#### Prerequisites & Bulletin Description

#### Course Objectives

The main objective of Algebraic Topology is to give students an introduction to the main ideas and techniques of algebraic topology. Students will investigate some of the major topics of algebraic topology ? two-dimensional manifolds, triangulations of surfaces, the Euler characteristic, homotopy, the fundamental group, free groups, free abelian groups, the Seifert and Van Kampen theorem, covering spaces, the fundamental group of a covering space. They will also apply these ideas to a wide range of problems that include the Brouwer fixed point theorem, an introduction to knot theory and the Borsak-Ulam theorem.

#### Evaluation of Students

Students will be evaluated on their ability to devise, organize and present complete solutions to problems. While instructors may design their own methods of evaluating student performance, these methods may include in-class examinations, homework assignments and a final exam.

#### Course Outline

Topics |
Number of Weeks |

Two-dimensional Manifolds | 3.5 |

The Fundamental Group | 3 |

Free Groups | 2 |

The Seifert and Van Kampen Theorem | 3 |

Covering Spaces | 3.5 |

#### Textbooks & Software

*Algebraic Topology: An Introduction*, William Massey

*Elements of Algebraic Topology*, James Munkres

Submitted by: Alex Schuster

Date: May 7, 2003