Combinatorics Bard College

## Announcements

Final Exam: The Final Exam is on Tuesday, May 24. Here are Practice Problems for the final exam:

Final Project: The final project for this course involves giving a talk on a topic related to Combinatorics. You can work in groups of 2 or 3 people, or you can work by yourself. The following page contains a list of possible project topics:

LaTeX: You are required to write homework solutions in LaTeX. Here are some links to get you started:

To download LaTeX to your own computer, Ethan recommends TeXShop for Mac users, and TeX Live for PC users:

## Course Requirements

• Homework: There will be weekly homework assignments. All homework solutions must be written in LaTeX. If you haven't used LaTeX before, I recommend starting with Ethan Bloch's LaTeX web page for Bard students, which has links to many helpful resources. I encourage you to work with others on the homework assignments; mathematics is generally easier and more enjoyable when working with others. You should write up your own solutions independently and acknowledge all collaborators.
• Exams: There will be two in-class exams: a midterm and a final.
• Project: There will be one project consisting of a class presentation. You can work on the project individually or in groups of two or three. More details about the project will be given later in the semester.

Your grade will be based on homework assignments (40%), two exams (40%), and a project (20%).

## Assignments and Syllabus

 Week Dates Topics Readings Homework Week 1 Feb. 2, 4 Introduction, Pigeonhole Principle Chapter 1 Week 2 Feb. 9, 11 Induction, Elementary Counting Chapters 2, 3 Homework 1 (TeX, PDF) Week 3 Feb. 16, 18 Binomial Theorem Chapter 4 Homework 2 (TeX, PDF) Week 4 Feb. 23, 25 Newton's Binomial Theorem Section 4.3 Homework 3 (TeX, PDF) Week 5 March 1, 3 Catalan Numbers Homework 4 (TeX, PDF) Week 6 March 8, 10 Partitions Chapter 5 Homework 5 (TeX, PDF) Week 7 March 15, 17 Midterm Exam Practice Problems (and Answers) Spring Break Week 8 March 29, 31 Permutations Chapters 6 Homework 6 (TeX, PDF) Week 9 April 5, 7 Inclusion-Exclusion Chapter 7 Homework 7 (TeX, PDF) Week 10 April 12, 14 Generating Functions Chapter 8 Homework 8 (TeX, PDF) Week 11 April 19, 21 Generating Functions Chapter 8 Homework 9 (TeX, PDF) Week 12 April 26, 28 Exponential Generating Functions Chapter 8 Week 13 May 5 Graph Theory Chapters 9, 10 Homework 10 Week 14 May 10, 12 Graph Theory Week 15 May 17, 19 Presentations Week 16 May 24 Final Exam