| 1 |
Groups, matrices, permutations |
Problem set 1 out |
| 2 |
Subgroups, cyclic groups |
|
| 3 |
Isomorphisms |
|
| 4 |
Homomorphisms |
Problem set 1 due
Problem set 2 out
|
| 5 |
Cosets |
|
| 6 |
Quotient groups |
|
| 7 |
Modular arithmetic, fields |
Problem set 2 due
Problem set 3 out
|
| 8 |
Fields |
|
| 9 |
Vector spaces, bases, dimension |
Problem set 3 due
Problem set 4 out
|
| 10 |
Computation with bases |
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| 11 |
The dimension formula |
|
| 12 |
First quiz |
Problem set 4 due |
| 13 |
Linear operators, Eigen vectors |
Problem set 5 out |
| 14 |
The characteristic polynomial |
|
| 15 |
Rotations |
Problem set 5 due
Problem set 6 out
|
| 16 |
Isometries |
|
| 17 |
Isometries of the plane |
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| 18 |
Finite groups of isometries |
Problem set 6 due
Problem set 7 out
|
| 19 |
Discrete groups |
|
| 20 |
Discrete groups (cont.) |
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| 21 |
Group operations |
Problem set 7 due
Problem set 8 out
|
| 22 |
Finite rotation groups |
|
| 23 |
The class equation |
|
| 24 |
Permutation representations |
Problem set 8 due
Problem set 9 out
|
| 25 |
The alternating group |
|
| 26 |
Second quiz |
|
| 27 |
Bilinear forms |
|
| 28 |
Symmetric forms |
Problem set 9 due
Problem set 10 out
|
| 29 |
Hermitian forms |
|
| 30 |
The spectral theorem |
|
| 31 |
Quadrics |
Problem set 10 due |
| 32 |
The special unitary group SU2 |
|
| 33 |
The rotation group |
|
| 34 |
One-parameter groups |
Problem set 11 out |
| 35 |
One-parameter groups (cont.) |
|
| 36 |
Third quiz |
|
| 37 |
The lie algebra |
|
| 38 |
Dimensions of the linear groups |
|
| 39 |
Simple groups |
Problem set 11 due |