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Polar Coordinates

Published August 19, 2020.

On July 7, 2020 I tweeted:

I failed Physics I and had to retake it.
I got a D in Physics II and a C in Physics III.
I got 50/200 in my multivariable calculus final.
Continuing the calculus final, I almost failed my graduate differential topology course.
The underlying theme: Can't work with Stokes Thm.

A couple of hours later, I received an email: Do you want to teach a multivariable calculus course that is starting in a few days?

I said yes. It was a different experience for me because I usually like to teach everything with my own words and my own style. But my role in this course was only to facilitate the already established structure. There were video lectures, notes, homework assignments all ready and all I needed to do was to meet with students occasionally and chat. I could do that.

I did change a couple of things in the syllabus, though. I added Self Reflection Essays which was worth 15 percent in the grade distribution. These are essay questions which basically ask "What did you learn this week?" in different ways. One example students really like was "This week you learned derivatives in multivariable calculus. Explain the topic to a student who recently finished single variable calculus". There are also questions like "What was the most challenging part of the course this week?" and "How many questions did you ask on Piazza this week?"

Another change that I made was removing midterms. I have very strong feelings about online proctoring services but I save them for my personal diary. Instead of two midterms, I gave the students an oral exam as a midterm.

Liam was a high school student who took this course. He always wrote very nice essays and contributed beautiful ideas in class meetings. In the oral exam, he answered everything so comfortably that I had to make up a question for him: How can you generalize polar coordinates to four or more dimensions? (In this course they only see up to three variables.)

That week's self reflection essay was about the question you found most difficult in the exam. So he wrote a beautiful essay. Here, I will share my favorite part:

Now, why did we look at all of that math? What purpose could this possibly serve? Who in their right mind would bother using all of this for a real life problem? The answer to the first two questions is because using 4-dimensional polar coordinates can be useful for certain topics in quantum physics. The answer to the last question is no one, because no physicist is ever truly in their right mind.

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