Algebra I

Calendar

SES #	TOPICS	KEY DATES
1	The general linear group GLn, groups, generators	Problem set 1 out
2	The symmetric group Sn, subgroups
3	Subgroups of Z+, cyclic groups
4	Homomorphisms and isomorphisms	Problem set 1 due Problem set 2 out
5	Cosets
6	The correspondence theorem
7	Product groups, quotient groups	Problem set 2 due Problem set 3 out
8	Fields
9	Vector spaces, bases, dimension
10	Computation with bases	Problem set 3 due Problem set 4 out
11	The dimension formula
12	Linear operators, eigenvectors
13	First quiz
14	The characteristic polynomial	Problem set 4 due Problem set 5 out
15	Jordan form
16	Rotations	Problem set 5 due Problem set 6 out
17	Isometries
18	Finite groups of isometries
19	Discrete groups of isometries	Problem set 6 due Problem set 7 out
20	Discrete groups of isometries (cont.)
21	Group operations
22	Finite rotation groups	Problem set 7 due Problem set 8 out
23	The class equation
24	Second quiz
25	The icosahedral group
26	The symmetric and alternating groups	Problem set 8 due Problem set 9 out
27	Symmetric and hermitian forms
28	Orthogonality
29	The projection formula	Problem set 9 due Problem set 10 out
30	The spectral theorem
31	Quadrics
32	The special unitary group SU2	Problem set 10 due Problem set 11 out
33	The rotation group SO3
34	One-parameter groups
35	One-parameter groups (cont.)
36	Third quiz
37	The lie algebra
38	Simple groups	Problem set 11 due