SUNY at Stony Brook MAT 320: Introduction to Analysis
Fall 2006


Every student in MAT320 will need to complete a project related to mathematical analysis (typically working in groups of two or three people). Each group will need to produce a written paper, and to give a short (15 min or so) presentation in class. (Only one paper per group is needed; however, I'd like everyone to contribute to oral presentations.)

Your project paper must be written in such a way that it can be understood by other students in MAT 320. It should contain some rigorous proofs, not only descriptions or historical accounts (but feel free to include some extra mathematics without proof). The paper may be handwritten or typed.

A list of suggested projects is here. Many topics are quite flexible, so what exactly you write about is up to you. You're very welcome to suggest your own project, too.

Some relevant information for the projects can be found in our textbook; another helpful resource is the Internet, for example, Wikipedia. Many other analysis books can also be useful; I'd like to mention Principles of Mathematical Analysis by Walter Rudin (although this book is more advanced than our course). I will be happy to suggest specific references if needed.

You have to write the paper in your own words; projects copied from the textbook or Wikipedia (or anywhere else) will not be accepted.

Important dates:

Nov 1 Decide who to work with, pick a project and tell me (in class or by email).

Dec 1 Project paper due.

Dec 4–13 Project presentations (in recitation).

Presentation schedule:

Dec 4:

Convergence tests for series (10-15 min)

Decimal presentations for rationals and irrationals (10-15 min)

The Cantor set (20-25 min)

Dec 6:

Euler's number (10-15 min)

Metric spaces (10-15 min)

Compactness (20-25 min)

Dec 11:

Newton's method (10-15 min)

Space-filling curves (20-25 min)

Please plan carefully for your presentation. In most cases, it will not be possible to present everything you write in your paper, so you'll have to decide what to present. I'd like you to include at least some sketches of proofs; also, it's better to present less material in a clear way rather than include a lot into an incomprehensible talk. Practicing your presentation is strongly suggested (especially for groups, but also for individuals). For those doing a group work, every member of the group should present some of the material.