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 0–19) '
• Syllabus discussion.
• Simple Counting
• Multiplication Principle
• Examples

• 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. Complete the Syllabus Treasure Hunt!!! for Tuesday and make sure you get the correct answer.
• (Download / Print out) the notes for Tuesday's class (below)
• Complete Homework #1. It is to be prepared for presentation in class on Tuesday, September 1.
  Link to the homework guidelines.

• Notes from Sections 1.2 & 2.2 (Notes pages 20–28) '
• Counting pitfalls
• Overcounting, Counting the complement
• Pascal's triangle and the binomial theorem

• Overcounting, Counting the complement

• Notes from Section 1.3 (Notes pages 29–35) '
• Bijections
• Bijection Worksheet

• Notes from Section 1.4 (Notes pages 36–42) '
• Equivalence classes
• Counting using symmetry

• Notes from Sections 2.1, 2.2, and 4.2 (Notes pages 43–51) '
• Combinatorial proofs
• Tiling interpretation of Fibonacci numbers
• Worksheet on Combinatorial proofs

• Notes from Sections 2.1 through 2.4 (Notes pages 52–61) '
• Counting distributions
• The sixteenfold way
• Stirling numbers, Bell numbers
• Integer partitions

• Notes from Section 3.1 and pp. 165–166 (Notes pages 62–73) '
• Principle of Inclusion/Exclusion

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

• The first exam of the semester will take place on Tuesday, October 13.
• The exam covers all material covered through October 6.
• 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
• Generating function worksheet

• Notes from Sections 3.5 and 3.4 (Notes pages 84–91) '
• Solving recurrence relations
• Fibonacci generating function
• Products of generating functions
• Products and powers of generating functions

• Notes from external material (Notes pages 92–97) '
• Compositions of generating functions
• And their combinatorial interpretations

• Solving recurrence relations
• Fibonacci generating function
• Notes from Sections 2.4, 3.4, and 4.4 (Notes pages 98–105) '
• Integer partitions

• Integer partition bijections
• Standard Young Tableaux

• Catch-up with topics
• Remainder of class: Poster Work Day

• Notes from Section 4.1 PLUS additional material (Notes pages 106–114) '
• Catalan numbers
• Catalan number interpretations
• The "meta" method for Catalan numbers
• (Handy handout about Catalan numbers)
• (link to Stanley's Catalan Interpretations)

• Notes on Combinatorial Statistics (Notes pages 115–125) '
• 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

• Catch-up with topics
• Remainder of class: Poster Work Day

•••••• 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 126–143) '
• 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, not including class on Tuesday, November 24.
• 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