An introduction to the mathematical treatment of random phenomena occurring in the natural, physical, and social sciences.
Axioms of mathematical probability, combinatorial analysis, binomial distribution, Poisson and normal approximation,
random variables and probability distributions, generating functions, Markov chains, applications.
A first course in probability, by Sheldon Ross.
This course is intended for math majors and other students with a strong interest in mathematics. It requires fluency in calculus topics such as series, derivatives, (multi-variable) integration.
It makes sense to look through the textbook in advance to know what to expect.
Problem sets will be posted online. Solutions are usually to be submitted for grading every week. Late homework will not be accepted.
Two midterm exams and the final exam are in-class and closed book.
Two lowest weekly
homework scores will be dropped. The total homework score counts for 30% of the course grade. Each midterm counts for 15% of the course grade. The final exam counts for 40% of the course grade.
The semester begins on Thursday Sep 2, so no classes in the first week
Labor Day, no class
Introduction, some combinatorics. Reading: Sections 1.1, 1.2, 1.3, 1.4
More combinatorics. Sample space and events. Reading: Sections 1.5, 2.1, 2.2
Axioms of probability, inclusion-exclusion formula. Reading: Sections 2.3, 2.4
Some probability distributions on finite sets. Reading: Sections 2.4, 2.5