# Math 4990: UMTYMP Advanced Topics Course

# (Combinatorics)

# Fall 2020

## Instructor: |
Sam Hopkins (call me "Sam") Office: No physical office this semester! E-mail: shopkins@umn.edu |
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## Classes: |
Tue: 4-6pm (CDT), on Zoom (see email for link) | |||||||||||||||||||||||||||

## Office hours: |
By appointment, online (via Zoom, email, etc.) | |||||||||||||||||||||||||||

## Course content: |
This is a course in discrete mathematics, including enumerative combinatorics, graph theory, and optimization. We will try to cover as much of the textbook as possible, at the rate of about one chapter a week. There will be an emphasis on reading and writing proofs. When you finish this class, you should be well prepared for upper-division mathematics courses. |
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## Required text: |
A walk through combinatorics, by Bóna, 3rd edition (although other editions should be ok). Please contact me if you need help accessing the text. |
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## Course format: |
Class will be held once a week via Zoom. About half the class time will be spent on lecture, and the other half on working in groups on worksheets related to the material. I will post PDFs of the lecture notes, as well as the worksheets, on this page. Assignments will also be posted to this page. I plan to communicate with the class mostly via messages from Canvas. Although this will be the main webpage for the course, on the Canvas site you can engage in discussions with me and with other students. We will also use Canvas for submission and return of assignments. You can also check your grades on Canvas. And recordings of the classes will be posted to Canvas. If you have any suggestions for improving the class, please let me know! |
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## Grading: |
The overall grade for the course will be computed as follows: - Homework = 40% of grade
- Each of 2 midterms = 20% of grade
- Final exam = 20% of grade
- 2 weeks where there will be a week-long take-home midterm exam,
- a week at the end with a week-long take-home final exam.
I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page their collaborators. Late assignments will not be accepted. As mentioned, homework submissions will be via Canvas. The take-home midterms and final exam are open-book, open-library, open-web, but in contrast to the homework on exams, no collaboration or consultation of human sources is allowed (except you can ask me questions for clarification). Solutions should be well-explained; I won't give credit for an unsupported answer. Complaints about the grading should be brought to me. If you have a disability which requires accommodation, please let me know (and also contact the Disability Resource Center). |
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## Assignments: |
The tentative schedule of assignments is as follows. All HW exercises are from the text (3rd edition; check with me if you have another edition):
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## Class worksheets: |
Worksheet for 9/8 on induction and the pigeonhole principle Worksheet for 9/15 on poker hand probabilities, and solutions Worksheet for 9/22 on binomial coefficients and Pascal's triangle Worksheet for 9/29 on Stirling numbers of the 2nd kind Worksheet for 10/6 on Stirling numbers of the 1st kind Worksheet for 10/13 on the Principle of Inclusion-Exclusion Worksheet for 10/20 on (ordinary) generating functions Worksheet for 10/27 on Catalan numbers Worksheet for 11/3 on walks in graphs Worksheet for 11/10 on trees Worksheet for 11/17 on coloring Worksheet for 11/24 on matchings Worksheet for 12/1 on planar graphs Worksheet for 12/8 on Ramsey theory |
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## Lecture notes: |
Tuesday, Sept. 8th: here Tuesday, Sept. 15th: here Tuesday, Sept. 22nd: here Tuesday, Sept. 29th: here Tuesday, Oct. 6th: here Tuesday, Oct. 13th: here Tuesday, Oct. 20th: here Tuesday, Oct. 27th: here Tuesday, Nov. 3rd: here Tuesday, Nov. 10th: here Tuesday, Nov. 17th: here Tuesday, Nov. 24th: here Tuesday, Dec. 1st: here Tuesday, Dec. 8th: here Tuesday, Dec. 15th: here |