# **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:**

- David Vogan, 2-355, dav@math.mit.edu, 617-253-4991

- Tristan Bozec, 2-167, tbozec@mit.edu, 617-253-6544

- Thao Do, 2-231D, thaodo@mit.edu, 857-259-7344

- Susan Ruff, 2-370, ruff@math.mit.edu, 617-455-8248

- Malcah Effron, E39-368, meffron@mit.edu, 617-324-2302

- Ari Nieh, E39, anieh@mit.edu, 510-292-0899