The audience for your technical paper is your peers: namely, junior/senior mathematics majors. Thus you can assume that your readers know calculus and the method of proof by induction, but you cannot 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 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. 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
  • hypergeometric functions
  • Thomae's function (the ruler function)
  • the Lambert W function
• Discuss one of the following paradoxes.
  • the surprise examination paradox [Austin]
  • Hempel's paradox of the ravens
  • the liar paradox [Kelly claimed this topic on September 2]
  • Zeno's paradoxes [Emily]
  • the Banach–Tarski paradox
  • Newcomb's paradox
  • the prisoner's dilemma [Elizabeth S. claimed this topic on September 4]
  • the Petersburg paradox [Kala]
  • the exchange paradox (two envelopes problem) [Samuel]
  • Braess's paradox
• continued fractions
• Fibonacci numbers [Devin]
• Pascal's Triangle and its applications [Kat claimed this topic on September 5]
• the mathematics of voting (what is the best voting method?) [Sarah R.]
• tessellations [Aylor]
• Latin squares [Steven]
• the mathematics of sudoku [Jennifer]
• fractals [Elizabeth B.]
• cryptography [Ashley claimed this topic on August 29]
• error-correcting codes
• the five-color theorem
• p-adic numbers
• the Königsberg bridge problem [Ian]
• the Monty Hall problem [Michelle claimed this topic on September 3]
• Nim
• the isoperimetric problem
• Conway's game of life [Landon claimed this topic on September 4]
• quaternions
• Stirling's formula
• the Skewes number
• nonstandard calculus [Charlie claimed this topic on August 30]
• correlation between music and mathematics [Shamah]
• mathematical patterns in nature [Sarah B.]