Differential Geometry and Lie Groups

This textbook set offers both an introduction to differential geometry designed for readers interested in modern geometry processing, as well as an exploration of more advanced topics. In the first volume, the authors work from basic undergraduate prerequisites to develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. The second volume then uses analytic and algebraic perspectives to augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications.The first volume, Differential Geometry and Lie Groups: A Computational Perspective, offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed.Volume two, Differential Geometry and Lie Groups: A Second Course, captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. As with the first, this volume is suitable for both classroom use and independent study.