We present Mathematics for Machine Learning, a one-semester mathematics course designed to strengthen students’ mathematical foundations before further rigorous study and research in machine learning and data science. Oftentimes, the mathematical prerequisites needed for serious study of machine learning are taught in a disjointed manner without focus towards the specific concepts heavily used in the field. Our course is designed to bridge this gap and provide greater emphasis on the concepts heavily employed in modern machine learning, such as spectral analysis in linear algebra or convex optimization in calculus. We structured our course around the three “pillars” of mathematics that underlie much of modern machine learning: (i) linear algebra, (ii) calculus and optimization, and (iii) probability and statistics. Weaving each of these together is a central story — all concepts, ideas, and proofs are introduced relative to two ubiquitous concepts in machine learning: least squares regression and gradient descent. By revolving the course around least squares and gradient descent, we provide students with a consistent anchoring narrative, constant motivation for key ideas in each of the three mathematical areas, and greater depth than introductory courses. All the while, least squares and gradient descent provide a motivating preview and gentle “on-ramp” towards a serious graduate-level course in machine learning.