## MAT 475, Problem solving seminar, Winter 2019

#### Instructor

Prof. Kasra RafiOffice: BA 6188 (Bahen Centre)

Email: rafi@math.toronto.edu

#### Meetings

Tuesdays 12-2 pm in BA 1200.Thursdays 12 - 1 pm in BA 1200.

#### Office hours

Mondays and Thursdays 3-4 pm or by appointment.#### Teaching Assistant

Abhishek OswalE-mail: abhishek@math.toronto.edu

You can contact Abhishek to set an appointment if you need to discuss the grading of quizzes.

#### Textbook

*Problem-Solving Strategies*, by Arthur Engel (Main)

*Problem-Solving Through Problems*, by Loren C. Larson (sumplimentary).

*How to Solve It: A New Aspect of Mathematical Method*, by George Polya (Suplimentary).

#### Course description

We will get more competent at solving math problems and writing their solutions by solving many math problems and writing their solutions.

#### Marking scheme

Your course grade is computed as follows:

- Quizzes 50%
- Class Participation 10%
- 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 15
- Read Chapter I of the text book titled
*The Invariance Principle*and think about the problems at the end of the section.

- Read Chapter I of the text book titled
- Due January 22
- Read Chapter II of the text book titled
*Coloring Proofs*and think about the problems at the end of the section.

- Read Chapter II of the text book titled
- Due January 29
- Read Chapter III of the text book titled
*The Extremal Principle*and think about the problems at the end of the section.

- Read Chapter III of the text book titled
- Due February 5
- Read Chapter IV of the text book titled
*The Box Principle*and think about the problems 1--51.

- Read Chapter IV of the text book titled
- Due February 12
- Think about the problems 51--83 in Chapter IV .

- Due February 26
- Read Chapter V of the text book titled
*Enumerative Combinatorics*and think about the problems at the end of the section.

- Read Chapter V of the text book titled
- Due March 12
- Read Chapter VI of the text book titled
*Number Theory*and think about the following problems: 22, 26, 27, 30, 32, 37, 39, 41, 46, 56, 62, 63, 66, 70, 73, 77, 82, 120, 133, 146, 167.

- Read Chapter VI of the text book titled
- Due March 19
- Read Chapter VII of the text book titled
*Inequalities*and think about the following problems: 6, 9, 10, 14, 17, 19, 22, 26, 37, 57, 59, 71, 80, 92.

- Read Chapter VII of the text book titled

#### Final Exam

The time and the location of the Final Exam will be announced later.

#### Study hints

The problems are assigned on Thursdays. You should read the problems immediately and if you have trouble understading what the problem is asking, you can stop by during the THursday office hours. You should then form study groups and solve these problems together to prepare for the quiz. If after working on a problem you need to discuss them further, you can stop by for the Mondays office hours. The Quiz may be one of the assigned problems or a different but similar problem.

#### 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

MAT224H1/MAT247H1, MAT235Y1/MAT237Y1/MAT257Y1, and at least 1.0 FCE at the 300+ level in APM/MAT.

You need to be comfortable with proofs and with using the language of writting mathematics. Familiarity with Linear Algebra, elementary number theory and modular arithmetic and plane geometry is also useful for some of the problems examples will discuss.

#### Academic integrity

The University of Toronto Code of Behaviour on Academic Matters can be found here.

#### Accessibility needs

The University of Toronto is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom or course materials, please contact Accessibility Services as soon as possible: email disability.services@utoronto.ca or visit here.