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 |