Machine learning is the science of getting computers to learn the hidden patterns from the massive size of data and it is the most important methodology run on computers for artificial intelligence. The theoretic core of the machine learning consists of three elements: the mathematics to characterize the hidden structures and relations of the data, the statistical learning theories to build the correct models and assessment tools, and lastly, the computational algorithms to practically solve the final numerical problems.

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.

This course will introduce the basic concepts of machine learning (supervision and unsupervised learning) and review the popular models used in machine learning and explain the underlying mathematical theories behind these models: linear regression, logistic regression, support vector machine, Gaussian process regression, model reduction, etc. Besides, this course also focuses on the neural network models. The machine learning algorithms such as unsupervised learning, stochastic gradient descent and deep learning techniques will be also an important part of this course. The examples of specific application will be given as exercises which require some programming work. During this course, the students are encouraged to apply the techniques to solve some realistic appreciations in the framework of Discovery & Innovation Curriculum. The students who complete this course are expected to be prepared for the modern development of more advanced machine learning theories and practical techniques.