Welcome to Topology! For homework submission and grades, log into Moodle. If you need help, contact Prof. Wright.
Prof. Wright's office hours: Mon. 2–3pm, Tues. 9–10am, Wed. 12–1pm, Thurs. 10–11am, Fri. 1–2pm, and other times by appointment (in RMS 405)
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Thursday
September 10
September 10
Introduction, set theory, continuous functions
Do the following before next class:
- Complete the Introductory Survey, if you haven't done so already.
- Read the syllabus carefully and complete the Syllabus Quiz on Moodle before class on Tuesday.
- Read this review of set theory and logic.
- Read pages 1–14 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Tuesday.
- Optionally, take a look at Homework 1.
Tuesday
September 15
September 15
Continuity and open sets
Do the following before next class:
- Begin Homework 1, which is due next Tuesday, September 22.
- 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.
Bonus video: Paths to Math: John Urschel
Do the following before next class:
- Finish Homework 1, and upload your solutions to the Homework 1 assignment on Moodle. Try to do this before class, though there is time after class to ask last-minute questions.
- Re-read all of the examples in Sections 3.1 and 3.2, then continue through the end of Section 3.3 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Tuesday.
MSCS Colloquium: What is big? Understanding geometric notions of size. Monday, September 21, 3:30–4:30pm in RNS 210
Do the following before next class:
- Review the problems and solutions from class today.
- Begin Homework 2, which is due next Tuesday, September 29.
- Read Section 3.4 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Thursday.
Thursday
September 24
September 24
Subspaces and Bases
Do the following before next class:
- Read Section 4.1 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Tuesday.
- Read two perspectives on proofwriting: Eugenia Cheng describes the logic of mathematical proofs in How to write proofs: a quick guide, and Ted Sundstrom gives style guidelines for mathematical writing in Guidelines for Writing Mathematical Proofs (Appendix A of his Mathematical Reasoning text).
- Finish Homework 2 and upload your soloutions to the Homework 2 assignment on Moodle. Note that Homework 1 solutions are on Moodle, and a Homework 2 template is available on Overleaf.
Northfield Undergraduate Mathematics Symposium Tuesday, September 29, 3:15–7:05pm at Carleton
Do the following before next class:
- Re-read Section 4.1 and read Section 4.2 at least through the proof of Proposition 4.21 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Thursday.
- Begin Homework 3, which is due next Tuesday, October 6.
- Read the Exam 1 Info.
Thursday
October 1
October 1
Compactness
Do the following before next class:
- Re-read Section 4.2 and read Section 4.3 at least through page 51 in the text. Complete the reading questions and rbmdling your completed reading questions to class on Thursday.
- 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.
Math Across the Cannon: Dr. Po-Shen Loh, public lecture Monday, Oct. 5 at St. Olaf and student colloquium Tuesday, Oct. 6 at Carleton. Attend either talk and answer these questions on Moodle to receive extra credit.
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 8
October 8
Exam 1
Have a great fall break! No class October 13.
Do the following before next class:
- Read "Examples of Topologies in Applications" by Adams and Franzosa, available on Moodle (pages 44–54) or on the Internet Archive (pages 62–72).
Thursday
October 15
October 15
Hausdorff property
Do the following before next class:
- Complete Homework 4, which is due on Tuesday, October 20.
- More to be announced...
Do the following before next class:
- To be announced...
Thursday
October 22
October 22
Disjoint unions and product spaces
Do the following before next class:
- To be announced...
Tuesday
October 27
October 27
Quotient spaces and configuration spaces
Homework 5
due at 11pm
due at 11pm
Do the following before next class:
- To be announced...
Thursday
October 29
October 29
Homotopy
Do the following before next class:
- To be announced...
Tuesday
November 3
November 3
Homotopy
Homework 6
due at 11pm
due at 11pm
Do the following before next class:
- To be announced...
Thursday
November 5
November 5
Homotopy and the circle
Do the following before next class:
- To be announced...
Tuesday
November 10
November 10
Homotopy and the circle
Homework 7
due at 11pm
due at 11pm
Do the following before next class:
- To be announced...
Thursday
November 12
November 12
Exam 2
Do the following before next class:
- To be announced...
Tuesday
November 17
November 17
Simplices
Do the following before next class:
- To be announced...
Thursday
November 19
November 19
Simplicial complexes and Euler characteristic
Do the following before next class:
- To be announced...
Tuesday
November 24
November 24
Simplicial homology
There is no assignment over break.
Have a great Thanksgiving break! No class November 26.
Tuesday
December 1
December 1
Simplicial homology
Do the following before next class:
- To be announced...
Thursday
December 3
December 3
Computing homology
- To be announced...
Tuesday
December 8
December 8
Computing homology
Do the following before next class:
- To be announced...
Thursday
December 10
December 10
Simplicial complexes from data; Persistent homology
Do the following before next class:
- To be announced...
Tuesday
December 15
December 15
Persistent homology; Topological data analysis
We've made it to the end of the semester!
- To be announced...
Saturday
December 19
December 19
Final Exam 1:00 – 3:00pm
