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Reading Courses

Jul 28, 2022

A reading course, or independent study project, is an opportunity to work with me directly on a project. Typically, I only take individual students for reading courses but it is possible to work with a group of two or three highly motivated students. Typically, students take reading courses in their third or fourth year. It is a helpful preparation for graduate skill and develops a personal connection which can lead to reference letters, mentorship, and help throughout the end of your undergraduate years.

I have some expectations of students who take reading courses with me:

  1. You must write. You will need a publically accessible summary of your work on the reading course This is usually a blog or wiki. Every week, you must document what you did in the course.

  2. You must do the readings. I will typically assign readings from mathematics, and also some material outside of mathematics. The readings will be relevant to the course, but also help you develop good reading and writing skills.

  3. You must bring questions and ideas to every meeting. Typically, the more that you read and write, the more questions you will have. I expect students to drive the course by bringing their own questions and ideas to every meeting. It helps to write them down in advance on your blog.

The grading scheme, or assessment, for a reading course depends on the course and the student. At a minimum, I require students to meet with me every week, give a presentation in the UTSC Undergraduate Seminar, and write a piece for the U(t)-Mathazine.

There are broadly two types of reading courses that I offer: study courses, and exploration courses. The study courses consist of reading through sections of a well-known book, solving problems, and studying an established theory. Usually, the topics are ones that I know well and can guide students through. In contrast, the exploration courses are about topics which I know almost nothing about but which I’d like to learn. In exploration courses, students explore a new-to-me topic, work on a project, and learn the theory with me.

Currently, I am most interested in leading reading courses on:

  1. Regular Polytopes
  2. Differential Forms

Topics For Study

  1. Riemannian Geometry
  2. Differential Forms in Algebraic Topology
  3. Regular Polytopes
  4. Hyperbolic Geometry
  5. String Figure Calculus

Topics For Exploration

  1. Boolean Fourier Analysis
  2. Combinatorial Game Theory
  3. Random Permutations
  4. The Probabilistic Method
  5. The Thurston Geometries

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