This course is designed primarily for Mathematical Sciences majors and those interested in the deeper mathematical issues underlying probability theory. The purpose of this course is twofold: (1) To introduce fundamental ideas and methods of mathematics using the study of probability as the vehicle. These ideas and methods will include systematic theorem-proof development starting with basic axioms; mathematical induction; set theory; applications of univariate and multivariate calculus. (2) To introduce the student to probability. Topics to be covered will be chosen from: axiomatic development of probability; independence; Bayes theorem; discrete and continuous random variables; expectation; special distributions including the binomial and normal; moment generating functions; multivariate distributions; conditional and marginal distributions; independence of random variables; transformations of random variables; limit theorems. A more applications-oriented course with similar content is MA 2621 Probability for Applications which is primarily designed for students in departments other than Mathematical Sciences.
Credit may not be earned both for this course and for MA 2621.
Multivariable Differential and Integral Calculus (MA 1024, or equivalent).