Matthew L. Wright
Associate Professor, St. Olaf College

Topology

MATH 348 ⋅ Fall 2024

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Thursday
September 5
Introduction; Continuous functions
Do the following before next class:
Tuesday
September 10
Do the following before next class:
  • Begin Homework 1, which is due next Tuesday, September 17.
  • Read Sections 3.1 and 3.2, at least through Example 3.24, in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Thursday.
Thursday
September 12
Topological spaces

Bonus video: Paths to Math: John Urschel

Do the following before next class:
Tuesday
September 17
Subspace topology
Homework 1
due at 5pm
Do the following before next class:
  • Begin Homework 2, which is due next Tuesday, September 24.
  • Read from the beginning of Section 3.4 through page 39 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Thursday.
Thursday
September 19

Bonus video: Eugenia Cheng on The Late Show

Do the following before next class:
Tuesday
September 24
Connectedness and Compactness
Homework 2
due at 5pm
Do the following before next class:
Thursday
September 26
Compactness

Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg and article The Psychology of Statistics by Jordan Ellenberg

MSCS Showcase Thursday, September 26, 4:30pm, Tomson 280

MSCS Colloquium: How many ways are there to juggle? Monday, September 30, 3:30–4:30pm in RNS 210

Do the following before next class:
  • Re-read Sections 4.1 and 4.2 in the text. There are no reading questions for Tuesday.
  • Finish Homework 3 and upload your soloutions to the Homework 3 assignment on Moodle.
  • Read the Exam 1 Info. Recall the precise definitions for each concept, as well as examples of things that satisfy or don't satisfy each definition. Think through the proofs of the results stated on the exam info page.
Tuesday
October 1
Hausdorff property
Homework 3
due at 5pm

Northfield Undergraduate Mathematics Symposium Tuesday, October 1, 3:15–6:45pm at Carleton

Do the following before next class:
  • Review the Exam 1 Info.
  • Re-read sections 2.1 through 4.2 in the text.
  • Make sure you can state precise definitions and give examples (with justification) of the concepts on the exam info page.
  • Make sure you can give proofs of the five results on the exam info page.
Thursday
October 3
Do the following before next class:
  • Read Sections 4.3 in the text. There are no reading questions for Tuesday.
  • Begin Homework 4. This homework is shorter than usual and is due on Thursday, October 10.
Tuesday
October 8
Homeomorphisms
Do the following before next class:
Thursday
October 10
Unions and products
Homework 4
due at 5pm

Terence Tao: blog and "The Potential for AI in Science and Mathematics"

MSCS Research Seminar: Craig Kaplan, "Computing Tiling Properties of Polyforms," Thursday, October 10, 11:30am–12:30pm in RNS 203

Have a great fall break! No class October 15.
Do the following before next class:
Thursday
October 17

Kathryn Hess: "Scientists discover hidden patterns of brain activity" and "Digital Neuroscientist of the Future"

Do the following before next class:
Tuesday
October 22
Quotient spaces and configuration spaces
Homework 5
due at 5pm
Do the following before next class:
Thursday
October 24
Finish quotient spaces; Begin homotopy

Bonus: Steven Strogatz "How things in nature tend to sync up" and The Joy of x podcast

Do the following before next class:
Tuesday
October 29
Homotopy
Homework 6
due at 5pm
Do the following before next class:
Thursday
October 31
Homotopy and the circle

Bonus: Why is Mathematics Useful — Robert Ghrist, and Intro to Topological Data Analysis

MSCS Colloquium: Prof. Steven McKelvey: "One Person, One Vote: The Electoral College, Gerrymandering and the Mathematics of Optimization" Monday, November 4, 3:30pm in RNS 210

Do the following before next class:
  • In the Essential Topology textbook, read as much as you like from Section 6.3.
  • Work on finding at least three sources for your term paper. Refer to the Term Paper Information.
  • Finish Homework 7 and upload your soloutions to the Homework 7 assignment on Moodle.
  • Study for Exam 2. Make sure you know the definitions from Chapters 4–6 and can demonstrate examples that satisfy or don't satisfy each definition. Review homework problems, and study the proofs of the five results listed on the Exam 2 info page.
Tuesday
November 5
Homotopy and the circle
Homework 7
due at 5pm
Do the following before next class:
  • Study for Exam 2.
  • Re-read Sections 4.1 through 6.2 in the Essential Topology textbook.
  • Make sure you know the definitions from Chapters 4–6. Make sure you can give examples and justify why they satisfy or don't satisfy each definition.
  • Practice writing the proofs of the five results on the exam info page.
  • Review homework problems (solutions are posted).
Thursday
November 7
Exam 2
Do the following before next class:
  • Work on finding your term paper. Read sources and prepare an outline of your paper. Your paper outline will be due Thursday, Nov. 14. Refer to the Term Paper Information.
Tuesday
November 12
Simplices
Do the following before next class:
Thursday
November 14
Simplicial complexes and Euler characteristic
Term paper
outline due

Bonus video: Francis Su — Mathematics for Human Flourishing short version and long version

Do the following before next class:
  • Read Section 9.1 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Tuesday.
  • Begin Homework 8, which is due next Thursday.
  • Work on your Term Paper. Continue reading sources and start writing a draft of your paper.
Tuesday
November 19
Do the following before next class:
Thursday
November 21
Simplicial homology
Homework 8
due at 5pm

Bonus videos: Satyan Devadoss — Blue Collar Mathematics and Mage Merlin's Unsolved Mathematical Mysteries

Do the following before next class:
  • Re-read Section 9.1 in the Essential Topology textbook.
  • Work on your Term Paper. Continue reading sources and start writing a draft of your paper. A draft of your paper is due Tuesday, November 26. One person from your group should upload your draft to the Term Paper Draft item on Moodle.
Tuesday
November 26
Term paper
draft due
There is no assignment over break.
Have a great Thanksgiving break! No class November 28.
Tuesday
December 3
Simplicial complexes from data
Do the following before next class:
  • To be determined
Thursday
December 5
Persistent homology
Term paper
due
Do the following before next class:
  • To be determined
Tuesday
December 10
Topological data analysis
Homework 9
due at 5pm
We've made it to the end of the semester!
Friday
December 13
Final Exam