The audience for your technical paper is your peers: namely, junior/senior mathematics majors. Accordingly, you may assume that your readers know calculus and the method of proof by induction, but you must not assume that they know the Sylow theorems or the Lebesgue integral.

Your paper should be written in LaTeX using a standard documentclass. The length should be about 2,000 words.

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. LaTeX has a “thebibliography” environment intended for typesetting reference lists.

Here is a nonexhaustive list of potential topics for the technical 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 [claimed by Jeffrey on January 22]
  • hypergeometric functions
  • Thomae’s function (the ruler function)
  • the Lambert W function
• Discuss one of the following paradoxes.
  • the surprise examination paradox
  • Hempel’s paradox of the ravens
  • the liar paradox
  • the Socrates paradox: “I know that I know nothing.”
  • Zeno’s paradoxes
  • the Banach–Tarski paradox
  • Newcomb’s paradox
  • the prisoner’s dilemma [claimed by Alicia on January 23]
  • the Petersburg paradox [Jesse]
  • the exchange paradox (two envelopes problem)
  • Braess’s paradox
• continued fractions
• Fibonacci numbers [claimed by Kelly on January 20]
• Pascal’s Triangle
• the mathematics of voting
• tessellations
• Latin squares
• the mathematics of sudoku [claimed by Laura on January 18]
• fractals
• cryptography [claimed by Ally on January 22]
• error-correcting codes [claimed by Annalisa on January 23]
• 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
• nonstandard calculus
• correlation between music and mathematics [claimed by Edwin on January 17]
• mathematical patterns in nature
• the mathematics of Rubik's cube [claimed by Todd on January 22]
• calculus of variations [one of the Nicks]
• the mathematics of sports [one of the Nicks]
• mathematical modeling of infectious disease [Christopher]