Your final project is due at the same time as the final exam is held; I recommend you turn it in earlier (say, the Friday of reading period) to keep your finals week workload down. Seniors must have it in earlier, of course.

This page describes the project, and possible ideas for what to do. You will be required to meet with me sometime to discuss what you will do, to make sure it's the right size (not too small, but also not so large it's impossible). It should be around 3-7 pages, depending on the content.

The overall format is thus: you will prove some theoretical statement (such as the fact about d=ma+nb from Exercise 4.7), with the help of a book or the text; you will do some calculations to show mastery of the theory (like Exercise 4.8 calculating some actual d=ma+nb); finally, you will find an application, real-life or not, to your theory (like Exercise 4.9 and Bruce Willis). This overall format can be tailored, of course, if you choose something very non-theoretical but with lots of cool examples, or if you choose something so theoretical that it really has no applications yet. But all of these will have to be run by me first in any case.

Here are some examples of topics which are discussed in the book.

Gaussian integers, Exercise 1.25

Matrices, Exercise 6.22

Weird orderings, Exercise 2.20

The Induction Principle, Exercise 2.21

Properties of primes, Ch.3

The functions on divisors (phi, sigma, tau), Ch.3-6

Egyptian Fractions, Ch. 5.2

Check Digits for ISBN, UPC, Ch. 7.3

The Day of Week for any Date, Ch. 7.2

Some other ideas you might have to look a little more for.

Cryptography

Error Correcting Codes

Origami

Transcendental Numbers

Possible and Impossible Chess Patterns

Mathematics of Juggling

Groups or Sets in Music Theory

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