Day 22 in Mat115H

Today:

• Announcements:
  • You have an exam coming up Thursday. It will feature some elements from Dodgson's life (from Fit the Fourth through Fit the Sixth), as well as some of the mathematics that we've discussed since our last exam. To be covered:
    • Modular arithmetic in the form of UPCs, ISBNs, checks, ...
    • Geometry
      • basic constructions (e.g. dropping perpendiculars, drawing equilateral triangles)
      • puzzles related to those that we did for our homework (even if some of them are from Fit the Seventh!
      I'll be providing you with a compass and straight-edge for the exam.
    • Determinants -- simple example only! 2x2 case.
    • Election schemes, and how to game them
    • Dodgson's suggestions for Tournaments
    • Memoria Technica
  • I'll pass around a book which might give you an idea for a project. Remember that your first pass at a project subject is due (as a one-page, typed concept) on Thursday....
  • You have an assignment for next Tuesday, as well. See our assignment page.

• Fit the Sixth
  • Questions on your Heart of Mathematics homework?

  • Lawn Tennis Tournaments
    • This Contribution of Carroll in "social choice" (also includes a section on how to write letters, and lots of other good stuff!).
    • See the (bad) scheme on page 143.
    • We consider the scheme in which 8 players play each other so that the top three players are not knocked out prematurely, then how can we proceed?

      Carroll basically proposes double-elimination tournaments.

    • Lawn Tennis Tournaments: The True Method of Assigning Prizes with a Proof of the Fallacy of the Present Method (p. 143)

  • Parlimentary Representations
    • Principles of Parliamentary Representation
    • Francine Abeles: Dodgson "made important contributions both to political science with his proposals for proportional representation and to mathematics with ideas that half a century later became known as game theory."

      Abeles points out, "Dodgson's main concerns were selecting the most preferred candidates to hold office, conducting elections properly, promoting minority representation, and achieving fair representation"

    • Looking at his list of "desiderata" suggests that this is so (p. 147).

  • What new things do we learn about Dodgson in this Fit?
    • Family life
    • At work
    • At "play":
      • Ariel's Song from The Tempest

        Full fathom five thy father lies;
                      Of his bones are coral made;
            Those are pearls that were his eyes:
                      Nothing of him that doth fade,
            But doth suffer a sea-change
            Into something rich and strange.
            Sea-nymphs hourly ring his knell:
                                      Ding-dong.
            Hark! now I hear them -- Ding-dong, bell.

• Fit the Seventh
  • There are more puzzles featured here:
    • A Tangled Tale
      • Let's look at "Knot the first": Excelsior
      • There are nine knots in A Tangled Tale beyond the first one, which we looked at in class. You may choose one of the others, or I'll assign one, and your job is to explain the problem (also summarized in our text, in Fit the Seventh), and to summarize the solution. You should write (or, better yet, type!) your commentary on a single sheet of paper. Due: 11/17.
    • Arithmetical puzzles
      • 142857
      • 1089
      • 12345679
    • River-crossing problems
      • three cannibals, three missionaries
    • Finding the Day of the Week