Day 11: mat385

• 2.2 homework returned: graded #24, 28, 63
  • First of all, don't forgot that $P(n)$ is a proposition, perhaps an equality: it is not a quantity. We use colons with $P(n)$, not equal signs.
  • #24: P(1) is easy (but you've got to do the anchor!); then a lot of algebra.
  • #28: Consider the left hand side, and move to the right. Don't work with the entire inequality that you want to demonstrate: it's clumsy.
  • #63: no anchor
  • I noticed that many of you didn't do #60. Good thing I didn't grade that one.... But how would you prove that there is no tiling of a particular configuration? Cases (and exhaustion...).

• 2.4 homework isn't finished yet -- sorry. I did have a request to look at #23, however, so let's go over that first.

• I postponed your 2.5 homework until next time, Monday.

• You have an exam next Wednesday (10/5). It will cover everything through 2.4.

  We'll review as long as you have questions, and then we'll switch to 3.1 if you run out of questions.

I want to look at one more example: #8, p. 165, which doesn't fit the two patterns of recurrence relations we've solved in closed forms (it doesn't have constant coefficients). Instead we try "guess, check, and verify".