Day 15: mat385

• Announcements
  • Homework graded, #2, #16, and #40
    • #2 was straightforward: Equation 8, p. 150.
    • #40 was straightforward: Equation 21, p. 163.
    • #16 was rough (I was very lenient in grading it!:)

      Sam and Liam have the recurrence relation that our author intended.

      You can't run the infection and cleaning separately, and see where they're equal: cleaning means that the infection rate will decline, so they confound each other (or rather cleaning confounds the infections).

    • There was a question about #9....

  • Some have asked about projects. A couple of things:
    • One year I asked students to work on a game of interest, and these were the results. That would be a nice thing to try, if you're interested.
    • You can "double-dip" -- if you're doing a project in another class, but you can tie it into this one, then you might do that!
    • You might do something related to a section that we don't cover.
    • In terms of a rubric, here's my working version: project rubric.
    • Your project proposal is due by 11/14.

  • No class Monday -- have a good break!

• Let's wrap up section 3.1: Sets
  • We were going to show that infinite sets come in different sizes.... but so far, they're all the same size (integers are the same size as the natural numbers, since they can be put into one-to-one correspondence.

    Turns out that the reals are bigger than the natural numbers however, as we'll see using Cantor's diagonalization argument.

  • Then we'll take a look at binary versus unary operations on a set; and then a
  • Venn diagram applet (shows all possible subsets using two sets and intersection, union, and complement -- binary and unary operations on the power set of the universal set).

• Then we'll begin section 5.1: Graphs and Their Representations

Links:

• The Logic Diagrams Of John Venn
  • Venn's Symbolic Logic
• The Logic Diagrams Of Lewis Carroll
• Lewis Carroll's Logic
• Graph Terminology