Schedule

This is the tentative course schedule; there may be small changes as the semester progresses


Week 1 (Wed Jan 12)

Classes start on Wednesday Jan 12.

Sections and topics covered:

  • § Introduction and Motivation: Why is topology important?

Week 2 (Wed Jan 19)

No class on Monday (Martin Luther King Jr. Day)

Sections and topics covered:

  • § Review of set theory (Chapter 1)

Week 3 (Monday Jan 24 - Wednesday Jan 26)

Sections and topics covered:

  • §12 Topological spaces
  • $13 Basis for a topology
  • §14 The order topology

Week 4 (Monday Jan 31 - Wednesday Feb 2)

  • §15 The product topology
  • $16 The subspace topology
  • §17 Closed sets

Week 5 (Monday Feb 7 - Wednesday Feb 9)

  • §17 Boundary, Interior and Hausdorff Spaces
  • §18 Continuous functions.

Week 6 (Monday Feb 14 - Wednesday Feb 16)

  • §20-21 Metric spaces
  • §22 The quotient topology

First midterm material ends here


Week 7 (Monday Feb 21 - Wednesday Feb 23)

  • §23 Connected spaces
  • §24 Connected spaces of R
  • §25 Components and local connectedness

Week 8 (Monday Feb 28 - Wednesday Mar 2)

  • First Midterm Exam Monday Feb 28.
  • §26 Compactness
  • §27 Compact subspaces of R

Week 9 (No classes)

Spring break: Mar 5 - Mar 13.


Week 10 (Monday Mar 14 - Wednesday Mar 16)

  • §28 Limit point compactness
  • §29 Local compactness

Week 11 (Monday Mar 21 - Wednesday Mar 23)

  • §43 Complete metric spaces
  • §45 Compactness in metric spaces
  • §46 Convergence in metric spaces

Second midterm material ends here


Week 12 (Monday Mar 28 - Wednesday Mar 30)

  • Review of group theory
  • §51 Homotopy of Paths
  • §52 The fundamental group

Week 13 (Monday Apr 4 - Wednesday Apr 6)

  • Second Midterm Exam Monday Apr 4.

  • §53 Covering spaces


Week 14 (Monday Apr 11 - Wednesday Apr 13)

  • §54 The fundamental group of the circle
  • Further topics in homotopy theory

Week 15 (Monday Apr 18 - Wednesday Apr 20)

  • Manifolds and Surfaces

Week 16 (Monday Apr 25 - Wednesday Apr 27)

  • Classification of Surfaces

Last day of classes

Final Exam: Tuesday, May 03, 830am