Project Proposal
This should be a one or two page document which explains the topic you have chosen for your method, your goals in exploring this topic, a list of at least three sources you intend on using for your presentation, and descriptions of any experimentation you intend on carrying out or code you plan to write. The sources should simply be listed at the end of the document.
Informal Check Point
Final Project Submission
The main part of the paper should be written in English and look like a typical research paper. This should be a .pdf file. (If you do it in Word, just save to pdf.) If you write some code or have other data to share, please share with me in a format that I'll be able to see easily (for code please give me either .cpp, .c, .java or .py files, ask me if you have something else you'd like to share and I'll let you know what file formats are permissible.) Sample Project Ideas
Probability Topics
Taking a game, such as Monopoly, Risk, or any card game, and analyzing the probabilities involved in the game. In addition to this analysis, a simulation can be written to see if the experimental results coincide with the theoretical findings.
Markov Chains
Counting Topics
Catalan Numbers
Derangements
Stirling Numbers
Other Topics
Summation techniques not taught in class
Recurrence relations
Special Numbers
Harmonic numbers
Fibonacci numbers
Bernoulli numbers
Number Theory
Probabilistic Algorithms - Primality Testing (Miller-Rabin Algorithm)
Properties of the Euler-phi function
Brief introduction into group theory
RSA encryption, or another encryption technique that uses discrete mathematics
Linear Algebra
Introduction to Linear Algebra
Basics of Linear Algebra as related to image processing
Specific Problem Idea
Take a harder problem (maybe an AIME problem), solve it a couple different ways, and or generalize the problem and write a computer program to solve it as well
Anything else you can think of!
