Math 543: Advanced Probability 1
Advanced Probability 1.
Math 314 or equivalent.
Math 341, Stat 441(?); or equivalents.
Foundations of the modern theory of probability with applications. Probability spaces, random variables, independence, conditioning, expectation, generating functions, and Markov chains.
Desired Learning Outcomes
This should be an advanced course in probability and,therefore, clearly distinguishable from an introductory course like Math 431. Furthermore, it is supposed to be a course in the modern theory of probability, which suggests that it should be based on Kolmogorov's measure-theoretic approach, or something equivalent.
The official prerequisite is multivariable calculus. Other prior courses that will contribute to student success include:
- an introductory course in probability;
- a course in rigorous mathematical reasoning;
- an introductory course in analysis.