Math 181

Tu-Th 2:30-3:50
Kassar 205
Prof. Rich Schwartz
Office Hours: Tu 12-1 and Th 4-5
TA: Henning Ulfarsson

This is a topics course about surfaces and their structure,
designed for undergrads who are very interested in math.

• Handout 0: postscript or PDF
  Topic: Course Info
  
  
• Handout 1: postscript or PDF
  Topic: Metric Spaces; definition of a surface
  
  
• Handout 2: postscript or PDF
  Topic: Constructing Surfaces and Manifolds
  
  
• Handout 3: postscript or PDF
  Topic: The Fundamental Group
  
  
• Handout 4: postscript or PDF
  Topic: The Fundamental Group Computed for some Familiar Objects
  
  
• Handout 5: postscript or PDF
  Topic: Covering Spaces and the Deck Group
  
  
• Handout 6: postscript or PDF
  Topic: Smooth Surfaces and Riemannian Metrics
  
  
• Handout 7: postscript or PDF
  Topic: Intro to Hyperbolic Geometry
  
  
• Handout 8: postscript or PDF
  Topic: Hyperbolic Surfaces and Polygon Gluings
  
  
• Handout 9: postscript or PDF
  Topic: The Universal Cover of a Hyperbolic Surface
  
  
• Handout 10: postscript or PDF
  Topic: Basic Complex Analysis
  
  
• Handout 11 postscript or PDF
  Topic: The Schwarz-Christoffel Transformation
  
  
• Handout 12 postscript or PDF
  Topic: Riemann Surfaces and the Uniformization Theorem
  
  
• Handout 13 postscript or PDF
  Topic: Euclidean Cone Surfaces and Billiards
  
  
• Handout 14 postscript or PDF
  Topic: Veech Surfaces, Hyperbolic Geometry, and the Octagon