Description

The course is a solid introduction to the formulation and manipulation of probability models, leading up to a rigorous proof of the law of large numbers and the central limit theorem. The emphasis is on concepts: sets and combinatorics allow a precise mathematical formulation of probability models, multivariable calculus supplies machinery for changing variables and calculating probabilities and average values relating to vectors of real-valued random variables, and limit theorems allow event-occurrences which are individually unpredictable to become predictable in the aggregate.

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH340, MATH241).

Level of Rigor

Advanced

Sample Textbooks

A First Course in Probability, by Sheldon Ross

Applications

If you like this course, you might also consider the following courses

Additional Notes

Crosslisted with SURV410

Students interested in grad school in AMSC should consider this course

Students interested in grad school in MATH should strongly consider this course

Students interested in grad school in STAT should strongly consider this course

Topics

Text of Ross, chapters 1-8 including:

Axioms of Probability and basic properties

Combinatorial problems

Conditional probability

Random variables and distributions in one and several variables, including change-of-variable techniques

Expectation and conditional expectation

Moments

Moment generating functions

Law of Large Numbers and Central Limit Theorem

Optional Topics from among:

Characteristic functions

Fourier transforms

Borel-Cantelli Lemma

Meaning of convergence with probability 1

Filling in missing steps of the book's proof of the Central Limit Theorem