A project involves learning about some mathematical topic related to the course and writing an expository paper (in your own words) at a level that your classmates could understand. It should be 8-10 pages long, or comparable in length to slightly more than a section of your textbook. And it should have a bibliography that gives the sources you consulted. These cannot all be internet links. In your references must be at least one book or journal.
The grade on the project will be averaged in with your exam grades as explained in the grading section of the course home page.
There are many ways to choose a topic. There might just be a subject that you've always wanted to learn about. Or you could browse through math journals intended for undergraduates for something that looks interesting. (See the discussion of resources below.) Or you could take a topic we've studied in class and pursue it further. Here are some examples, but don't be limited by them.
Numerical Integration: You could learn about other techniques and implement some algorithms to compare the effectiveness of various techniques.
Newton's Method: This is a calculus-based method for finding a sequence that converges to the solution of an equation. You could analyze situations where Newton's method works well and situations where it doesn't. This could involve implementing algorithms.
Fourier Series: Any continuous periodic function can be approximated by a sum of trigonometric functions. This technique has applications in both the sciences and pure mathematics. The famous formula for the sum of the reciprocals of the squares can be derived from this theory.
Number e: The number e is transcendental, i.e., it is not the root of a polynomial with integer coefficients. The square root of 2, by contrast, is a root of x2-2=0 and is called an algebraic number. An exposition of the transcendentalness of e would be a good project.
Partial fractions: the partial fraction decomposition can be used as an integration technique. You could investigate the algebra that underlies the existence of partial fractions decomposition.
The internet is a fine place to start if you want, but it is only a start. After that (or before that), check out Cornell's Mathematics Library, located on the fourth floor of Malott Hall. It is outstanding, and the librarians will be glad to help you find things. You might just browse through the stacks and see what grabs your attention.
In addition to books, there are journals that specialize in articles for undergraduates. Here are a few, all of which are available in our library. Some of them also allow online access; check the library catalogue.
Math Horizons (QA11 A1 M413)
Mathematics Magazine (QA1 M46)
The College Mathematics Journal (QA11 A1 T97)
The UMAP Journal (QA11 A1 U12)
As soon as possible: Let me know that you expect to do a project, and make an appointment (or come to my office hours) to discuss possible topics.
November 5: Tell me (by email) what topic you have chosen, with at least one resource that you plan to use.
November 12: Turn in an outline (at most two pages).
December 1: Paper due in my office by noon.