Welcome to the homepage for Math 87 in Spring 2020. Course info sheet.

Prof: Moon Duchin (moon.duchin@tufts.edu)

TA: Mackenzie McPike (mackenzie.mcpike@tufts.edu)


This course will introduce you to techniques and themes of mathematical modeling, with python-based assignments. We’ll use Google Colab as our notebook environment. The two major topics are linear programming and Markov chains, each spanning about 1/3 of the course. The remaining 1/3 will be devoted to short treatments of other fundamental techniques interspersed throughout the semester.

There are two available 2-SHU companion courses and it’s strongly recommended that you consider taking one!

  • Coding Lab (Math 10, Tuesdays 6-8pm in BP6, Alex Coyoli)
  • Reading Lab (STS 10, Tuesdays 12-1:15pm in East 015, Amy Becker/Sarah Hladikova)

Lecture notes

I regularly update these hand-written lecture notes, in case that is useful. Current up to 3/12/20.

Here is a dropbox folder with some lecture notes from the Zoom meetings, in various formats.


Here is a worksheet I made for my complex analysis class a few years ago to help people brush up on three topics: linear algebra, multivariable calculus, and topology. For this class, we only need the first two topics. We will need a bit more extensive linear algebra later (eigenvalues & eigenvectors) but I’ll prepare a worksheet closer to then.

A handout on fair division to correspond to the lecture on 2/6/20.

Gerdus Benade gave a fantastic guest lecture on 2/10/20 covering two examples from his work: participatory budgeting and real-time resource allocation. [ video | slides ] Important note: you’re not being tested on this material in any sense! It’s just to see our concepts in practice. Don’t sweat the details.

Here is Emily Riehl’s Numberphile video about the stable marriage problem. [ part 1 | part 2 ] Please check it out!

Want to brush up on linear algebra? If you took Math 70 at Tufts from Lay’s book, the relevant chapter is Chapter 5 (eigenvalues and eigenvectors). Note that Chapter 10 is Markov chains, so if you have access to that it’s a great source as well!

Khan academy has some pretty limited lessons on eigenvalues and eigenvectors here: https://www.khanacademy.org/math/linear-algebra/alternate-bases#eigen-everything