This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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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

MATH 240 and MATH 241; or MATH 340 and MATH 341.

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