The course introduces mathematical foundations underlying modern algorithms for regression, classification, clustering, and dimension reduction in data-rich settings. These mathematical tools, needed to understand machine learning algorithms, are traditionally taught in disparate courses, making it hard for ML students to efficiently learn them. The course bridges a gap between mathematical and machine learning courses, introducing the mathematical concepts with a minimum of prerequisites and in the context of machine learning and data science applications. The goal is to build intuition into these mathematical concepts and practical experience with applying them. Numerical computations and applications with real data will accompany the theory. This course is meant to complement application-oriented machine learning and data science courses.