#### Study at Harvard this summer

Harvard Summer School courses are open for registration through May 19.

This online math course develops the mathematics needed to formulate and analyze probability models for idealized situations drawn from everyday life. Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy, national security, and theology. The emphasis is on careful application of basic principles rather than on memorizing and using formulas.

The Quicktime and MP3 formats are available for download, or you can play the Flash version directly. Each lecture is two hours.

- Video/Audio
- Probability by Symmetry; Probability by Experiment; Payoffs and Probability; Fair Price and Probability; Notation to Combine Sets; Venn Diagrams; Events and Sample Spaces; Event Spaces; Addition of Probabilities; Probability Functions; Inclusion-Exclusion Rule; Many Ways to Skin a Cat

- Class Materials

- Video/Audio
- Review of the Basics; DeMorgan's Laws; Inclusion-Exclusion; Cups and Saucers; Cups and Saucers # 2; Urns; Family Planning; Twenty-first-Century Sheherezade; Craps; Achilles Rolls of a 6

- Class Materials

- Video/Audio
- Count A Cartesian Product; The Binomial Theorem; Counting Poker Hands; Counting Bridge Hands; The Munchkin Problem; Genoese Lottery; Counting Suit Patterns; Negative Binomial Theorem; Count by Inclusion-Exclusion

- Class Materials

- Video/Audio
- St. Paul at Lystra; Conditional Four Aces; Conditional Probability; Independence of Events; Complimentary Events; The Bearded Man Problem; Lemons; Two Useful Theorems; Conditional Munchkins; Monty Hall Problem; Random Desserts

- Class Materials

- Video/Audio
- Independence of 3 Events; Compound Experiments; Accidental Independence; Sudden Death; Sampling Paradox

- Class Materials

- Video/Audio
- Wisdom of Solomon; Eddington's Controversy; Affirmative Action; Simpson's Paradox

- Video/Audio
- Discrete Random Variables; Event Space for a DRV; Bridge and Poker; Binomial Distribution; Geometric Distribution; Negative Binomial Distribution; Exponential Function; Poisson Distribution; Distribution Function; Distribution Examples; Function of Random Var; First Computer Project

- Class Materials

- Video/Audio
- Unconscious Statistician; Properties of Expectation; Binomial Expectation; Tail-Sum Theorem; Geometric Tail-Sum; Negative Binomial Expectation; Coupons Problem; Variance; Telescoping Series; Convergence

- Class Materials

- Video/Audio
- Infinite Expectation; Royal Oak Lottery; Poisson as Limit; Conditional Random Var; Conditional Expectation; Runs of Heads and Tails; Two Wins Takes All

- Class Materials

- Video/Audio

- Video/Audio
- Casino Night; Random Walk Examples; Random Walk Terminology; Gambler's Ruin; Ruin in Fair Casino; Time until Win or Ruin; A Fair Game; Walk as a Random Variable; Ballot Theorem; Hitting Time Theorem; Expected Lead Times

- Class Materials

- Video/Audio
- Another Bijection; Last Visit to Origin; First Visit to Final; First Visit to Max; First Return; Returning Just Once; Strange but True

- Video/Audio
- First Visit to Max; Sojourn Times; Independent Variables; Uncorrelated Variables: A Counterexample; Generating Function; Product of Gen Functions; A Simple Example; Gen Function for 2 Dice; Clever Loaded Dice; Well-Known Distributions

- Class Materials

- Video/Audio
- Basic Inequality; Markov's Inequality; Chebyshov's Inequality; Weak Law of Large Numbers; Weak Law, continued; Strong Law of Large Numbers

- Class Materials

- Video/Audio

If you enjoyed this free class, the Harvard Extension School offers a wide variety of courses in numerous fields. Search for classes and enroll for credit during the fall and spring registration periods.