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
Bonus: Susan D'Agostino book and interview
Do the following before next class:
- Read Section 5.1, at least through page 63, in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Thursday.
- Finish Homework 4, and upload your solutions to the Homework 4 assignment on Moodle.
Do the following before next class:
- Read Sections 5.2–5.3 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Thursday.
- Review your exam and the solutions (on Moodle). Make sure you understand the solutions that you may have missed on the exam. If you have questions, talk with Prof. Wright.
- Take a look at Homework 5, which is due next Tuesday, October 27.
Thursday
October 22
October 22
Disjoint unions and product spaces
Bonus: Steven Strogatz: How things in nature tend to sync up and The Joy of Why
Do the following before next class:
- Read Section 5.4 in the Essential Topology textbook, at least through page 82, and complete the reading questions. Bring your completed reading questions to class on Tuesday.
- Finish Homework 5, and upload your soloutions to the Homework 5 assignment on Moodle.
Do the following before next class:
- Finish reading Section 5.4 in the Essential Topology textbook.
- Read "Configuration Spaces and Phase Spaces" by Adams and Franzosa, available on Moodle (pages 105–111) or on the Internet Archive (pages 123–129).
- Read the Term Paper Information. Think about what topic you would like to study and who you would like to work with.
- Begin Homework 6, which is due on November 3.
Thursday
October 29
October 29
Quotient Spaces
Do the following before next class:
- Read Section 6.1 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Tuesday.
- Finish Homework 6 and upload your soloutions to the Homework 6 assignment on Moodle.
- Consider possible topics and groups for the Term Paper. By next Thursday, you will need to complete the Term Paper Planning Survey.
- To start preparing for the next exam, review the definitions and examples in Chapters 4 and 5.
Do the following before next class:
- Consider possible topics and groups for the Term Paper and complete the Term Paper Planning Survey.
- Re-read Section 6.1, then read Section 6.2 in the Essential Topology textbook. Complete the reading questions, and bring your completed reading questions to class on Tuesday.
- Take a look at the Exam 2 Info. Review the definitions and examples in Chapters 4 and 5.
- Begin Homework 7, which is due next Tuesday.
Thursday
November 5
November 5
Homotopy
Bonus video: Moon Duchin: "Political Geometry" and DistrictR
Do the following before next class:
- In the Essential Topology textbook, read as much as you like from Section 6.3. There are no reading questions for Tuesday.
- 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 six results listed on the Exam 2 info page.
Kathryn Hess: interview in the AMS Notices and TEDx Talk: Digital Neuroscientist of the Future
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.
Thursday
November 12
November 12
Exam 2
Do the following before next class:
- Work on finding at least three sources for your term paper. Refer to the Term Paper Information.
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
