John Connett's Master's Exam

When chatting with Assistant Provost Bob Wheeler one day in October 2000, gleaning career guidence wherever possible, Bob showed me a list of questions that he said John Connett felt anyone with a master's degree should be able to answer after only a moment's hesitation.  These questions are:

1. Prove there are an infinite number of primes.
2. Prove that a geometric series converges and find its sum.
3. Derive the quadratic formula.
4. Prove the Mean value Theorem.
5. Prove the Law of Cosines.
6. Prove that the square root of two is irrational.
7. Prove that there is no surjection from a set to its power set.
8. Prove Lagrange's Theorem.
9. Prove that any uncountable subset of the reals has a limit point.
10. Prove the harmonic series diverges.

Needless to say, having earned my master's degree this past Summer, I felt I should be able to answer each of these questions.  These are important results with which anyone with a master's should be quite familiar, but there are, of course, other results one should know.

I got into math in part because I don't have the raw memory for medicine or law, both areas of interest to me.  An unintended result of my attitude about this has been that I haven't held myself accountable for being able to derive fundamental results on demand.  I decided that whenever I come across such a basic result, I will ask myself "Can I prove this?" just to make sure I can.

View my solutions by downloading the Acrobat file (PDF)

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