Week 1: 25 January - 29 January
Monday: Welcome and warm up.
- Reading: Syllabus.
- Notes: day01.
- Homework due: Syllabus contract.
Wednesday: Topological spaces and bases.
Friday: Metric spaces and continuity.
- Reading: 0.1.
- Notes: day03.
Week 2: 1 February - 5 February
Monday: Categories.
- Reading: 0.2.1.
- Notes: day04.
Wednesday: Isomorphisms.
- Reading: 0.2.1.
- Notes: day05.
Friday: Functors.
Week 3: 8 February - 12 February
Monday: Examples and terminology.
- Reading: 1.1.
- Notes: day07.
Wednesday: Subspace topology.
- Reading: 1.2.
- Notes: day08.
Friday: Quotient topology.
Week 4: 15 February - 19 February
Monday: ❄ SNOW DAY ❄
- Exam 1 distributed via Slack.
Wednesday: ❄ SNOW DAY ❄
Friday: Product topology.
- Reading: 1.4.
- Notes: day10.
- Exam 1 due via Gradescope by 23:00.
- Homework due: none.
Week 5: 22 February - 26 February
Monday: The homotopy category.
- Reading: 1.6.
- Notes: day11.
Wednesday: Connectedness I.
- Reading: 2.1.1-2.
- Notes: day12.
Friday: Connectedness II.
Week 6: 1 March - 5 March
Monday: Connectedness III.
- Reading: None.
- Notes: day14.
Wednesday: Hausdorff spaces.
- Reading: 2.2.
- Notes: day15.
Friday: Compactness I.
Week 7: 8 March - 12 March
Monday: Compactness II.
- Reading: 2.3.2.
- Notes: day17.
- Supplement on uniform continuity: unif_cts.
Wednesday: NO CLASS.
Friday: Sequences.
Week 8: 15 March - 19 March
Monday: Filters.
- Reading: 3.3.
- Notes: day19.
Wednesday: Ultrafilters.
- Reading: 3.4.1.
- Notes: day20.
Friday: Tychonoff's theorem.
Week 9: 22 March - 26 March
Monday: Natural transformations and the Yoneda lemma.
- Reading: 0.2.3.
- Notes: day22.
- Exam 2 distributed via Slack.
Wednesday: NO CLASS.
- Exam 2 due via Gradescope by 23:00.
Friday: Diagrams, limits, and colimits.
- Reading: 4.1-2.
- Notes: day23.
- Homework due: none.
Week 10: 29 March - 2 April
Monday: Examples of (co)limits.
- Reading: 4.3.
- Notes: day24.
Wednesday: More examples + (co)completeness.
- Reading: 4.4.
- Notes: day25.
Friday: Adjunctions. REST.
Week 11: 5 April - 9 April
Monday: Adjoint functors.
- Reading: 5.1-2.
- Notes: day26.
Wednesday: Compactifications.
- Reading: 5.3-5.
- Notes: day27.
Friday: Exponentiation and the compact-open topology.
- Reading: 5.6-5.6.1.
- Notes: day28.
- Homework due: week11.
Week 12: 12 April - 16 April
Spring Break. 🌱🌈🌞
Week 13: 19 April - 23 April
Monday: The fundamental group(oid).
- Reading: 6.1-2.
- Notes: day29.
Wednesday: Suspensions and loops.
- Reading: 6.3-5.
- Notes: day30.
Friday: Fibrations.
Week 14: 26 April - 30 April
Monday: Going around in circles.
- Reading: 6.6.2.
- Notes: day32.
Wednesday: The Seifert-van Kampen Theorem.
- Reading: 6.7.
- Notes: day33.
Friday: Seifert-van Kampen applications + review.
- Reading: None.
- Homework due: None. (Or write up something interesting for extra credit.)
\(\LaTeX\) resources
- \(\LaTeX\)
(getting started in \(\LaTeX\))
- short
guide
- Change .pdf to .tex in the URL of (nearly) any file accessed from
this page to get the \(\LaTeX\) source code.