The course will explore mathematics underlying the practice and theory of various machine learning concepts and algorithms. Kernel methods, deep learning, reinforcement learning, generalization error, stochastic gradient descent, and dimension reduction or data embeddings will be introduced. The interplay between the mathematics and real applications will be a component of the course. Students can take both this course and Mathematics 465 for credit. Recommended prerequisite: Mathematics 230/340 and 218/216/221 and some familiarity with programing, preferably Python.