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

Homeworks and class pariticipation | 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 |
---|---|

Sept. 24 | Euler's formula, informal discussion of topology |

Sept. 29 | Metric spaces, continuity, topological spaces: definitions and examples |

Oct. 6 | Connectedness, path connectedness |

Oct. 13 | Quiz 1, compactness |

Oct. 20 | Space-filling curves, countability, separation axioms |

Oct. 27 | Function spaces, completeness, Banach fixed-point theorem, applications |

Nov. 3 | Tietze extension theorem, Urysohn metrization theorem, Quiz 3 |

Nov. 10 | Identification (quotient) spaces, topological groups, orbit spaces |

Nov. 17 | Quiz 4, projective spaces, manifolds |

Nov. 24 | Classification of 1-manifolds, classification of surfaces |

Dec. 1 | Classification of surfaces contd., Quiz 5 |