MATH 498/499

Margie Hale

More than just a body of knowledge, mathematics is a way of thinking and a persistence of effort. Senior research is meant to showcase the mathematics you have learned at Stetson. These tools, gained in your previous math courses, will serve you well in this capstone course. The senior research project has several goals:

- You should work independently.
- You should use some advanced math that you learned at Stetson.
- You should create some new mathematics.
- You should explain your work orally and in writing.

**Independent work** is solving problems, finding answers, proposing new questions, and making conjectures on your own. You can expect help from me in asking initial questions, giving hints and suggestions, and listening to your ideas. You may use the library, the internet, other students, and professors. You must give proper credit for ideas that are not your own. See the statement on ethics.

**Using advanced math** is being responsible for the content of your previous math courses and building on that knowledge.

**Creating new mathematics** is going beyond exposition of someone else's work. Ideally, your results will be interesting enough to publish.

**Explaining your work** requires that you present several talks during the year directed toward other math students and faculty. You must submit a final paper containing your results.

**Sources of project ideas:**

- The library contains
**math books**, both general and specific. Check out the QA section upstairs, south side. - The
**math courses**you have taken have provided numerous problems. Did any questions come to mind about how an idea could be generalized or expanded to another setting? - Have you been to a
**math meeting or department colloquium**? Listening and thinking can result in new questions for exploration. - A number of
**math journals**are accessible to you. Some contain open problems in a separate section. All contain articles that you can read, possibly with some help. They can be found alphabetically by name on the lower floor, north wing of the library. The names below are abbreviated; "J" stands for "Journal."- Amer Math Monthly
- College Math J
- J Recreational Math
- Math & Comp Ed
- Math Gazette
- Math Intelligencer
- Math Mag
- Pentagon
- Pi Mu Epsilon J
- School Sci & Math
- SIAM J Appl Math
- SIAM Review
- UMAP
- Quantum (my office)
- Math Horizons (my office)

- There are also
**electronic math journals**for undergraduates:

**Projects of interest to me:**

- Geometry: explore different definitions of distance, virtual images in mirrors, and other questions.
- Delay Differential Equations: find applications, investigate the theory, and develop numerical solution techniques.

**Others areas of interest:**

- Dynamical systems: discrete or continuous.
- Logic: fuzzy and otherwise.
- You propose something: I'll help you turn it into an acceptable proposal. I'm interested in learning new math too.