Topology

• Complete the Introductory Survey, if you haven't done so already.
• Read the syllabus carefully and complete the Syllabus Quiz on Moodle.
• Read pages 1–14 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Tuesday.

• 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.

Bonus video: Paths to Math: John Urschel

• Finish Homework 1, and upload your solutions to the Homework 1 assignment on Moodle.
• 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.

• 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.

Bonus video: Eugenia Cheng on The Late Show

• Finish reading Section 4.1, and read the first two pages of 4.2. Also read Topologies in Applications." Complete the reading questions and bring them to class on Tuesday.
• Read "How to write proofs: a quick guide" by Eugenia Cheng.
• Finish Homework 2 and upload your soloutions to the Homework 2 assignment on Moodle.

• Begin Homework 3, which is due next Tuesday, October 1.
• Re-read Section 4.1 and read Section 4.2 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Thursday.
• Read the Exam 1 Info.

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

• 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.

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

• 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.

• 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.

• 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.
• Read Section 5.1 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 soloutions to the Homework 4 assignment on Moodle.

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

• 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.
• Take a look at Homework 5, which is due on October 22.

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

• Read Section 5.4 in the Essential Topology textbook 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.
• Read the Term Paper Information. Think about what topic you would like to study and who you would like to work with.

• Read Configuration Spaces and Phase Spaces and also pages 89–92 in the Essential Topology textbook. Complete the reading questions and bring your completed reading questions to class on Thursday.
• Consider possible topics and groups for the Term Paper Planning Survey. Refer to the Term Paper Information.
• Begin Homework 6, which is due on October 29.

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

• Read Sections 6.1–6.2 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.
• To start preparing for the next exam, review the definitions and examples in Chapters 4 and 5.

• Re-read Section 6.2 in the Essential Topology textbook.
• Work on finding at least three sources for your term paper. Refer to the Term Paper Information.
• 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.

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

• 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.

• 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).

• 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.

• Read Chapter 7 in the Essential Topology textbook and complete the reading questions. Bring your completed reading questions to class on Thursday.
• Prepare an outline of what you plan to write for your term paper. Include citations of at least three sources. (Refer to the Term Paper Information.) Submit these items to the Term paper outline and sources item on Moodle.

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

• 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.

• Read this introduction to simplicial homology by Starbird and Su.
• Finish Homework 8 and upload your soloutions to the Homework 8 assignment on Moodle.
• Work on your Term Paper. Continue reading sources and start writing a draft of your paper. A draft of your paper is due next Tuesday, November 26.

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

• 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.

• To be determined

• To be determined