# 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!

- You are allowed a
- 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)

- You are allowed a
- The final exam date is scheduled by the registar, and will be posted here when it is determined.
- 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.

- You are allowed a