[1.] (GROUP THEORY) Either (a) give in detail the proof of the classification of the final simple groups, or (b) write your name in block capitals.
[2.] (LOGIC) Either (a) prove that P = NP or (b) prove that P ≠ NP.
[3.] (GRAPH THEORY) Give a one-line proof of the Four Color Theorem suitable for the visually-impaired. In how many ways can a color-blind student with ten tins of quick-drying paint, 4 brushes and 3.2734 x 10-9 ml. of turpentine, five-color a 1941 map of Europe?
[4.] (FOUNDATIONS) Write a short essay on any of the following:
[5.] (ALGEBRA) Discuss the advances made in algebra since the invention of the phrase "char F ≠ 2."
- How do Tarski and Church differ from Starsky and Hutch?
- Is mathematics still waiting for Gödel?
- Was Gomulka an essential singularity or a removable pole?
[6.] (NUMBER THEORY] Prove that as N → ∞ then something else is is very much greater than something with lots of logs and logs of logs, and even logs of logs of logs, with possibly an e-α thrown in, bounded by an unknown constant which is as sharp as possible.
[7.] (PROBABILITY) If infinitely many statisticians are working on a problem involving 26 variables a, b, c,...,x,y,z, what is the probability that in less than 100,000 years they will produce a script of Planet of the Apes? [Assume a typing rate of 1.001 characters per second.]
[8.] TRUE OR FALSE?
[9.] (ANALYSIS) Analysis is simply a discussion of the consequences of the triangle inequality. Discuss.
- Some lemmas commit suicide by jumping over discontinuities.
- Galois Fields are duel concepts.
- Quaternions are a remote group of Irish islands.
- Bertrand Russell had an electric razor.
- Double integrals can be used to calculate how green was my valley.