Day 9, MAT115

Last Time

Next Time

Announcements:
- Our first exam is Thursday, and today we'll review the topics you'll be tested over.
  If you don't justify your answers for the test, you're going to be in big trouble!
- Your Yanghui triangle homeworks are returned.
  You were to justify your answers.
  One thing to think about is how to use previous numbers to get the next. Aaron did a really nice job!
  By the way, here's a hint -- a 17th century Japanese version (source)
- Hey, I forgot the competition for best Babylonian short story. Pick your favorite and we'll vote next time (there will be a slot for your vote on the test). There are three. Whoops, there was a fourth!
- Your Fibonacci Nim homework is due. Any particular questions?
Question of the Day: What will be on that exam?
I'll take questions, and then, if time remains, we'll return to those Fibonacci numbers....
So what have we done? What are some of the big picture items?
- First of all, you should do your reading (we're read up to page 28). I'll have some questions about some aspects of the reading, which summarizes a lot of the history of what we've done so far -- but also covers some other things.
- Counting:
  - one-to-one correspondence (examples....)
  - Body counting
  - "Primitive counting"
- Number representations
  - blocking
  - prime
  - positional/place value
  - bases
  - Babylonians
  - zero
  - Mayans
  - Chinese
  - "Fraudini" (binary, base 2)
- Additional Concepts:
  - Fibonacci Nim
  - Fibonacci numbers and rabbits (first look at fractals)
  - Pascal's (Yanghui's) triangle
    - powers of 2
    - symmetry
    - counting numbers
    - triangular (and other) numbers
  - Unique representation
    - as primes
    - as powers of two
    - as non-consecutive Fibonaccis
  - trees as organizers
  - You should recognize
    - the birthday problem
    - the card games

Website maintained by Andy Long. Comments appreciated.