Grades in the course will be determined on the following basis:

Homeworks and class participation | 100 points |

Quizes | 100 points |

Take-home final | 200 points |

The following syllabus is somewhat tentative. It is possible that there might
be some slippage and some topics might be omitted. The precise quiz dates will
be announced at least one week in advance.

Week of | Topics Covered |
---|---|

Jan. 5 | surfaces and manifolds |

Jan. 12 | classification of compact connected surfaces |

Jan. 19 | Quiz 1, homotopy and the fundamental group |

Jan. 26 | fundamental group of the circle and applications, free groups and presentations |

Feb. 2 | Quiz 2, Seifert-van Kampen Theorem |

Feb. 9 | calculations of fundamental groups |

Feb. 16 | Quiz 3, definition and examples of covering spaces |

Feb. 23 | Quiz 4, liftings of maps, relation to fundamental group, universal covers |

Mar. 2 | Quiz 5, applications to graphs and surfaces |

Mar. 9 | Quiz 6, genus of smooth projective curves |