====== Monday - Day 1 ======

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[[.day1:test|Pre-test]]

Introduction
  * Go over the schedule
  * Go over the rules and sign contract
  * About me
  * Ice breaker

Decorate Notebooks
  * Make sure they are right-side up
  * Write a personal bio

Permutations and Combinations
  * Go over the problems

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http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Permutations: How many rainbows can you draw with these colors (red, orange, yellow, green, blue)? Each rainbow can only have 3 colors, no repeated colors.

<code>

Where n is the number of things to choose from, and you choose r of them (No repetition, order matters)

n!/(n-r)!

</code>

Permutations with Repetition: Each passcode is 5 numbers long. How many passcodes are possible?

  n^r

Combinations: How many ways can a group of three students be selected from a class of 21 students?

<code>

(21!)/(18!)(3!) = 1330

"n choose r"

Where n is the number of things to choose from, and you choose r of them (No repetition, order doesn't matter)

</code>

Combinations with Repetition: You get 4 scoops of ice cream, how many different combinations can you make from Chocolate, Vanilla, and Strawberry?

  "(n + r - 1) choose r"

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Game Theory
  * Story: Prisoner's Dilemma : Activity


{{:spcs:winter2014:math:prisoner_s_dilemma.jpg|}}

{{:spcs:winter2014:math:prisoners-dilemma-1.jpg|}}

{{http://math2033.uark.edu/wiki/images/0/09/Gametheory.gif|}}


  * Rock Paper Scissors
  * Dominant Strategy

Games
  * counterfeit coins: https://www.dropbox.com/s/y4x62yr6aenfs1h/Math%20Puzzles%20and%20Games.ppt
  * divide in groups of 4
    * bean game
    * x&o game
    * box game: http://www.math.ucla.edu/~tom/Games/dots&boxes.html
    * hex game

Writing Time
  * What are your best strategies for each game?
  * Which games are similar? How?
  * What is the prisoner's dilemma?
  * What did you do today?