## MAT 1302 / APM 461, Combinatorial Methods, Winter 2019

#### Instructor

Prof. Kasra Rafi
Office: BA 6188 (Bahen Centre)
Email: rafi@math.toronto.edu

#### Meetings

Tuesdays 11 - 12 pm in BA 6183.
Thursdays 12 - 1 pm in BA 6183.

#### Office hours

Mondays and Thursdays 3-4 pm or by appointment.

#### Textbook

Enumerative Combinatorics Volume 1, by Richard P. Stanley

#### Teaching Assistant

Mykola Matviichuk
E-mail: mykola.matviichuk@mail.utoronto.ca
You can contact Mykola to set an appointment if you need to discuss the grading of quizzes.

#### Course description

We will cover a selection of topics from such areas as counting problems, combinatorial algorithms, enumeration, construction of combinatorial identities and generating functions.

#### Marking scheme

• Quizzes 30%
• Midterm 30%
• Final exam 40%

#### Problems Sets and Quizzes:

There will be weekly homework assignments. However the homework will not be collected. Instead, there will be weekly quizzes based on the homework problems. Only the grades of the best 10 quizzes will count towards the final grade. Students are encouraged to work together on the homework problems.

• Due January 10
1. Read Section 1.1 "How to Count"
2. Chapter 1: 2 (a) -- (l), 3 (a) -- (f)
• Due January 17
1. Read Section 1.2 "Sets and Multisets"
2. Chapter 1: 8, 11, 13, 17, 21, 30, 32, 34, 35, 36, 37.
• Due January 24
1. Read the firs part of of Section 1.3 titled "Cycle Structure"
2. Chapter 1: 38, 39, 41, 42, 43, 44, 45, 46, 47, 48.
• Due February 7
1. Read Section 1.9 titled "The Twelvefold Way"
2. Chapter 1: 66, 67, 68, 69, 70, 71, 106, 107, 108, 109.
• February 28
1. Here is a Guide for the upcoming Midterm.
• Due March 14
1. Read Sections 2.1, 2.2 and 2.3
2. Chapter 2: 2, 3, 4, 5, 10, 14, 16, 17, 19, 27.
• Due April 4
1. Read Sections 3.1 -- 3.8 and 3.11
2. Chapter 3: 6, 12, 15, 20, 23, 25, 51, 54, 64, 70, 76, 85, 86, 87, 88, 89, 90, 92, 93, 98, 99, 100, , 108, 110, 112, 114, 115.

#### Final Exam

The Final will take place on Thursday April 11, 7:00 -- 10:00 pm in WY 119. Here is a Guide for the Final Exam.

#### Study hints

Before each class, you should both review the material from recent sections and read the section to be discussed that day. This will allow you to both understand the presentation of new material and identify questions that you need to resolve during class.

#### Policy on missed quizzes or exams:

There are no make up quizzes. If you miss more than two quizzes for a legitimate reason which you can document, your grading scheme will be adjusted by increasing the final exam component of your mark. The documentation must be submitted no later than 7 days after the date of the exam/quiz. You can find the University of Toronto Medical Certificate form here.

#### Prerequisite

Linear algebra, elementary number theory, elementary group and field theory, elementary analysis.