Adaptations

So far, the technologies I’m using for the remote semester are working pretty well (relative to expectations). Now I’m looking at pedagogy and (a) trying to abandon principles that are noble but irrelevant in the face of a global pandemic while (b) trying to maximize the joyful opportunities to engage with mathematics.

A few ideas so far at various stages of implementation:

• Mathematics for Human Flourishing: an invitation to read, reflect, and write about the value of mathematics independent of its applications. This seems to be a particularly timely opportunity for students, especially math majors, to reconnect with the joy of mathematics. The only hurdle right now is finding a way for students to access Francis Su’s book remotely. I’m honestly tempted to just buy and ship this book to students interested in this option.
• Student designed exam (thanks to @katemath on Twitter!):
  • Choose/create 4 problems whose complete and correct solutions show mastery of the big ideas in the course
  • Justify your choices
  • Submit complete and correct solutions
• Choose Your Own Adventure:
  • Select from a series of predefined Adventures
  • Adventure materials include YouTube playlists, books that can be accessed online through Hamilton’s library, and additional content created or curated by me for the students
  • For the interested: topics include…
    • Applied Cryptography. Extra stuff comes from a very nice Udacity course, https://www.udacity.com/course/applied-cryptography--cs387.
    • Elliptic Curves and Lenstra’s Algorithm. Additional content created by me that gives a very, very brief introduction to elliptic curves over finite fields and projective space.
    • Continued Fractions and Convergence. Additional content from a fair-use selection from one of my favorite texts, Hardy and Wright’s Introduction to Number Theory. I’ve also selected a portion of an MIT open courseware Number Theory course for undergraduates.
    • Quadratic Reciprocity and Polynomial Congruences. Content follows Number Theory through Inquiry. Still curating fun resources on the internet – send me your suggestions?
    • Pythagorean Triples to Pell Equations. Ditto the previous.
  • Students are also free to pitch me their own adventure and I will help as much as possible.

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