Math 4010 & 5530 Spring 2014
Tentative Schedule


January

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
2
3
4


5
6
7
8
9
10
11


12
13
Class 1
15
Class 2
17
18


19
No Class
Class 3
22
Class 4
24
25


26
27
Class 5
29
Class 6
31





February

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1


2
3
Class 7
5
Class 8
7
8


9
10
Class 9
12
Class 10
14
15


16
17
Class 11
19
Class 12
21
22


23
24
Class 13
26
Class 14
28





March

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1


2
3
Class 15
5
Class 16
7
8


9
No Class
No Class
No Class
No Class
14
15


16
17
Class 17
19
Class 18
21
22


23
24
Class 19
26
Class 20
28
29


30
31





April

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


Class 21
2
Class 22
4
5


6
7
Class 23
9
Class 24
11
12


13
14
Class 25
16
Class 26
18
19


20
No Class
No Class
23
Class 27
25
26


27
28
Class 28
30





May

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


Class 29
2
3


4
5
6
7
8
Final Exam
9-11:30am
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 #...

 Syllabus, Free Groups (DF Section 6.3)
 Factoring homomorphisms, universal property for Generators & Relations
 Examples of groups, group actions. (Surveying DF Chapter 1)
 More group examples (Finish surveying DF Chapter 1)
 Cosets, Lagrange's Theorem, & Orbit Stabilizer Theorem.
 Survey Chapter 2 (centralizers, normalizers, subgroups generated by a subset, cyclic groups, subgroup lattice) & Conjugacy classes and the class equation. 
 Survey Chapter 3
 Group actions again. Cayley's theorem, acting by conjugation (4.1-4.3)
 McKay's proof of Cauchy's Theorem, Sylow I, and Sylow II
 SNOW DAY
 Sylow III, Applications.
 More applications, Automorphisms.
 Survey Chapters 5 & 6
 Representation theory/linear algebra basics
 Irredicible, indecomposible, etc. Schur's lemma(s)
 More on indecomposibility/irreducibility (block matrices), examples, roots of unity
 complex inner product spaces, the averaging trick
 Maschke's theorem
 ??? 
 ???
 ???
 How to obtain normal subgroups from the character table.
 Algebraic integers and the dimension theorem
 Review for Test #2. Some bits from Galois theory and Burnside's theorem.
 Test #2
 Finished Burnside's theorem and started real characters & real conjugacy classes
 ???Finish real chars/conj. classes. Burnside's counting theorem.
 ???Tensor products???
 ???Frobenius Reciprocity???
 Final Exam ???GAP Demo???





Last Updated April 23rd, 2014.