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san diego talk

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Talk

Title: Using open source mathematics software to make your courses more interesting

Abstract: I have been using mathematics software in my teaching for a long time, and have created tools such as SageMath and CoCalc to make this easier for others. In this talk, I'll describe some of my experience and inspiration over the years, then demo some concrete ways you can easily add some computer programming to make your mathematics courses more engaging, and useful to students.


  • assume 50 minutes, including questions/discussion.

  1. (3 min) Introduction

  • William Stein

  • UC Berkeley number theory grad student

  • Harvard for five years, where I started Sage (the free open source competitor to Mathematica, Maple, Matlab, and Magma), and taught many undergrad and grad classes using computation, web interfaces, etc.

  • UC San Diego for a year, where Sage dev got a lot of momentum.

  • Univ of Washington for a decade, where Sage matured...

  • and CoCalc (collaborative web application for using free open source math software) got a lot of momentum.

  1. (6 min) Teaching linear algebra (vector spaces)

  • Students find the abstraction of "vector spaces", "kernels", etc. to be challenging.

  • Sage provides a way for them to experiment with them.

  • Show examples in QQ^n in a worksheet

  1. (6 min) Teaching elementary number theory (and public-key crypto)

  • Arithmetic modulo n is a new idea for students

  • Make it feel just as concrete by naturally working with it

  • Illustrate Fermat's Little Theorem: a^(phi(n)) = 1 (mod n).

  • Get a sense for the surprise that modular exponentation is very fast.

  • Example of RSA.s

  1. (6 min) Teaching abstract algebra (groups)

  • Students can get slowed down by how tedious working with permutations is.

  • Sage makes this very easy -- demo some basic arith.

  • But it's deeper: you can also just compute the group generated by some permutations

  • Or plot the Cayley graph

  • Or ask for all normal subgroups...

  1. (20 min) CoCalc -- web based way to use Sage, LaTeX, etc.

  • Students can get ∞\infty'ly slowed down by installing and configuring software.