Math 464, Exam 3/Final Exam
Katz, Dunham (Ch. 10-12), Class Notes

To be able to Prove or Explain:

DeMoivre's Problem III and Solution from the 1718 Doctrine of Chances.
Dunham Chap. 10: Great Theorem and Proof: Euler's 1732 refutation of Fermat's conjecture (4 theorems). [Preliminary Theorems A, B, C can be collapsed into one general result.]
Euler's 1735 solution to the Königsberg Bridge Problem.
Dunham Chap. 11: Great Theorem and Proof: Cantor's 1891 "diagonal" proof that $\QTR{Bbb}{R}$ is uncountable. Def of denumerable (countable); Proof that $\QTR{Bbb}{Q}$ is denumerable (countable)
Dunham Chap. 12: Great Theorem and Proof: Cantor's 1891 proof that the cardinality of any set is strictly less than the cardinality of its set of subsets (its power set)