# Teaching

Whenever I award a student a course grade of A+, I write a congratulatory email and ask for advice on how to succeed in my classes, which I distribute without modification to students the next time I teach that course.

I am on sabbatical during the academic year 2019–2020 and will not teach courses again until Fall 2020.

In Spring 2018 I taught MATH 341, Algebra III: Groups.

In Fall 2017 I taught MACM 201, Discrete Mathematics II and MATH 480W, The Art and Craft of Problem Solving.

In Spring 2017 I taught MATH 155, Calculus II for the Biological Sciences.

One of my favourite courses to teach is MATH 480W, The Art and Craft of Problem Solving, which shows you how to solve problems like:

• A calculator is broken so that the only keys that still work are the sin, cos, tan, sin-1, cos-1, and tan-1 buttons. The display initially shows 0. Given any positive rational number q, show that pressing some finite sequence of buttons will yield q. Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians.
• Sal the Magician asks you to pick any five cards from a standard deck. You do so, and then show them to Sal's assistant Pat, who places one of the five cards back in the deck and then puts the remaining four cards into a pile. Sal is blindfolded, and does not witness any of this. Then Sal takes off the blindfold, takes the pile of four cards, reads the four cards that Pat has arranged, and is able to find the fifth card in the deck (even if you shuffle the deck after Pat puts the card in the deck). Assume that neither Sal nor Pat has supernatural powers, and that the deck of cards is not marked. How is the trick done?

One year after completing MATH 480W, a student wrote to me: “MATH 480W, despite having a bad reputation (the Putnam is scary business) is absolutely worth taking if you're a student who wants to sharpen their problem solving (and writing) skills. The problems are difficult but doable, and the marking is harsh but Jonathan's grading is generous — he understands that the course material is difficult, but is completely fair in final grade assignment (the average for this class is much higher than other math classes I've taken). Marking is harsh because it needs to be harsh, if it weren't, then you wouldn't be prepared for the Putnam at the end of the semester (which will be marked with similar scrutiny to the assignments, but doesn't count towards your final mark.) More importantly, you'll learn strategies, perspectives and tricks to deal with difficult problems — strategies which I've personally applied to solve problems I've come up against in later studies. In terms of potential payoff versus risk (it's a low risk course, really) it's an underrated gem of a course.”