**Opinion papers (3 pages = 750 words)**

**Paper I:** We covered several Greeks: Thales, Pythagoras, Euclid, and Archimedes. Each had a unique contribution to mathematics. Who made the greatest? You can make a case for any one of these.

**Paper II**: Are you really impressed with Cantor’s work? Sure he talks about different types of infinity. But are the results truly impressive or is it interesting because it contains interesting words such as “infinite” and “transfinite”.

**Major papers (8 pages = 2000 words)**

**Paper I:** Although the mathematician G. H. Hardy says that nothing he ever did in mathematics was useful, sadly, mathematics is actually useful. With my help, choose a **useful** application of mathematics and write a research paper explaining it to a novice. Please come by and talk to be about the theme of your paper as well as what sources you plan to use. Here are some topics students have written about in the past:

- RSA public key cryptography
- Error correcting codes
- Huffman encoding
- Wavelets (noise reduction)
- Wavelets (image compression)
- Predator-Prey models
- The mathematics of spying
- The Van Meegren art forgeries

You are, of course, allowed to write on some other topic. The above topics are merely suggestions.

**Paper II:** Write an expository paper on some topic not covered in this course. I”ll be happy to give you some guidance in selecting your topic. This paper should be well referenced and should contain at least two formal proofs. Please come by and talk to be about the theme of your paper as well as what sources you plan to use. Here are some topics students have written about in the past:

- P vs. NP
- The Poincare conjecture
- Transcendental numbers
- The Banach-Tarski paradox
- Tellesllations of the plane
- Solving polynomial equations by radicals
- Space filling curves
- Weierstrass’ non-differentiable function
- Jordan curve theorem
- Constructable numbers

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