/6

13.4

Algebraic Closures


3/16

13.5

Separable Extensions


3/18

13.6

Cyclotomic Extensions

13.5 1, 3, 5, 8, 10; 13.6 1, 3, 6

3/20

14.1

Field Automorphisms


3/23

14.1

Field Automorphisms


3/25

14.1

Field Automorphisms

14.1 5, 6, 8, 10; 14.2 3, 5, 9, 12 
3/27

14.2

Fundaamental Theorem of Galois Theory


3/30

14.2

Fundamental Theorem of Galois Theory


4/1

14.2

Fundamental Theorem of Galois Theory


4/3


Review


4/6


Midterm 2


4/8

14.4

Primitive element Theorem

14.2 15, 17, 18, 22, 23

4/10

14.4

Primitive element Theorem


4/13

14.5

Abelian Extensions


4/15

14.6

Galois Groups of Polynomials

14.4 1, 2, 5; 14.5 3, 8; 14.6 22, 23

4/17

14.7

Solvable and Radical Extensions: Insolvability of the Quintic


4/20

14.9

Transcendental Extensions


4/22

15.1

Noetherian Rings

14.6 2, 6, 13, 15; 14.7 3, 9, 10 
4/24

15.2

Radicals and Affine Varieties


4/27

15.3

Hilbert's Nullstellensatz


4/29

15.3

Hilbert's Nullstellensatz


5/1


Review


5/6


Final Exam

7:30 am
