Format for Final Projects.

1. Factoring primes Explain how factoring primes is related to the effectiveness of encryption. Outline the basics of the RSA encryption algorithm (or other, e.g. MD5, DES, etc). Write a Maple code to implement the RSA algorithm. [starting point]

2. Chaos Study literature on how period doubling and other behavior associated with iterated function systems (such as "strange attractors") can be tied to physical behavior, such as turbulence in fluids. Write a maple program to simulate a system with period doubling/chaos. Investigate the Lorenz attractor

3. Geometry - Examine how the ideas and problems of projective geometry have influenced modern computer graphics. Explore mathematical issues in solid body modeling, surface rendering, lighting, rigid body dynamics, etc. [starting point]

4. Algorithmic Complexity Theory - Examine how the search for more efficient ways to solve "hard" problems such as the travelling salesman problem (or 4 color problem or graph coloring problem) have influenced mathematics. Summarize (in your own words) Karmakar's algorithm. [starting point]

5. Infinitesimals - Examine the early development of the calculus, via "fluxions", and explore the resurgence of "transfinite mathematics" or "nonstandard analysis." [starting point]

6. Non-Euclidean Geometry. Find, and develop, at least one "real-world" application of non-euclidean geometry (e.g. hyperbolic or spherical geometry) and explain its importance. [ starting point]

7. N-body Problem - Explore the history of attempts to solve the problem of gravitational attraction between N (N>2) bodies. An example is our solar system. Describe the current status of this problem. [starting point]

8. Non solvability of polynomial equations of degree 5 or more. Summarize the history of this problem (finding roots of polynomials) and present (in your own words) a synopsis of the proof. [starting point].

9. Fractals and fractional dimensions. Explore the relationships between Mandelbroit and Julia sets, as well as Feigenbaum's universal constants. [starting point]

10. Fermat's Last Theorem. Explore the history of this problem, from Euclid's Elements (finding Pythagorean triples), to Fermat's comments, to classical attempts to solve it, culminating in Weil's solution in 1995. In your own words, summarize the proof (in broad terms). [starting point]