This term, you will do two papers. The first one should be at least five pages long and double spaced. It can be about any topic in discrete mathematics (using a fairly generous interpretation of this field), and should include at least some material which is not covered in the course. It should have a coherent introduction, and be written clearly. The final paper should be ten pages long, and may be an extension of the first one, on the same topic.

## Paper Topics

The basic idea is that you should take some topic preferably one not covered in the course, and imagine that you were to give a lecture on it, which would convey to someone of reasonable intelligence but no particular knowledge of the field, what the subject was about and at least one interesting and non trivial result in it. For those of you who are juniors or above this can be your phase 2 paper though you may have to work on it some so that others can take a seminar somehow in perfecting it. Among possible topics are:

- Hashing
- Matching Theory
- Other Error Correcting Coding Schemes
- The New Primality Testing Algorithm
- Novel Linear Programming Algorithms
- New Ideas on Linear Programming and Complexity
- New Linear Programming Algorithms

## List of Topics Chosen in Previous Years

- Beating the House at Blackjack
- Big Integer Math
- Black Scholes Model
- Black Scholes Model Calculation
- Catalan Numbers - an Introduction
- Chaos and Fractals
- Combinatorial Optimization
- The TSP Comparisons Containing a Biological Attack
- Domino Tilings of Theaztec Diamond
- Economic Game Theory and Auctions
- Efficient Algorithm for Archtypical Gradebased Scoring
- Electronic Voting
- Elementary Fractal Geometry
- Enigma Breaking Environmental Accounting
- Evolution of the Four Color Theorem
- Information among Peers
- Introduction to Game Theory and Various Applications
- jpeg Compression
- Marriage Problem
- Mathematics of Solving a Rubik's Cube Blindfolded
- Modern Cryptography
- Morse Code vs. Huffman Coding
- Optimal Solutions to the Stable Marriage Problem
- Probability and its Importance in Gambling
- Support Vector Machine
- Survey of Graphs and Coloring
- Survey of the Jacobsthal Numbers
- The Boosting Algorithm and Game Theory
- The Five Color Theorem
- Topics in the Theory of Computation
- Variations in the Gamblers Ruin Problem
- Wavelet Analysis