Math 281: Combinatorics (Spring 2024)

This course emphasizes enumerative combinatorics, a classical subject in mathematics related to the theory of counting. Problems in this area often pertain to finding the number of possible arrangements of a set of objects under some particular constraints. This course incorporates a wide set of problems involving enumerative combinatorics, as well as theory and applications.

Time and location

• Monday, Wednesday, and Friday, 10:00-10:50am (SMUD 204)

Help hours

• My regular office hours in SMUD 401:
  • Tuesday 2:30-4:30
  • Wednesday 10:00-10:50
  • Friday 10:00-10:50
• Our Math Fellow (TA) is Alan Li. His regular help hours are:
  • Monday 9:00-10:30pm in SMUD 205
  • Wednesday 7:30-9:00pm in SMUD 205

Handouts and links

• Syllabus
• Textbook, freely available in pdf
• Boardwork from days when I teach from a tablet
• Review handouts on Sigma notation and Induction (gratefully borrowed from Prof. Folsom)
• Two proofs of a first theorem (gratefully borrowed from Prof. Folsom)

Problem Sets

• Gradescope instructions for all problems sets. Our course code is RKEDB2.
• There is a course survey on Gradescope. Please fill it out during the first week of class.
• Problem Set 1 (due Wednesday 2/7 Friday 2/9 at 10pm)
• Problem Set 2 (due Friday 2/16 by 10pm)
• Problem Set 3 (due Wednesday 2/21 by 10pm)
• Problem Set 4 (due Wednesday 3/6 by 10pm)
• Problem Set 5 (due Wednesday 3/13 by 10pm)
• Problem Set 6 (due Friday 3/29 by 10pm)
• Note: PSet 6 is due on a Friday due to Spring break, but PSet 7 will be posted by Wednesday 3/27 and due Wednesday 4/3.
• Problem Set 7 (due Wednesday 4/3 by 10pm)
• Problem Set 8 (due Friday 4/19 by 10pm)
• Problem Set 9 (due Friday 4/26 by 10pm)
• Problem Set 10 (due Friday 5/3 by 10pm)
• Problem Set 11 (for practice only; not to be submitted)

Exams

There will be two midterms and a three hour final exam. Mark the midterm dates on your calendar now.

• Midterm 1 will be in class on Wednesday 2/28.
  • You are allowed a one page notesheet, front and back, so that you don’t need to memorize formulas. Put some time into it – deciding what to put on the note sheet is a very useful study process!
• Midterm 2 will be in class on Wednesday 4/10.
  • You are allowed a one page notesheet, front and back, so that you don’t need to memorize formulas. Put some time into it – deciding what to put on the note sheet is a very useful study process!
  • The exam is not cumulative – covered material begins with the first topic not covered on Midterm 1.
    • Topics: end of 2.3 (counting sequences chosen from a given word) through beginning of 2.6.6 (Catalan recurrence, but not the generating function)
• The final exam date is on Friday 5/17, from 9am to noon.
  • You are allowed a one page notesheet, front and back, so that you don’t need to memorize formulas. Put some time into it – deciding what to put on the note sheet is a very useful study process!
  • The exam will be cumulative, though with increased emphasis on the material not yet covered on the midterms.