Saturday, March 29, 2014

Review, due March 31

  • Which topics and theorems do you think are the most important out of those we have studied?
    • The Schroder-Bernstein Theorem
    • The Fundamental Theorem of Arithmetic
    • gcd
    • The Division Algorithm
    • Cardinality of denumerable and nondenumberable sets
  • What kinds of questions do you expect to see on the exam?
    • I expect to see a lot of definitions, and proofs
    • Specific proofs I expect to see are ones using the Schroder-Bernstein theorem, which should be pretty straight forward.  I hope not to see one where I need create a bijective function that from a subset of the real numbers to the real numbers but I will be prepared.  I expect to see some questions on relative primes and the division algorithm.  It should be a fun exam.
  • What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
    • I need to understand problems that involve uncountable sets and using the decimal expansion to prove things.  I think 10.36 would help me understand things better.

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