Day 13 in Mat115H

Today:

• Announcement:
  • Our first exam is Thursday:
    • It will encompass both Lewis Carroll's story through Fit the Third. You should be have a thorough understanding of
      • Dates
      • major characters
      • major events
      (you may want to revisit the timeline).
    • You should recognize his characters in their native environments. You might get "what's wrong with this picture?" questions....
    • Have a thorough understanding of those scenes that we discussed in class.
    • And you should know, and be able to do, the mathematics we have discussed, especially
      • Mobius bands
      • Fortunatus's Purse
      • The Tricks of p. 65
      • The binary card trick
      • Bases
      • Carroll's ciphers
      • Modular arithmetic

• 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?

  • Expanding binomials and Pascal's Triangle:
    

  • 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
      • Do we need to keep track of all the digits in our sum?
    • 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?
    • What if two digits are transposed -- will a computer discover the error?

  • Let's check a few samples...

  • Checking checks: my routing number is 242175874. Does it check out?
  • Checking checks (see your handout for the scheme):
    • my routing number is 242175874. Does it check out?
    • does someone have another routing number we can try?