This elective course is to provide the elementary mathematical and numerical theories relevant to the machine learning for data sciences. The basic knowledge of linear algebra, probability theory and statistical models is required and the familiarity of basic numerical methods and one programming language (Python or R or MATLAB or C or SAS, etc) is also preferred or required. The course will discuss fundamental rules, major classes of models, and principles of standard numerical methods. There will be a careful balance between heuristic vs rigorous, simple vs general. The perspective is from the applied and computational mathematics rather than an attitude of “alchemy”. This course is a highly integrated undergraduate course for computational math major and it has a wide spectrum in various math knowledge and computational techniques. It can be also a companion theoretic course to a hands-on-experience-oriented machine learning course, for engineering major students with an exceptional math background.