Math 155r Combinatorics (Fall 2019)
Instructor: Sebastien Vasey
Office: Science Center 321H
Email: sebv (at) math (dot) harvard (dot) edu
Course assistant: George Han (hanz (at) college)
Lectures: Tuesday and Thursday, 10h30AM-11h45AM (SC 222)
Canvas page (for administrivia)
Do not forget to evaluate the class on the Q!
Office hours and problem session
George will have office hours on Friday, Dec. 6, at a time to be announced. No other office hours are scheduled. Enjoy your break!
Latest news / Announcements
The last exam will be a 48 hours take home from Dec. 3 to Dec. 5. More information about the last exam.
Reading assignments
Unless noted otherwise, chapter and section numbers are from Matoušek and Nešetřil, Invitation to discrete mathematics, 2nd ed., Oxford University Press 2008.
- For the week of Sep. 2-Sep.6: Chapter 1 (most of it should be review) and Chapter 2 (for Thursday).
- For the week of Sep. 9-Sep. 13: Sections 2.3, 2.4, 3.1, 3.2 (for Tuesday) and sections 3.3, 3.4, 3.5 (for Thursday).
- For the week of Sep. 16-Sep. 20: Sections 3.5-3.8 (for Tuesday) and sections 4.1-4.3 (for Thursday).
- For the week of Sep. 23-Sep. 27: Sections 4.4-4.5 (for Tuesday) and sections 4.6-4.7 (for Thursday).
- For the week of Sep. 31-Oct. 4: Sections 4.7, 7.3 (for Tuesday) and sections 5.1, 5.3, 5.4, 5.5, 8.1, 8.2 (for Thursday).
- For the week of Oct. 7-Oct. 11: Sections 6.1, 6.2 (for Tuesday) and sections 6.3, 6.4 (for Thursday).
- For the week of Oct. 14-Oct. 18: Read section 7.1 for Tuesday. Review for the midterm on Thursday.
- For the week of Oct. 21-Oct. 25: section 7.2 (for Tuesday) and section 9.1 (for Thursday).
- For the week of Oct. 28-Nov. 1: sections 9.1-9.2 (for Tuesday) and sections 9.3-9.4 (for Thursday).
- For the week of Nov. 4-Nov. 8: no reading for Tuesday, read sections 9.4 and 10.1 for Thursday.
- For the week of Nov. 11-Nov. 15: section 10.2 (for Tuesday), section 10.3 and 10.4.1, 10.4.2 (for Thursday).
- For the week of Nov. 11-Nov. 15: section 10.2 (for Tuesday), section 10.3 and 10.4.1, 10.4.2 (for Thursday).
- For the week of Nov. 18-Nov. 22: 10.4.3 and the notes on the Erdős-Ko-Rado theorem (for Tuesday), chapter 11 (for Thursday).
- For Nov. 26: The notes on Schur's theorem and Fermat's last theorem modulo a prime.
- For Dec. 3: No reading. Let me know if you would like to give a short presentation of your project (for extra credit).
Assignments
- Assignment 1 (due Tuesday, September 10). Latex source. Questionnaire. Solution.
- Assignment 2 (Updated Sep. 11 to clarify Dilworth's theorem. Due Tuesday, September 17). Latex source Solution.
- Assignment 3 (Due Tuesday, September 24). Latex source Solution.
- Assignment 4 (Due Tuesday, October 1). Latex source Solution.
- Assignment 5 (Due Tuesday, October 8). Latex source Solution.
- Assignment 6 (Due Tuesday, October 15, 11h59pm). Latex source Solution.
- Assignment 7 (Due Thursday, October 24). Latex source Solution.
- Assignment 8 (Due Tuesday, October 29). Latex source Solution.
- Assignment 9 (Due Wednesday, November 6, 11h59pm). Latex source Solution.
- Assignment 10 (Due Wednesday, November 13, 11h59pm). Latex source Solution.
- Assignment 11 (Due Tuesday, November 19). Latex source Solution.
- Assignment 12 (Due Tuesday, November 26, 11h59pm). Latex source Solution.
Exams
Other course documents
Other resources
- More combinatorics books:
- J. H. Van Lint and R. M. Wilson, A course in combinatorics, 2nd ed., Cambridge University Press 2001.
- Ronald L. Graham, Donald E. Knuth, Oren Patashnik, Concrete mathematics: a foundation for computer science, 2nd ed., Addison-Wesley 1994.
- If you are struggling with proofs, I recommend Hammack's Book of Proof.
- For LaTeX (completely optional) :
- Just for fun: