An Inside-Out Course on Number Theory (Pt 5)

Link to previous posts: Pt1 Pt2 Pt3 Pt4

Class is going really well, at least from a mathematical perspective. Next week is our last class meeting and we are on track to be able to wrap up the whole class in which we use all of the tools that we’ve been building up over the entire semester to explain how the RSA cryptosystem works. (This book by my colleague Mohamed Omar has been super helpful.)

Today, we took care of the final two mathematical tools that we’ll need to understand the RSA cryptosystem.

(1) We learned about how to use the Euclidean Algorithm to find the greatest common divisors between any two numbers. The students were particularly enamored with the “square-cutting” visual (see below) that I learned from Bowen Kerins as we have co-taught the math course for the Teacher Leadership Program at IAS/Park City Mathematics Institute.

(See http://projects.ias.edu/pcmi/hstp/sum2018/morning/darryl/day03-summary-notes.pdf for an animated version.)

(2) We also learned how to solve problems of the form “ax=1 in mod n”. We learned the conditions under which such problems will have a solution.

And, a few students got to the fun part, which is that while (1) and (2) seem unrelated, it turns out that you can use (1) to help you find the answer to (2).

Finally, I just got a copy of Mathematical Outreach: Explorations in Social Justice Around the Globe, edited by Hector Rosario. In it, Robert Scott makes some great observations about teaching mathematics in prisons. One quote has been resonating in my head since I read it:

“A math pedagogy premised upon following the rules, accepting that there is only one right answer, and relying on practice/repetition in order to habituate oneself to pre-determined axioms would seem to reprise the culture of incarceration itself.”

Robert Scott, “Math Instructors’ Critical Reflections on Teaching in Prison”, page 213 of Mathematical Outreach: Explorations in Social Justice Around the Globe, edited by Hector Rosario, 2020

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