Day 9: mat385

Last time

Next time

Today:

• Announcements:
  • Reminder: turn off your rectangles.

  • I thought that you all might appreciate this comic:
    

  • Your 2.2 homework is returned (graded 4, 32, and 61). I see way too much "P(n) = ", rather than "P(n):"

    This is an example of something I call "equality abuse". Don't be guilty of it....

    P(n) is a statement -- an equation, or inequality -- and not one part of that (e.g. the left-hand side!).

    • #4:

      1. Just a lot of algebra. Avoid expanding unless you have to!

      2. I saw some of this: $P(n) = \frac{n(n+1)(n+2)}{6}$.

    • #32: justify $4k+4>2k+5$ ...
    • #61: at the end you may need to make an assertion about something being an integer....
    Finally, when all is said and done, say "We've established $P(n)$ for $n \in\ N$, by induction." (or whatever is appropriate -- but indicate the starting integer).

• Today:
  • Today we finish off Recurrence Relations.

  • Then we'll start section 3.3: Analysis of Algorithms