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Lecture 1
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Administrivia
Intro to probability
Demo: intransitive dice
Modeling experimental events/philosophy
Sample spaces
Events
Finite probability spaces
Tree diagrams
Proofs

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Lecture 2
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Demo: pennies on edge
Numeracy
Set theory and probability
Predicates
Logic notation
Cardinality
bijections, injections, surjections


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Recitation 1
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Lecture 3
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Demo: Monty Hall
Well-posedness of problems (game theory)
More numeracy
Sum rule
Difference rule
Complement rule
Basic inclusion/exclusion
Boole's inequality
Ex: prob that chip fails
Demo: red-black ``stop'' card game



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Lecture 4
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Conditional probability
Bayes's rule
Law of total probability
Demo: Carnival dice
Problem: two-out-of-three series
Problem: racial discrmination
Demo: Red-Red, Black-Black, Red-Black cards
Demos from innumeracy book.


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Recitation 2
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Well-posedness problem: MVS's chicken in boxes 



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Lecture 5
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Independence
Aunt Daisy: Babies and IO
Definitions of independence
Symmetry
Birthday paradox



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Lectures 6-8:

What is a proof?
Lots of false proofs.
(Probability examples).


Induction.
Demo: Tiling game. 
Better examples of buildup error.
Using probability examples, if necessary
well ordering
Pigeonhole - example

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Lectures 9-10.

Parameterized sample spaces
Combinatorics
Permutations
Combinations
Rule of sum/product/division
Induction usage

Uncountability.


1 to n counting, simple series
Finite sums
Infinite geometric sums
Proofs













Week 4:  General topic: Counting
         Demos: Birthday paradox, coupon collector,
                Love machine

         Combinations and Permutations
         Balls into bins


Week 5:  General topic: Expectation
         Demos: carnival dice, random vs. nonrandom sequences

         Random variables
         Expectation - conditional, total, linearity, products, quotients


Week 6:  General topic: Graphs
         Demos: Die Hard 2, three friends or strangers among six people

         Induction on graphs
         Invariants


Week 7:  General topic: Counting/Probability
         Demos: Derangements, Triangular Duel

         Derangements
         Triangular Duel
         Numeracy


------------------ SPRING BREAK -----------------------------

Game theory - Many games

Harmonic series: Book-stacking, Desert Storm

Linear Recurrences - Hanoi, different variants
                   - Paper cutting with Fibonacci numbers
Pigeonhole Principle

Counting - Mind-reading trick
Probabilistic sums - Card trick with sums

Wald's theorem - Jenga blocks
Random walks
Gambler's ruin
