Mathematical understanding of uncertainty

The first part of the series (three weeks) discusses the basics of probability theory such as the mathematical formulation of probability, random variables, expectation, and variance in a creative way as a means to quantify uncertainty. The second part of the series (five weeks) introduces a few universal principles of probability theory. Standard theorems in probability theory such as the law of large numbers and the central limit theorems are introduced as fundamental examples of universal principles, and hence, are discussed from a unique perspective. These universal principles are used to explain uncertainty in the real-world, and numerous interesting examples are introduced for illustration. The third part of the series (four weeks) introduces the concept of Markov chain and then discusses various randomized algorithms as examples of Markov chains. For example, riffle shuffle of playing cards, Markov chain Monte Carlo, and deep learning algorithms are discussed based on the modern theory of Markov chains. The lecture series requires knowledge of calculus, but knowledge of higher mathematics and probability is not a pre-requisite.

• - Basic probability theory including random variable, expectation, and variance- Universal principles in probability theory such as law of large numbers, central limit theorem, and large deviation principles, and their applications - Heavy-tailed phenomenon- Theory random processes and applications to real world problem- Theory of Markov chains and applications to simulation, randomization, and deep learning.