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The Final Examination of Life

[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:

  • 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?
[5.] (ALGEBRA) Discuss the advances made in algebra since the invention of the phrase "char F ≠ 2."

[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 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?

  • 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.
[9.] (ANALYSIS) Analysis is simply a discussion of the consequences of the triangle inequality. Discuss.

Source: Desmond MacHale's Comic Sections, 1993, pp. 153-154