Mathematics for Machine Learning: A Bridge Course

We present Mathematics for Machine Learning, a one-semester mathematics course designed to strengthen students' foundations before further study and research in machine learning (ML) and data science. Oftentimes, the mathematical prerequisites needed for serious study of ML are taught in a disjointed manner. Our course is designed to bridge this gap and provide emphasis on concepts heavily employed in modern ML, such as spectral analysis in linear algebra or convex optimization in calculus. We structured our course around the three "pillars'' of math that underlie much of modern ML: (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, providing a consistent anchoring narrative and constant motivation for mathematical ideas.