# Sets, Counting, and Probability

### Course Description

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.

All rights reserved to Prof. Paul Bamberg and Harvard University. If you enjoyed this free class, the Harvard Extension School offers a wide variety of courses in numerous fields. Check out http://www.extension.harvard.edu/
Paul G. Bamberg received an undergraduate degree in physics from Harvard and a doctorate in theoretical physics from Oxford. For 28 years, he taught premedical physics at Harvard College, the Extension School, and the Summer School. He helped develop the math and computer science curricula at the Extension School. Bamberg received the Extension School’s Petra T. Shattuck Excellence in Teaching Award and the Dean’s Distinguished Service Award.
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### Video Lectures & Study Materials

Visit the official course website for more study materials: http://www.extension.harvard.edu/open-learning-initiative/sets-counting-probability

# Lecture Play Lecture Notes & Slides Assignments
1 Probability, Intuition, and Axioms (1:58:41) Play Video
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2 Probability by Counting and Inclusion-Exclusion (1:55:13) Play Video
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3 Principles of Counting (1:51:03) Play Video
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4 Conditional Probability (1:47:48) Play Video
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5 Conditional Craps (59:10) Play Video
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6 Lying Witnesses and Simpson's Paradox (1:52:23) Play Video
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7 Random Variables & Distributions (2:00:55) Play Video
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8 Expectation I: Binomial Expectation & Variance (2:00:07) Play Video
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9 Expectation II: Infinite & Conditional Expectation (1:57:59) Play Video
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10 Geometric & Negative Hypergeometric Distributions (1:02:32) Play Video
11 Gambling: Random Walks & Gambler's Ruin (1:59:17) Play Video
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12 Expected Lead Time & Bijections between Paths (1:53:03) Play Video
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13 Variables: Independent, Uncorrelated, & Generating Functions (1:51:19) Play Video
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14 Basic Inequality, Markov's Inequality & Chebyshov's Inequality (1:54:09) Play Video
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15 Review and Questions #1-10 (1:26:50) Play Video
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