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!

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

• 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%.

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

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

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

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

• Discussion of Homework 2

• 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

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

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

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

• Discussion of Homework 4

• 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.

• Question and Answer Day

• Exam 1

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

• Generating function manipulations

• 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

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

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

• Poster Work Day

• 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)

• Discussion of Homework 6

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

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

•••••• Please fill out the college-wide course evaluations, distinct from the course evaluations that will be given out in class. Thank you for your feedback! ••••••

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

• 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.

• Question and Answer Day

• Exam 2

• Poster Work Day

• Poster Session

•••••• Please fill out the college-wide course evaluations, distinct from the course evaluations that will be given out in class. Thank you for your feedback! ••••••

• Podcast recording Session

• Discussion of Homework 8