Math 342

Topology (& Categories), Spring 2021

Exams:
  • Exam 1: distributed Monday 15 February, due Wednesday 17 February.
  • Exam 2: distributed Monday 22 March, due Wednesday 24 March.
  • Final Exam: distributed Monday 10 May, due Wednesday 12 May.
Lecture notes
Current week
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.
  • Reading: 2.1.3-4.
  • Notes: day13.
  • Homework due: week05.
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.
  • Reading: 3.4.2-3.
  • Notes: day21.
  • Homework due: week08.
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
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  • short guide
  • Change .pdf to .tex in the URL of (nearly) any file accessed from this page to get the \(\LaTeX\) source code.