Review of Material to be covered on Test 1
Heart of Mathematics

Strategy:

• Since I like to give partial credit, you should attempt all problems (even if you cannot solve them).
• Look over your homework - the mindscapes - and check that you can do those sorts of problems. A few will be modeled on your homework.
• As I said, I can't get too tricky, because we don't have much time. But be prepared for a few little twists and turns.

Subject Matter:

• There will be a fair number of problems testing content, from the reading or from class: e.g.
  • "Write the first ten Fibonacci numbers"
  • Show a one-to-one correspondence between the natural numbers and the positive rational numbers.
  Note: even if we did not discuss something at length in class, you are still responsible for it on the test!

• There will be some slight twists on old problems: e.g.
  • I might introduce a different series than the Fibonacci numbers.
  • I might ask you to analyze a game different from, but similar to, Fibonacci nim, or one of the puzzles at the beginning of the book.
  • I might ask you for a one-to-one correspondence of a set we haven't considered before.

• You should know your definitions: e.g.
  • What are the rationals, naturals, reals, etc.
  • What is Cantor's diagonalization procedure (and can you apply it?)?
  • What is the Pigeonhole principle?

• Know the tricks from the fun and games:
  1. Genie
  2. Damsel
  3. Fountain
  4. Trou
  5. Dodge
  6. Weave
  7. Deal
  8. Dot

• What questions do you have?