SES # | TOPICS | KEY DATES |
---|---|---|
1 | The general linear group GL_{n}, groups, generators | Problem set 1 out |
2 | The symmetric group S_{n}, 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 SU_{2} |
Problem set 10 due Problem set 11 out |
33 | The rotation group SO_{3} | |
34 | One-parameter groups | |
35 | One-parameter groups (cont.) | |
36 | Third quiz | |
37 | The lie algebra | |
38 | Simple groups | Problem set 11 due |