This page is for a past course. Find your current course here.

For each date below, you will find the homework assignment that is due that day, any lecture notes for downloading, and the key topics that are covered that day.

This schedule is approximate and subject to change!

Thursday, August 28

- Notes from Section 1.1 (Notes pages 0–10) '
- Syllabus discussion.
- Material from Section 1.1 and more

Tuesday, September 2

Before class:

- Email me at chanusa@qc.cuny.edu with the following three or four things: (1) Your name, (2) Your class (Math 636) (3) the email address where you are best contacted. If you are an undergraduate also send me (4) your graduation year.
- Thoroughly read the class web page including the syllabus and schedule. This should answer all the questions that you may have about the class. Next, take the
**syllabus quiz**on Blackboard. Retake the quiz as necessary to earn a score of 100%.

In class:

- Notes from Sections 1.1 and 1.2 (Notes pages 11–23) '
- Simple Counting
- Multiplication Principle
- Examples

Thursday, September 4

- Notes from Sections 1.2 & 2.2 (Notes pages 24–32) '
- Counting pitfalls
- Overcounting, Counting the complement
- Pascal's triangle and the binomial theorem

Tuesday, September 9

Homework #1 is due on Tuesday, September 9. (.tex file)

- Notes from Section 1.3 (Notes pages 33–39) '
- Bijections
- Bijection Worksheet

Thursday, September 11

- Notes from Section 1.4 (Notes pages 40–46) '
- Equivalence classes
- Counting using symmetry

Tuesday, September 16

Homework #2 is to be prepared for presentation on Tuesday, September 16. (.tex file)

- Discussion of Homework 2

Thursday, September 18

- Notes from Sections 2.1, 2.2, and 4.2 (Notes pages 47–55) '
- Combinatorial proofs
- Tiling interpretation of Fibonacci numbers
- Worksheet on Combinatorial proofs

No class on September 23 and 25

Tuesday, September 30

- Notes from Sections 2.1 through 2.4 (Notes pages 56–65) '
- Counting distributions
- The sixteenfold way

Thursday, October 2

Homework #3 is due on Thursday, October 2. (.tex file)

- Stirling numbers, Bell numbers
- Integer partitions
- Notes from Section 3.1 and pp. 165–166 (Notes pages 66–77) '
- Principle of Inclusion/Exclusion

Tuesday, October 7

- Principle of Inclusion/Exclusion
- Derangements
- Formulas for Stirling numbers and Bell numbers

Thursday, October 9

Homework #4 is to be prepared for presentation on Thursday, October 9. (.tex file)

- Discussion of Homework 4

Exam 1 Information

- The first exam of the semester will take place on Thursday, October 16.
- The exam covers all material covered through October 9.
- Here are more details about the first exam.
- My students often ask for an example of the style of exam that I am liable to give. I am including my exam from last year. The topics covered by the exam are the same topics, but you should expect your exam to be very different because there are many ways for me to ask questions that test your knowledge on these topics. Click here for last year's exam.

Tuesday, October 14

- Question and Answer Day

Thursday, October 16

- Exam 1

Tuesday, October 21

- Notes from Sections 3.3 and 3.4 (Notes pages 78–87) '
- Introduction to generating functions
- Application: Fruit baskets
- Application: Dice

Thursday, October 23

- Generating function manipulations

Tuesday, October 28

Project topic due Tuesday.

- Notes from Sections 3.5 and 3.4 (Notes pages 88–95) '
- Solving recurrence relations
- Fibonacci generating function
- Products of generating functions
- Products and powers of generating functions

Thursday, October 30

- Notes from external material (Notes pages 96–101) '
- Compositions of generating functions
- And their combinatorial interpretations
- Generating function worksheet

Tuesday, November 4

Homework #5 is due on Tuesday, November 4. (.tex file)

- Notes from Sections 2.4, 3.4, and 4.4 (Notes pages 102–109) '
- Integer partitions
- Integer partition bijections
- Standard Young Tableaux

Thursday, November 6

- Poster Work Day

Tuesday, November 11

- Notes from Section 4.1 PLUS additional material (Notes pages 110–118) '
- Catalan numbers
- Catalan number interpretations
- The "meta" method for Catalan numbers
- (Handy handout about Catalan numbers)
- (link to Stanley's Catalan Interpretations)

Thursday, November 13

Homework #6 is to be prepared for presentation on ~~Tuesday, November 11~~ Thursday, November 13. (.tex file)

- Discussion of Homework 6

Tuesday, November 18

Project outline due ~~Thursday 11/13~~ Tuesday, 11/18.

- Notes on Combinatorial Statistics (Notes pages 119–129) '
- Combinatorial statistics
- Descent statistic des(π)
- Inversion statistic inv(π)
- Major statistic maj(π)

Thursday, November 20

Continue work on Poster.

- (no new notes)
*q*-analogs*q*-factorial*q*-binomial coefficients- PDF about
*q*-analogs

Tuesday, November 25

Start work on Homework #7.

- Notes (Notes pages 131–145) '
- Research topics in algebraic combinatorics

Exam 2 Information

- The second exam of the semester will take place on Thursday, December 4.
- The exam is NOT cumulative. It covers all material since the first exam.
- Here are more details about the second exam.
- My students often ask for an example of the style of exam that I am liable to give. I am including my exam from last year. The topics covered by the exam are the same topics, but you should expect your exam to be very different because there are many ways for me to ask questions that test your knowledge on these topics. Click here for last year's exam.

Tuesday, December 2

Homework #7 is due on Tuesday, December 2. (.tex file)

- Question and Answer Day

Thursday, December 4

- Exam 2

Tuesday, December 9

Continue work on Poster.

- Poster Work Day

Thursday, December 11, 4:30-6:30pm

- Poster Session

Individually scheduled

- Podcast recording Session

- Discussion of Homework 8