Mathematical Communication is a developing collection of resources for engaging students in writing and speaking about mathematics, whether for the purpose of learning mathematics or of learning to communicate as mathematicians.

Discrete Mathematics–Sami Assaf

The purpose of this undergraduate seminar at M.I.T. is to give students experience reading, writing and presenting results in mathematics. There is no fixed set of topics to be covered, instead students may choose from a broad selection of topics within discrete mathematics.

Course Structure

  • Give at least 3 presentations on some topic(s) in discrete mathematics. At least one of your talks should be based on a research paper published in a reputable mathematics journal.
  • Submit an abstract and before each of your presentations, and provide possible quiz questions after your presentation.
  • Write 3 quizzes based on the content of the presentations.
  • Write a term paper of approximately 10 pages on a topic in discrete mathematics.
  • Do not fall asleep during someone else’s (or your own!) presentation.

Grading Policy

Grades are based on the quality of your presentations (40%), term paper (30%), quizzes (15%) and class participation (15%).

About the quizzes

Previously when I taught this course (Spring 2009), I had students write 3 one page summaries of presentations by other students. That worked well enough, but all the summaries came in around the same time as the term papers, and they were mostly on the same (outstanding) presentations. This time I tried something new with the quizzes, which I think is working much better. Here’s the strategy.

Each presenter comes up with 2-5 questions that anyone who attended the talk should be able to answer. The questions should get at the main point that the speaker hopes the audience will take away from the talk. They should be relatively easy and not involve too much notation. For example, one question for my presentation on Standard Young Tableaux asked the students to write down the SYT of shape (3,3), of which there are only five.

After each student has given one presentation, I compile their questions into a quiz, one problem per talk. If the questions weren’t appropriate, I send them back to the presenter asking for revisions or, if they’re close enough, I just edit them a little myself. I tell the students that it should not be necessary for them to study for the quiz, but maybe just look over their notes briefly the day before. I give them the length of a presentation (40 minutes since this term is T/H) to complete it.

The grading scheme goes like this: you get one point for every question you correctly answer and one point for every person who correctly answers the question based on your talk. This is why it’s important to screen the questions first. They shouldn’t be too easy (define a partition) or too hard (derive a closed form for the Catalan numbers based on the generating function).

I had a good crop of students, and they actually seemed to enjoy the quizzes. It was fun seeing which talks people remembered best and which were a total blur. I gave three quizzes, after each round of presentations, and overall it seemed more effective for getting participation than the summaries.

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