Math 490, Spring 2012

Curl (Collaborative Undergraduate Research Lab)

Latex Resources
Class Room: Wed: VAN VLECK B337
Mon, Fri: VAN VLECK B107
Class Time: MWF 11:00AM - 11:50AM
Final Paper Due: May 18, Noon
Instructor:Melanie Matchett Wood
Instructor's Office: 315 Van Vleck
TA: Lalit Jain
Office Hours: Prof. Wood: Mon 10-11AM, Fri 1:30-2:20PM
Computer Lab Office Hours: Lalit Jain, Van Vleck B107, Tues 4-5PM, Wed 3:30PM


Enrollment in this course requires consent of the instructor. If you are interested, please apply by completing the application avilable here.

An introduction to mathematical research

Algebraic curves over finite fields are beautiful and subtle objects at the nexus of number theory and algebraic geometry. They can also be defined simply in terms of polynomial equations whose coefficents are in a finite field, such as the integers modulo a prime. They are also typically not the topics of undergraduate courses.

This course is both an opportunity to get aquainted with algebraic curves over finite fields and an introduction to mathematical research. For the first third of the course we will learn the background material. There will not be traditional lectures, but rather presentations by the lecturer interspersed with working through examples in groups. Participation is crucial to your success in the course. During this part of the course there will be quizzes and homework problems (including some which require the use of the computer), and the homework solutions will need to be written up using the mathematical typsetting language LaTeX. The remainder of the course will be focused on the research projects -- I will assign research projects, to groups of 2-3 students, related to these topics, and our class meetings will consist of reports from the groups, with the occasional presentations from the lecturer when questions come up. The projects will be largely computational (meaning using the computer a lot!) and will be exploring questions at the frontier of current mathematical knowledge. The last two weeks will be devoted to working on the final papers, which will give a full report of the research done by each group. There is no required textbook, so students' notes from the presentations will be critical as a reference.

I will have a small number of summer research intern positions in Summer 2012 for students from the course to continue their research program with me.

Goals of the course


Some recommended reading

Here's a bit of mathematics to begin learning or review before the semester begins. I've included links to wikipedia pages which contain definitions and examples; in addition pick up almost any undergraduate or graduate book on the subject and read a bit, or google around and find notes if you are not close to a library.

Course requirements

Math 490 will require a lot of work, at least as much as other advanced math classes, but also requiring much more initiative and independent work. The class is a serious commitment, but the payoff for you will be getting a glimpse of mathematical research and some really interesting open (unsolved) questions in mathematics. Please only consider this class if you will have time in your schedule for a serious commitment to a research project.

Caveat : We will be doing mathematical research, and by it very nature, we can't predict the outcome and so it is possible that the course requirements may change to better reach our resaerch goals, e.g. perhaps groups will be merged or split if it turns out two questions have a common thread or one question splits into two, or perhaps presentations will be longer and less frequent if we need more time to devote to each presentation.

Preparation: First 5 weeks (Jan 23-Feb 24)

Projects: February 27-April 27

Final Papers: April 30-May 11


Grades will be based on your effort in all of the above, in the given percentages. Historically most students (the students who worked very hard) in Math 490 get a A, and most of the rest get an AB.

LaTex Resources

You'll want to download a LaTeX editor for writing up your assignments and the eventual write up of your project. Please set this up before the semester begins. Next, it's important to have somewhere to turn when you've got an error that WON'T GO AWAY, or when you can't remember what the heck that symbol was.


Lalit Jain has created a nice Sage/Linux reference which is available here. His other computing documents are available here. I like this Sage reference manual

Math department linux machines you can work on are listed here.