Algebraic Topology I
  
Notes 
    
  1. Introduction
    1. What is Algebraic Topology
    2. Knot Theory
    3. Knot coloring
  2. Introduction to Topology
    1. Topological Spaces
    2. Limit Points and Sequences
    3. Continuous Functions
    4. Connectedness
    5. Compactness
    6. Quotient Spaces
  3. Manifolds
    1. Definitions and First Examples
    2. 1-manifolds
    3. 2-manifolds
  4. Groups
    1. Basic group theory
    2. Group presentations
  5. The Fundamental Group
    1. Definition of the Fundamental Group
    2. Fundamental Group of S^1
    3. Applications
  6. Seifert-Van Kampen Theorem
    1. Free products with amalgamation
    2. The Seifert-Van Kampten theorem
    3. The fundamental group surfaces, and first homology
    4. Groups and Topology
    5. Free products and topology
  7. Knot Groups and colorings
    1. Knot groups
    2. Colorings
  8. Covering Spaces
    1. Covering Spaces
    2. Subgroups
    3. More of Free Products
  9. Brief Intorduction to Homology