Math 20
Discrete Probability
Last updated April 10, 2014

## Syllabus

The following is a tentative schedule for the course.

Dates Sections in Text Brief Description Materials
3/24 1.1-1.2 Probability: mathematics and empiricism R code for deMere
3/26 1.2 Measures, Axioms and Distributions Worksheet
3/27 n/a Introduction to R R as a calculator, Intro workshop
3/28 1.2, 3.1 More measures, intro to counting Polya Urn model
3/31 3.1 Counting and Permutations fixedPoints.R
4/2 3.1,3.2 Combinations
4/3 R programs Tossing coins and Polya's urn Templates: coinTosses.R, polyaUrn.R
4/4 3.2 Binomial distribution, inclusion-exclusion Worksheet
4/7 4.1 Conditional probability
4/9 4.1 Independence Worksheet, solutions
4/10 R Programs Gambler's ruin Template: gamblersRuin.R
4/7 - 4/11 4.1-4.3 Conditional probability and paradoxes
4/14 6.1 Expected value
4/16 6.1 More expected value
4/18 6.2 Variance
4/21 5.1 Uniform, binomial and geometric distributions Worksheet
4/23 5.1 Poisson, negative binomial and hypergeometric distributions Worksheet
4/25 8.1 Coupon collector, Markov and Chebyshev inequalities Worksheet
4/28 - 5/2 8.1 Law of large numbers
4/30 - 5/2 2.2,5.2 Continuous probability and the law of large numbers
5/5 - 5/9 9.1,9.2 The central limit theorem
5/12 - 5/16 11.1,11.3,11.4 Ergodic Markov chains
5/19 - 5/23 11.2 and more Absorbing Markov chains
5/28   Review