MAT199: Aha! Mathematical Discovery and Creative Problem Solving, Winter 2024

Instructor

Kasra Rafi
Office: BA 6236 (Bahen Centre)
Email: rafi@math.toronto.edu

Teaching Assistant

Vivian He
Office: PG 301
Email: vivian.he@mail.utoronto.ca

Meetings

Thursdays 11:00 am - 2:00 pm
Location: BA 2195

Office Hours

Tuesdays 2 pm -- 3 pm
Thursdays 4 pm -- 5 pm or by appointment.

Course Description

This course is an exploration into the creative process and use of imagination as they arise in the context of mathematical problem solving. The problems, which are all at a pre-calculus level, are chosen primarily by the criterion of aesthetic appeal, and emphasize reasoning rather than technique. Still, many of them are quite challenging, and substantial independent thinking will be required, the course is therefore appropriate for students from a variety of backgrounds and disciplines, including hard sciences. Its goal will be to hone each participant's creativity and mathematical problem-solving skills while guiding them towards the `Aha!' experience which accompanies independent discovery. Restricted to first-year students. Not eligible for CR/NCR option.

Prerequisites

High school level algebra.

Textbooks/ Course Readings

• The Heart of Mathematics: An invitation to effective thinking,   by E.B. Burger and M. Starbird.
• Game Theory, Alive,   by Anna R. Karlin and Yuval Peres.

Problem Sets

• Problem Set I, read Chapter 1 in Game Theory, Alive.
• Problem Set II, read Sections 2.1-2.4 in The Heart of Mathematics.
• Problem Set III, read Sections 3.1-3.4 in The Heart of Mathematics.
• Problem Set IV, read Section 4.5 in The Heart of Mathematics.
• Problem Set V.
• Problem Set VI.
• Problem Set VII.

Evaluation/ Grading Scheme

The final grade is based on the following:

• Attendance and participation — 35%
• Final Project / presentation — 65%

The students should form groups of 2-3 people, choose a topics and prepare/give a presentation on that topic. Also, the notes for the presentation should be handed in. The presentation on the notes are graded based on quality and timeliness. Here is the timeline:

• Settle on a group and contact Vivian with the names of people in your group, January 24 — 5%
• Settle on a topic and send a short description of the topic to Vivian, February 15 — 10%
• Send the written notes to Vivian, April 4 — 25 %
• Schedule and give presentation in class, April 4 — 25 %

Each stage of the project will be penalized by 5% per day late, up to a maximum of five days, after which the grade for that stage will be zero.

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.