This course aims to equip the students with fundamental mathematical tools frequently used in data science and prepare them for more advanced study in various directions of data science. It is designed for students who have basic knowledge of linear algebra, calculus, and probability (e.g., undergraduate courses in these topics) and would like later to pursue an in-depth investigation of data science. For this goal, the course will cover fundamental mathematical tools for data science and focus particularly on their connections to data science. Topics include basic concepts in probability/statistics, linear algebra, and optimization, such as MLE/MAP, elementary information theory, concentration, spectral decomposition, convexity, gradient descent, etc. These are illustrated with the corresponding examples in data science, such as statistical learning, PCA, SGD on empirical loss, etc.
Basic knowledge of linear algebra, calculus, and probability (e.g., undergraduate courses in these topics) is recommended. The course is open to beginning graduates with the required math background.
There are no required textbooks. We will organize and maintain resources, references, and material on the course website. There are no required textbooks. But the following books are good references: