“Differential Geometry and Lie Groups: A Computational Perspective” by Jean Gallier and Jocelyn Quaintance is a relatively new book (2020) about differential geometry. It seems that this book is written for a audience including students especially in computer science (in its preface).
I’m an undergraduate in computer science, and I wish to self-study differential geometry recently. Modern pure mathematical differential geometry is good to me, but if some computational aspects are regarded then I’m more glad with that. A friend of mine mentioned this book to me, but its reviews are scarce. Can anyone compare this book to any classical textbook in differential geometry? The book claims it is geared towards majors including computer science, how exactly does it come across?
I’m new in differential geometry, so I have read questions “Teaching myself differential topology and differential geometry” and “Where to start learning Differential Geometry/Differential Topology?”, but I’m dazzled by tons of recommendations. It seems that the classical textbooks include:
- “Introduction to Smooth Manifolds” (2013) by John Marshall Lee.
- “Differential Geometry of Curves and Surfaces” (this seems to be outdated) or “Riemannian geometry” (1992) by Manfredo Perdigão do Carmo.
- “An Introduction to Manifolds” (2011) by Loring Wuliang Tu.
- “Manifolds and Differential Geometry” (2009) by Jeffrey Marc Lee.
- ... much more
Do I need to study (point-set) topology first before differential geometry? Furthermore, what do you mean by “classical” or “modern” in prefix of differential geometry? Does the “modern” part of differential geometry help in computer science? Also, differential geometry seems to have close relation to differential topology, is that insightful in computer science?
