Visual Differential Geometry and Forms

“Finalist for the PROSE Award in Mathematics, Association of American Publishers”“Needham proposes to provide a truly geometric ‘visual’ explication of differential geometry, and he succeeds brilliantly. I know nothing like it in the literature.”—Frank Morgan, EMS Magazine”[The] book offers a truly unique and original take on differential geometry, and it amply deserves inclusion within the pantheon of textbook deities.”—Eric Poisson, Notices of the AMS“This is a valuable and beautifully created guide to what can at first seem a confusing area of mathematical physics. There are other contenders that try to teach this subject, but this is the best that I have come across so far and I will continue to enjoy learning from it (and almost certainly teaching from it) over the coming years, I am sure.”—Jonathan Shock, Mathemafrica”[Proactively] rethinks the way this important area of mathematics should be considered and taught.” * MathSciNet *“The book is a remarkable and highly original approach to the basic stem of differential geometry. And that mathematical trunk has roots and branches in so many other unexpected yet related subjects, each of which can be equally well approached from the same geometrical point of view.”—Adhemar Bultheel, MAA Reviews”[Visual Differential Geometry and Forms] is a book that stands out among its peers. It is fun to read and provides a unique and intuitive approach to differential geometry. The author’s passion for the subject is evident throughout the book. Although Needham’s approach is unorthodox, it is rewarding, and complements the exposition found in standard textbooks.”—Sean M. Eli & Krešmir Josić, SIAM Review

Tristan Needham is professor of mathematics at the University of San Francisco. He is the author of Visual Complex Analysis.