Content
Course Description:
Our capacity to fathom the world around us hinges on our ability to understand inherently unpredictable quantities. To gain more accurate mathematical models of the natural world, we therefore must incorporate probability into the mix. This course will serve as an introduction to the foundations of probability theory.
Tentative Syllabus:
- Week 1: Discrete Probability Distributions
- Week 2: Continuous Probability Densities
- Week 3: Combinatorics
- Week 4: Conditional Probability
- Week 5: Midterm exam
- Week 6: Distributions and Densities
- Week 7: Expected Value and Variance
- Week 8: Sums of Random Variables
- Week 9: Law of Large Numbers
- Week 10: Central Limit Theorem
Textbook:
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Introduction to Probability (2nd edition) by Charles M. Grinstead and J. Laurie Snell, 1997, American Mathematical Society.
(The course will be primarily based on this textbook, which is freely available at https://chance.dartmouth.edu.) -
Introduction to Probability (2nd edition) by D. Bertsekas and J. Tsitsiklis, 2008, Athena Scientic.
(You might want to use this book as additional reading material. It contains many illustrative examples.)