Linear Algebra, Data Science, and Machine Learning

Jeff Calder received his Ph.D. degree in applied and interdisciplinary mathematics from the University of Michigan under the guidance of Prof. Selim Esedoglu and Prof. Alfred Hero in 2014. Between 2014 and 2016 he was a Morrey Assistant Professor at the University of California, Berkeley, under the mentorship of Lawrence C. Evans and James Sethian. He has been on the faculty of the School of Mathematics at the University of Minnesota since 2016, full professor since 2025, where he has supervised 5 PhD students, 4 postdoctoral scholars, and a number of undergraduate and high school students on research projects. Calder's research interests lie in applied probability, numerical analysis, and partial differential equations, with a specific interest in applications to machine learning and data analysis. Calder has published over 50 articles in journals and conferences spanning pure and applied mathematics and related areas, and holds several patents. His research has been recognized with an NSF Career Award and Alfred P. Sloan Research Fellowship in 2020, a University of Minnesota McKnight Presidential Fellowship and Guillermo E. Borja Award in 2021, and he currently holds the Albert and Dorothy Marden Professorship in Mathematics (2023-2028).Peter J. Olver received his Ph.D. from Harvard University in 1976 under the guidance of Prof. Garrett Birkhoff.  After being a Dickson Instructor at the University of Chicago and a postdoc at the University of Oxford, he has been on the faculty of the School of Mathematics at the University of Minnesota since 1980, and a full professor since 1985.  He served as the Head of the Department from 2008 to 2020.  He has supervised 23 Ph.D. students, and mentored over 30 postdocs, visiting students and scholars from around the world, as well as supervising numerous undergraduate research projects.  He is a Fellow of the American Mathematical Society, the Society for Industrial and Applied Mathematics (SIAM), the Institute of Physics, UK, and the Asia-Pacific Artificial Intelligence Association (AAIA).   Over the years, he has contributed to a wide range of fields, including symmetry and Lie theory, partial differential equations, the calculus of variations, mathematical physics, fluid mechanics, elasticity, quantum mechanics, Hamiltonian mechanics, geometric numerical methods, differential geometry, classical invariant theory, algebra, computer vision and image processing, anthropology, and beyond. He is the author of over 160 papers in refereed journals, and has given more than 500 invited lectures on his research at conferences, universities, colleges, and institutes throughout the world.  He was named a "Highly Cited Researcher” by Thomson-ISI in 2003, and an inaugural "Highly Ranked Scholar" by ScholarGPS in 2024..  He has written 6 books, including the definitive text on Applications of Lie Groups to Differential Equations, and two additional undergraduate texts: Partial Differential Equations and Applied Linear Algebra, the latter coauthored with his wife, Chehrzad Shakiban.

• Preface.- 1 Vectors.- 2 Inner Product, Orthogonality, Norm.- 3 Matrices.- 4. How Matrices Interact with Inner Products and Norms.- 5 Eigenvalues and Singular Values.- 6 Basics of Optimization.- 7 Introduction to Machine Learning and Data.- 8 Principal Component Analysis.- 9 Graph Theory and Graph-based Learning.- 10 Neural Networks and Deep Learning.- 11 Advanced Optimization.- Bibliography.- Index.