Math 5220 Spring 2015
Tentative Schedule


January

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
2
3


4
5
6
7
8
9
10


11
FIRST DAY
13
14
15
16
17


18
No Class
20
21
22
23
24


25
26
27
28
29
30
31




February

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
2
3
4
5
6
7


8
9
10
11
12
13
14


15
16
17
18
19
20
21


22
23
24
25
26
27
28




March

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
2
3
4
5
6
7


8
No Class
No Class
No Class
No Class
No Class
14


15
16
17
18
19
20
21


22
23
24
25
26
27
28


29
30
31





April

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
2
3
4


5
No Class
No Class
8
9
10
11


12
13
14
15
16
No Class
18


19
20
21
22
23
24
25


26
27
28
29
30





May

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


LAST DAY
2


3
4
5
6
7
8
9


10
11
12
13
14
15
16


17
18
19
20
21
22
23


24
25
26
27
28
29
30


31









Tentative Topic for Class #...

 Categories - introduction/examples
 Functors & natural transformations
 Universal properties, limits & colimits
 Adjoint functors
 Derived functors & Yoneda embedding
 Ring preliminaries
 Euclidean domains, PIDs, UFDs
 Gauss's lemma, chain conditions
 Computations in polynomial quotient rings
 Finish factorizations
 Module basics
 Free, projective, injective, flat modules
 Classifying PID modules
 Finitely generated Abelian groups
 Rational canonical form, Jordan form, Smith normal form
 Finish modules
 Field extensions, finite fields
 Splitting fields, algebraic closures
 Galois groups
 Galois correspondence
 Solvability
 
 
 
 
 
 
 





Last Updated January 8th, 2014.