- Syllabus.
- Textbook: Hatcher, Algebraic Topology.
- Lecture 1: Welcome.

notes, worksheet. - Lecture 2: What spaces are we interested in?

notes, worksheet. - Reading 1 (due 10/4):

Chapter 0: pages 1–14 (skip “The Homotopy Extension Property”) and also look at the exercises.

Chapter 1: pages 21–28 (stop at “The Fundamental Group of the Circle”) - Homework 1 (due 10/5): pdf, tex. Solutions: pdf, tex.
- Lecture 3: Homotopy.

notes, worksheet. - Lecture 4: Homotopy equivalence.

notes, worksheet. - Lecture 5: The fundamental group.

notes, worksheet. - Reading 2 (due 10/11): Finish §1.1.
- Homework 2 (due 10/12):

Chapter 0 #1, 12, 18; §1.1 #5, 6.

Solutions: pdf, tex. - Lecture 6: The fundamental group of the circle, I.

notes, worksheet. - Lecture 7: The fundamental group of the circle, II.

notes, worksheet. - Lecture 8: First fruits of π
_{1}(S^{1}).

notes, worksheet. - No reading due 10/18.
- Homework 3 (due 10/19): pdf, tex. Solutions: pdf, tex.
- Lecture 9: Induced maps.

notes, worksheet. - Lecture 10: π
_{1}(*X*×*Y*) and π_{1}(*S*).^{n}

notes, worksheet. - Lecture 11: Free products, statement of van Kampen’s theorem.

notes, worksheet. - Reading 3 (due 10/25): §1.2.
- Homework 4 (due 10/26): pdf, tex. Solutions: pdf, tex.
- Lecture 12: Proof of van Kampen’s theorem.

notes, no worksheet. - Midterm 1 (due 10/30): pdf, tex. Solutions: pdf, tex.
- Lecture 13: Attaching discs; projective space.

notes, worksheet. - Lecture 14: Some knots via van Kampen’s theorem.

notes, no worksheet. - Reading 4 (due 11/1): §1.3. This is long, but there’s no homework this week.
- Lecture 15: Covering spaces.

notes, worksheet. - Lecture 16: Covering spaces, continued.

notes, no worksheet. - Lecture 17: Lifting criterion.

notes, worksheet. - No reading for 11/8.
- Lecture 18: Deck transformations.

notes, no worksheet. - Homework 5 (due 11/11):

§1.2 #9 (take g = 2 and h = k = 1 if you want).

§1.3 #8, 12.

Draw a simply-connected cover of each of the four spaces from Homework 3 #4. Hint: They all have π_{1}= ℤ, so the fiber will have to be ℤ.

Solutions: pdf, tex. - Lecture 19: Universal covers.

notes, worksheet. - Lecture 20: Homology.

notes, worksheet. - Reading 5 (due 11/15): Chapter 2; stop at “Exact Sequences and Excision” on page 113.
- Lecture 21: Induced maps.

notes, worksheet. - Lecture 22: Relative homology.

notes, no worksheet. - Midterm 2 (due 11/20): pdf, tex. Solutions: pdf, tex.
- Lecture 23: Long exact sequence of a pair: statement, examples.

notes, worksheet. - Reading 6 (due 11/22): Continue reading Chapter 2; stop at “Excision” on page 119.
- Lecture 24: Long exact sequence of a pair: proof.

notes, worksheet. - Lecture 25: Long exact sequence of a pair, continued.

notes, worksheet. - Reading 7 (due 11/29): “Cellular Homology” starting on page 137. Some details are important and some are not, so feel free to skim, but be sure to catch Examples 2.36 and 2.42.
- Homework 6 (due 11/30):

§2.1 #12, 15, 20. Challenge: 21.

Solutions: pdf, tex. - Lecture 26: Miscellaneous.

notes, no worksheet. - Lecture 27: Homology of surfaces.

notes, worksheet. - Lecture 28: Cellular homology.

notes, no worksheet. - Final Exam (due 12/11): pdf, tex. Solutions: pdf, tex.