__Course
title:__
Math 21-499: Introduction to Undergraduate Research

__
Instructor:__
Steven J. Miller (Email:
sjm1@williams.edu,
Phone: 617-835-3982, Skype: stevenmiller1701)

Greetings. The purpose of this class is to introduce you to mathematical research. There are many components to this, ranging from lectures on needed background material to discussions on how to ask a good research question to what tools and techniques can be fruitfully applied. The course will be a mix of general and individual lectures, and a lot of guided research. Students will work in small groups. For a description of possible projects and links to reading, click here. I will be visiting several times a semester (mostly Sunday nights through Mondays); thus physical meetings will often be every other week late Sunday and sometime Monday, with numerous additional meetings through skype, plus constant emails. Evaluation will mostly be through participation and write-ups of work. I have general ideas of some topics I want to pursue, but I prefer to not finalize the projects until I know who is in each group and what their interests and backgrounds are. Thus, you should view these as starting points of a conversation. The articles below (and in the linked document) are meant to give you a rough sense of my interests, and once you tell me what you find fascinating I'll provide more specific reading below, and some links to short video introductions.

**Research Areas: **
See the list of projects here; this is a subset
of possibilities. For more information on the areas of research, including some
problem statements and links, click
here.

**Introductory Lectures:**

- Lecture 1: Zeckendorf: Video: https://youtu.be/FiTOQgonntU Slides: click here for part 1 (Introduction to Zeckendorf decompositions) and click here for part 2 (Fibonacci game)
- Lecture 2: MSTD: Video: https://youtu.be/51yNvBkhvMM Slides: click here for divots and click here for a more general introduction
- Lecture 3: L-functions and Random Matrix Theory:
https://youtu.be/O-XKcJcw5WA
(video should be up by 8:30pm): slides below (note only did a subset)
- Slides: L-functions and some RMT: Part 1, Part 2 (part 2 is far more technical)
- Slides: Introduction to RMT: click here

- Lecture 4: Benford's Law:
https://youtu.be/e-qLwCiBIEM
- Old lecture on Benford's law: Gave this at CMU a few years ago: Carnegie Mellon: http://youtu.be/z2Rx1w5UDnk (slides here, technical talk: L-fns, 3x+1, Decompositions)

- Lecture 5: Short 10 minute video on some probability used in random matrix theory: https://youtu.be/kgCgga5ebBs

**Research Lectures:**

- Zeckendorf: Lecture 2: https://youtu.be/3CfLSuaW33Y
- Fibonacci-Schreier: Lecture 1: https://youtu.be/YuVfHHIj_Yw
- MSTD: Lecture 2: https://youtu.be/Kv0ipdKSCGo
- RMT: Lecture 2: https://youtu.be/EoSwdK_HNbY

**Subpages:**

- TBD

**Links for All:**

- arxiv: http://arxiv.org/list/math/new
- OEIS: https://oeis.org/
- MathSciNet: http://www.ams.org/mathscinet/ (under tools can play the Erdos game)

**Video Introductions (subitems are
research / colloquia talks): See also
https://web.williams.edu/Mathematics/sjmiller/public_html/math/talks/talks.html
**

- Introduction to Benford's Law (9 minutes):
https://youtu.be/GXRCoHXanjU
- Longer Benford introductions:
- Carnegie Mellon: http://youtu.be/z2Rx1w5UDnk (slides here, technical talk: L-fns, 3x+1, Decompositions)

- Longer Benford introductions:
- Tutorials:
- Mathematica tutorial: https://www.youtube.com/watch?v=g1oj7CIqGM8 (webpage with templates here)
- LaTeX tutorial: http://www.youtube.com/watch?v=dKUtJpG4Rt0 (webpage
with templates here)

2016 Homepage: Click here.