12. Appendix: Math for research - sample lesson plans

Teaching the “math for research” material can clearly be sliced up in many different ways. I have taught it several times, and I always followed a similar logistical format: class length of 1 hour and 15 minutes, and new material once/week, with catch-up sessions twice/week.

But the order in which I teach the various pieces, and the choice of which pieces to teach, depends largely on the makeup of the group of students I work with.

Similarly, the amount of extra background material and the choice of “visions into advanced material” anecdotes depend on the group of students I have.

In this appendix I will start collecting some of the specific lesson plan sequences I have chosen.

12.1. Winter/Spring 2025

We had a total of ?? lessons, from 2025-02-03 to 2025-??-??.

Opening lesson 1:

  • Introduce myself, discuss how researchers see mathematics

  • Discussion of logistics and what I expect of students

  • Visualizing $sin(x) approx {rm 9th degree Taylor polynomial}

  • Section “An example to whet your appetite”

  • Approximating functions with series (Chapter 2). From that chapter we do “Sequences and sums”, “Do sums converge?”, “Approximating pi with series”, and up to Section 2.4 - “A digression on the factorial”.

Lesson 2:

Lesson 3: