UNDERGRADUATE

RESEARCH IN 

MATHEMATICS
110.503
Dr Mark Haskins
E-mail address: mhaskin@math.jhu.edu
Telephone: 410-516-4047
Department: Mathematics
Office: Krieger 312
Office Hours: by appointment

As well as doing some interesting math, through the course you will develop some of the necessary (and transferable) technical skills for a scientist -- choosing a research project, searching the math literature here at Hopkins and online, and the arts of writing, talking and typesetting mathematics. For those interested in math grad school this is a good chance to find out what doing research is all about (and probably looks good on applications).

The course is aimed at students who already have  experience with the idea of proof in mathematics. If you are not such a student, but are interested in taking the course, please email me to discuss your individual situation. 

Course Organization

The basic idea of the course is for you to choose a topic of research at the beginning of the semester and then to spend the rest of the semester doing research in this area. You may work individually or in pairs. 

There are two regular meetings associated with the class:

1. once-weekly class meeting (time TBA) for 1 hour

2. regular meetings with me on an individual project basis (approx one meeting every 2 weeks)

Everyone should plan to attend the once weekly class meeting. I will give some talks about finding research topics, searching the math literature, math typesetting etc. You will also be expected to give presentations about your projects. This will also be a time for other people in the class to hear about your project and to give their ideas.

Course Components

I.  An informal daily record of your work on your research project. 

Email a copy to me the day before your meeting with me. This "math journal" should contain basic information like: the papers you're reading, the relevant results from them, possible directions, conjectures, counterexamples etc and questions that come up from your reading/ thinking.

II. In-class presentations

Everyone will give the following presentations during the weekly class meeting:

• Early in the semester, a short introduction to your research problem

• Through the semester, several progress reports

• Near the semester end, a final report on the results of your research.

III. Formal papers

Everyone will hand in three properly typeset (preferably in LaTeX) papers.

• A short (a few pages) paper containing a statement of your problem, some larger context for it, relevant definitions, references and some simple cases/ illustrative examples if appropriate. Due 3-4 weeks after semester begins.

• A draft version of your final paper, containing your results written in the style of a math paper i.e. typeset, with bibliography, abstract etc. This is your chance to get my feedback on writing style, your presentation etc before the final paper. Due around Thanksgiving.

• A final version of the draft above. Due near the end of the semester.

Your grade will be determined on the following basis:

Class participation (including introductory talk, progress reports and final report) -- 20%

Journal -- 20%

1st paper -- 10%

Draft and finished versions of final paper -- 50% total

Choosing a project

We will discuss this fully in the first class meeting periods. I will make some suggestions for projects, but you need not follow me if you have your own ideas. I will also try to indicate how you could find your own projects if you have some clear idea of what kind of mathematics you'd like to work on.

Some possible projects (in pdf format):

1. Pi in the Mandelbrot set
2. Points and meshes on the sphere
3. Tracking tangles
4. Rotation subgroups, tilings and platonic solids

Note: the current versions of projects 1 and 3 available here do not include the figures. To get copies of these projects which include the figures as intended, please stop by my office and pick up a copy.