This will be an introductory course on Probability Theory, with an emphasis on discrete probability. We will cover the basic formalisms of probability, discrete and continuous distributions, combinatorial methods, generating functions, conditioning, Law of Large Numbers and Central Limit Theorem. The latter part of the course will introduce the theory of stochastic processes including random walks, Poisson process and Brownian motion. Applications to Biology, Computer Science, Economics, Engineering, and Physics will be discussed as examples.
David F. Anderson, Timo Seppalainen, Benedek Valko, Introduction to Probability Cambridge Mathematical Textbooks