The lectures will focus on an introduction of modern data science techniques and the foundational mathematical concepts in linear algebra, probability, and basic optimization related with these techniques. Sufficient case studies with real-world data sets will be provided to illustrate how to use the learned techniques and how to choose an appropriate model.
This course is a mathematical introduction to probability theory, covering random variables, moments, multivariate distributions, law of large numbers, central limit theorem, and large deviations.
Introduction to probability, probability distributions, point estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance.
This course will cover important topics in linear algebra not usually discussed in a first-semester course, featuring a mixture of theory and applications.
Mathematical logic and proof, mathematical induction, counting methods, recurrence relations, algorithms and complexity, graph theory and graph algorithms.