MAT 447, Seminar in Mathematics, Winter 2021


Prof. Kasra Rafi
Office: BA 6236 (Bahen Centre)


Thursdays 5 - 8 online.

Office hours

Mondays and Wednesdays 5 - 6 pm or by appointment.


A simple introduction to ergodic theory by Karma Dajani and Sjoerd Dirksin
Lecture Notes.

Ergodic Theory by Karl Endel Petersen
Cambridge University Press (1983)

Other references will be added throughout the course.

Course description

The purpose of this course is for the students to get some experience in reading, comprehending and presenting mathematics. To make the course more coherent, we start by focusing on one topic, namely the study of dynamical systems. However, in the second half, the scope of the course can be widened as we shall focus on the areas of interests to students.

Marking Scheme

Your course grade is computed as follows:

Every student is expected to give 2-3 presentations during the semester. Your presentation have to be well prepared and understandle. As a presenter, you should allow and envourage questions from the audience and discussions. As a listener, you need to be engaged and to participate in the dicussion. All this will be factored in to determine your final grade.


MAT347Y1,   MAT354H1,   MAT357H1.

Presentation schedule

Date Presenters Topic
January 14 Kasra Rafi What is Ergodic Theory?
January 21 Curtis Crant Section 1.5 and Proposition 1.8.1
January 21 Vivian He Theorem 2.1.1
January 21 Kunal Chawla Exercise, Corollary and Proposition 2.1.1
January 28 Kerwin Yi
January 28 Kate Ing
January 28 Mingyu Heu
February 4 Silvia Tao
February 4
February 4

Academic integrity

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

Policy on Missed Work or Class Participation

Verification of Illness forms (also known as a doctor's note) are temporarily not required. Students who are absent from class for any reason (e.g., COVID, cold, flu and other illness or injury, family situation) and who require consideration for missed academic work should report their absence through the online absence declaration. The declaration is available on ACORN under the Profile and Settings menu.

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 or visit here.

Mental Health Care

The Health and Wellness Centre offers mental health services to students. To get more information, visit their website here.