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Math E-102 - Sets, Counting, and Probability (Fall 2005, Harvard Extension School). Instructor: Professor Paul G. Bamberg.
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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.
Course content
- Lecture 01 – Probability, Intuition, and Axioms Unlimited
- Lecture 02 – Probability by Counting and Inclusion-Exclusion Unlimited
- Lecture 03 – Principles of Counting Unlimited
- Lecture 04 – Conditional Probability Unlimited
- Lecture 05 – Conditional Craps Unlimited
- Lecture 06 – Lying Witnesses and Simpson’s Paradox Unlimited
- Lecture 07 – Random Variables Unlimited
- Lecture 08 – Expectation I Unlimited
- Lecture 09 – Expectation II Unlimited
- Lecture 10 – Tartan Dice; Terminated Geometric; Coin Tossing Unlimited
- Lecture 11 – Gambling Unlimited
- Lecture 12 – Expected Lead Time; Bijections Between Paths Unlimited
- Lecture 13 – Variables Unlimited
- Lecture 14 – Inequality Unlimited
- Lecture 15 – Questions Unlimited
Instructor
