MATH 309 - Theory of Probability
MATH 309 covers the following topics: Probabilities of events on discrete and continuous sample spaces; random variables and probability distributions; joint and conditional probability distribution; expectations; transformations; Markov & Chebyshev`s Inequalities; law of large numbers and central limit theorem. The theory is applied to problems in physical and biological sciences. The course mixes discrete and continuous mathematics. A key concept in probability is conditioning - how partial knowledge changes how one thinks about a problem. The technique of conditioning will be used throughout the course to solve interesting problems in probability and expectation.
Prerequisites: MATH 023 or MATH 033 or MATH 052
Why is it interesting for Probabilistic Modelers?
Probability courses teach students how to think systematically and mathematically about uncertainty and randomness. Students learn that rigorous and logical reasoning is essential to read, model and analyze stochastic problems. They experience the use of a simple axiomatic system in working with probability defined on properly constructed sample spaces. They learn combinatorial reasoning in working with discrete sample spaces. A probability course builds students’ skill in looking for multiple strategies for solving a stochastic problem. It encourages better understanding of the role of modeling in applied mathematics, and leads to some degree of comfort in incorporating the role of risk when modeling real-life applications.
Offered every Fall Semester.