Day 11 in Mat115H

Today:

• Announcements
  • There is one more assignment to hand in before your exam (which is on 10/8, a week from Thursday): about Crazy Clock and Checking Out Bars
  • Your base problems are due today.
  • Binary Card Trick pieces returned.

• The Mathematics of Fit the Third
  • Three tricks, p. 65
    • The addition sum
      • Who can play?
      • Can you do it more easily using smaller numbers?
      • How does it work?
      • Can you do it in binary?
    • Counting alternately up to 100
      • Who can play?
      • How does it work?
      • How could you beat Charles?
    • The '9' trick
      • Who can play?
      • Can you do it more easily using smaller numbers?
      • How does it work?
      • Why is it important to avoid "0"?

  • Ciphers (pp. 76--)
    • his matrix cipher (1858)
      • How is modular arithmetic used in this cipher?
      • What's the message on p. 77?
      • Encode "The Jaws that bite, the claws that catch" using the matrix cipher.
    • his alphabet cipher (1868)
      • Can you use his alphabet cipher?
      • What's the message on p. 79?
      • Encode "The Jaws that bite, the claws that catch" using the alphabet cipher.
    • Find a partner, and exchange (short!) messages, using each of these codes. Make sure that you know how to use them!

  • Crazy Clocks and Checking Out Bars (from The Heart of Mathematics)
    • What is "clock arithmetic" (i.e. modular arithmetic)?
      • What time will it be 27 hours from now?
      • What time will it be 27*24 hours from now?
      • What time will it be 25²⁴ hours from now?
      • What time will it be 30²⁴ hours from now?
      • What is 27 mod 24? What does "mod" mean?

    • Not all "clocks" have 12 hours:
      • Today is Tuesday, September 9th: on what day of the week will September 9th fall next year? How about Christmas, 2009?

      • A related problem: if your birthday this year is on Monday, what day will your birthday fall on next year?

      • Problem #8 from your handout

    • Here's a sneaky one:
      What is 2³⁰⁰⁰ mod 7? Why is this important? (Secret codes!)

    • What are UPCs? "Universal Product Codes" (a sort of "secret code")
      • How do they work?
        • First of all, they identify manufacturer and item
        • "3 1 3 1 3 1 3 1 3 1 3"
        • mod 10
        • What is a "check digit"?
        • Example: Kroger's Crunchy Peanut Butter
          0 11110 73933 9
      • On my last birthday I enjoyed one of the following beers:
        • Moerlein OTR Ale: 8 97232 00070 7
        • Great Lakes Commodore Perry India Pale Ale: 7 04361 94001 1
        • Sierra Nevada Porter: 0 83783 47521 0
        (but just one -- I had to prepare for my classes!;). The incorrect UPC will tell you which I had. Which was it?

      • Why is correctly reading a UPC important?
      • What if a single digit is wrong in the UPC -- will a computer discover the error?

    • Let's check a few samples...
      • Life Cereal
      • Keebler Club Crackers