- Roll Call
- Announcements:
- Please hand in your class agreements
- Also hand in your second assignment.
- You have a new assignment --
check it out. It's mostly due next week, however.
- The return of your first assignment:
- I was gentle this time (and on your second assignment) --
but I'm going to get tougher!
- Make sure that you type what's easy to type (and do diagrams, etc. by hand)
- Watch your writing! We all need to go out and impress our
bosses someday, so make sure that you write well.
- Now, back to fun and games!
- "Let's Make a Deal!" recap:
- Through simulation, we got close to the true probabilities
(switching is twice as good as sticking in the three door
problem). Lots of trials (or simulations) of a game can work to
show us the "expected" outcome.
- Sometimes it helps to extend a game, to help us reason
through it.
- Now let's recap the homework games: The "two monster" problem:
- Could either of the following two questions work, spoken
to one of the monsters (chosen at random)?
- "If I were to ask him which way to heaven, which way would
he point?"
- "If I were to ask you which way to heaven, which way would
you point?"
- "That answer is best that assumes the least." What does the
first question assume? What does the second assume?
- What general assumptions are we making, regardless of the
two questions above?
- We are not allowed to assume that truth-tellers guard the
path to heaven!
- Some of you slipped into "angels and devils", indicating
that you may have been reading someone else's similar
problem. If you use someone else's work, you need to
cite it. It's okay to struggle for awhile, then
finally decide that it's time to go to the internet and
track down a solution. But give credit where credit is due!
- Recap of the cup problem:
- Did you have to assume more than two cups?
- Can you do it with two?
- You're not allowed to figure out where the halfway point
is on the cup: that assumes that your cup possesses
some symmetry (e.g. is a perfect cylinder), or that it
has a marking for "half way" on it....
- I liked the word "repeat" in several of the
solutions. Many times in mathematics we develop a good
procedure and then just "do it again". We'll hear "do
it again" over and over in here!
- Nice "out of the box" solution: buy 16 ounces!
- A good generalization of this problem would be "Given only
two cups, what are the allowable portions that can be served?"
("Explore the consequences of new ideas.")
- Three missionaries, three cannibals:
- How does the canoe get back across the river? (My bad: I
put "you" into the problem, when I only meant for "you"
to figure out how to explain to them -- not to ferry them!)
- Why not draw a diagram?
- Why not play the game with skittles? (Simulation)
- The importance of simplifying notation (C for Cannibal, M
for Missionary)
- What is the best method? Fewest steps?
- What makes a solution beautiful? (Symmetry!)
- If you couldn't do it with three and three, could you do
it with two and two?
- Generally:
- Write more! Some of you are way too terse.
- Watch for homonyms (e.g. poor, pour), that your
spell-checker will also miss.
- Edit your work! Read your own work, to catch grammatical
and spelling mistakes.
- Cite any sources used (anything less is academically
dishonest).
- In particular, while you may work together, you must not
copy from each other (or directly from an uncited
source).
- Some of you should consider running your writing past the
Writing Center:
(859) 572-5611. I'm going to start cracking down harder
on this as of the third assignment.
- You were asked to carry out two activities for today:
- What is the biggest number that you can express with your two
hands (assuming 10 fingers)?
- Well: what are our candidates?
- Who's got the trickiest, most imaginative answer?
- What does each of the digits in the number 1729 mean?
- "Break a difficult problem into easier ones." What does the digit 1 mean?
- The story of 1729....
- The story of base 10....
- Today's Topic: Busting up numbers (bases)
- We're going to be busting up numbers in different ways. The first
way is illustrated by the number 1729, and its base 10
representation. To move into the more unfamiliar, we begin with ...
- A "Fun and Game" to begin: a visit from the Great Fraudini!
- How does the game work?
- Can you win at the game?
- Each of you will be part of a team of three, taking turns playing
the roles of contestent, Fraudini, and someone to check the
play.
- You should be able to do it every time!
- Here's the handout for the cards, if you want to print off another copy.
- For your homework, you should read this bases
reference. Other bases are used constantly -- for example, in this web
page.
- What are some other bases that we use in our lives? Where?
- One of my favorite early introductions to bases was Tom Lehrer's New
Math.
Website maintained by Andy Long.
Comments appreciated.