18.821 (Mathematics Project Laboratory) Home Page


General information:

Introductory survey:

At the first class on Wednesday September 7, we'll ask you to fill out this questionnaire in order to form the research teams in which you'll work during the semester. If you can print and fill out the form before class, that would be great!

Research projects:

The main activity in this class is working in teams on mathematical research projects. We provide (slightly updated 9/7/16) a long list of possibilities. They represent a lot of effort by a lot of faculty members over the past ten years, to design projects that are interesting, and accessible, and not easily settled by Google.

The projects that were chosen for the first round were 5 (Avoidance), 10 (Sums of cubes), 15 (Factoring mod p), 16 (Fibonacci base), 25 (Deterministic growth), 30 (Monomial relations), 33 (Percolation), 38 (Random walks), and 45 (Coin toss). By Monday 10/3 (sooner is much better!) each team should email David Vogan with a first and second choice for your second project.

October 10: The projects chosen for the second round are 7 (Chips), 8 (Geometry of Zeros), 11 (Determinants equal to one), 13 (Eigenvalues of sums of matrices), 14 (periodic Schrodinger), 17 (Expansions of infinite products), 21 (Gluing polygon edges), 40 (Repeating decimals).

December 14: Just to complete this web page before I take it offline, I will list the projects chosen for the third round: 9 (Conics), 12 (Diagonalization mod p, chosen by two teams), 19 (Eigenvalues of matrices of roots of unity), 27 (Touching circles), 32 (Pascal mod p), 33 (Invasion), and 41 (Self-referencing sequences).

If you would like to pursue a project not on this list, probably that's not possible, because deciding whether it satisfies these criteria is too difficult. But you can always ask; even if we say no now, some future students may benefit from your ideas!

Writing tools:

We have assembled a collection of tools for preparing your papers and presentations. You will find in particular a LaTeX template you can (if you wish) use for your papers, and a beamer template you can use for a slide presentation. If you know of other resources you find particularly helpful, please let us know; additions are welcome!

Diaconis lecture

For the last class we listened to a YouTube lecture by Persi Diaconis called The search for randomness. He mentioned some papers about some serious uses of statistics. One of them was From Mouse-to-Man: The Quantitative Assessment of Cancer Risks by David Freedman and Hans Zeisel. A second was at least related to Census Adjustment: Statistical Promise or Statistical Illusion?, by Freedman and Kenneth Wachter. A third related one is From Association to Causation via Regression by Freedman. Like everything (that is

$$\text{(everything on the internet)}\cup \text{(everything not on the internet)}$$)

these papers should be taken with a grain of salt; but I did want to make them accessible to you.

Instructors: