As an introduction to probability theory, Math 531 serves as a higher-level alternative to Math/Stat 431. Math 531 is also recommended to students who have completed Math/Stat 431, Stat 309 or Stat 311 and are interested in learning probability in a deeper way.
The course is aimed at math majors and Master’s degree students, or students in other fields who will need probability in their future careers. It might be useful for graduate students in other fields (e.g. engineering) who need a rigorous introduction to probability, but may not be ready for the graduate probability course. It could also provide a stepping stone for students interested in taking Math 632: Introduction to Stochastic Processes.
Math 632, 635, and more
The course is a rigorous introduction to probability theory on an advanced undergraduate level. Only a minimal amount of measure theory is used (in particular, Lebesgue integrals will not be needed). The course gives an introduction to the basics (Kolmogorov axioms, conditional probability and independence, random variables, expectation) and discusses some of the classical results of probability theory with proofs (DeMoivre-Laplace limit theorems, the study of simple random walk on Z, applications of generating functions).