The definition of “data science” is nebulous, with experts from various scientific fields claiming the name for almost anything involving statistics, machine learning, scalable algorithms for mining large data sets, or new sources of large-scale data such as modern telescopes or DNA sequencers. But almost any definition is grounded in numerical computing; and work in data science, broadly construed, is driving research in numerical methods design in new and interesting directions. These courses, and a book-in-progress, reflect how my thinking about numerical methods has evolved over the past decade from working on a variety of data science and machine learning problems. Starting from a foundation of numerical linear algebra, statistical computing, optimization, and function approximation, we proceed to explore applications of these ideas near the research frontiers in network analysis, topic modeling, large-scale regression, and modeling of dynamics from data.