This course introduces students to various topics in mathematical probability theory. Topics include basic concepts (such as probability, random variables, expectations, conditional probability) from a mathematical point of view, examples of distributions and stochastic processes and their properties, convergence results (such as the law of large numbers, central limit theorem, random series, etc.), various inequalities, and examples of applications of probabilistic ideas beyond statistics (for example, in geometry and computer science).
This course introduces students to various topics in mathematical probability theory. Topics include basic concepts (such as probability, random variables, expectations, conditional probability) from a mathematical point of view, examples of distributions and stochastic processes and their properties, convergence results (such as the law of large numbers, central limit theorem, random series, etc.), various inequalities, and examples of applications of probabilistic ideas beyond statistics (for example, in geometry and computer science).
