Math 396, Spring 2012
Guidelines for term papers

Your paper should be written in LaTeX using a standard documentclass. The length should be about six pages (using the default single spacing). You should cite at least one each of a journal article, a hard copy book, and a reliable internet source. Remember that in the academic world, plagiarism is a major offense, so document your sources carefully.

Here is a nonexhaustive list of potential topics for term papers. You should select a topic before the second class meeting. Each student must select a unique topic—first come, first served. You are welcome to write about a topic that is not on the list, but please consult with the instructor about the suitability of your topic.

• Investigate a named special function.
  • the Gamma function
  • Bessel functions
  • Legendre polynomials
  • Hermite polynomials
  • Laguerre polynomials
  • elliptic functions
  • the Riemann zeta function
  • hypergeometric functions
  • Thomae's function (the ruler function)
  • the Lambert W function
• Write about one of the following paradoxes.
  • the surprise examination paradox
  • Hempel's paradox of the ravens
  • the liar paradox
  • Zeno's paradoxes
  • the Banach–Tarski paradox
  • Newcomb's paradox
  • the prisoner's dilemma
  • the Petersburg paradox
  • the exchange paradox (two envelopes problem)
  • Braess's paradox
• continued fractions
• Fibonacci numbers
• Pascal's Triangle and its applications
• the mathematics of voting (What is the best voting method?)
• tessellations
• Latin squares
• the mathematics of sudoku
• fractals
• cryptography
• error-correcting codes
• the five-color theorem
• p-adic numbers
• the Königsberg bridge problem
• the Monty Hall problem
• Nim
• the isoperimetric problem
• Conway's game of life
• quaternions
• Stirling's formula
• the Skewes number