Day 8 in Mat115H

Today:

• Announcements
  • Your Mobius homework is returned. As I said last time,
    One word answers are (almost) never acceptable.

    I'm not so interested in the answers -- I generally know them -- I'm interested in your thought process. More words are (generally) better than too few. "Yes" or "No", without reasons, are just 50/50 crap-shoots, as far as I can tell. "One", "Two", "Four" were all answers I received RE the number of faces on a thickened mobius band.

    • What do I do with one word answers that are wrong?

    • What do I do with one word answers that are right?

      Do they deserve full credit, when it may have just been a lucky guess, and compared to the guess of another person who carefully reasons out their answer before my eyes?

      Some many word answers are also just one word answers: there is no substance associated with the build-up: let's face it,

      "From my perspective, it is undoubtedly the case that there is still exactly and perfectly one side to the band." == "one"

    I realize that that is how many of you have been trained, mathematically: to write terse answers, that a teacher can check against a key. I am not that teacher.

    Just for fun, re-examine at Carroll's work on the geometry problem, p. 28, done when he was twelve....

    Issues/Questions you could have addressed, answered:

    • #8: what relationship do the new "rings" bear to the original? What are their characteristics, compared to those of the original?
    • #9: How is this exercise related to #8? Again, what are the characteristics of the new rings, compared to those of the original?
    • #10: the object was called a "mess", a "tangle", a "mess of tangles". A mathematician's job is to make sense of messes. How many twists should it have? What do you see inside (some answered this -- what did you see?)
    • #18, 19, 20:
      • Make a model! Did you? How could you?
      • Can you use the strategy we learned in class?

  • You have no new assignment for next time. You have enough on your plate.

  • Please hand in your commentaries on Dodgson's Hints for Doing Mathematics.

• More about bases
  • What questions do you have about bases?
  • Let's look again at the trick of the Great Fraudini (and your next assignment). There's been some consternation....

• Hits from Fit the Second
  • What new insight do we get into Carroll's character?
  • What do you think of Carroll's hints for doing math?
  • Let's look at some Algebra problems, of p. 50