Geometric Methods and Applications: For Computer Science and Engineering

Rating:
Summary: Fantastic! One of a kind.
Review: This is a beautiful and unique book. The style is lively and the explanations are remarkably clear. The author makes a significant effort to demistify concepts before defining them rigorously and proving facts about them. It is impressive to see the variety of the topics covered in the book. For example, there is a nice and easy introduction to Lie groups and Lie algebras, and an exquisite treatment of the elementary differential geometry of curves and surfaces. As the author states, this material is a write-up of lectures given by the famous geometer Eugene Calabi (of the Calabi-Yau manifolds!), and this is quite a treat. Gallier's presentation definitely rivals do Carmo, one of the best. It is also refreshing and illuminating to see topics such as QR-decomposition and decomposition in terms of Householder matrices, treated from a geometric point of view. For that matter, the treatment of polar forms and SVD is superior, although perhaps a bit abstract for my taste. There are lots of problems, including programming projects. At first glance, the problems are on the hard side. This could turn off some students. In conclusion, this is a great book. Even though it is very well written, this is not an "easy book". However, perseverant readers will find its reading very rewarding. It is a great preparation for more advanced books on Lie groups, differential geometry, and projective and algebraic geometry. The sections on applications are very nice, but there should be more and they should be more extensive. Oh, I was forgetting, the internet supplement is great. For example, there is a wonderful treatment of rational curves and surfaces. Every geometry lover should have this book!