Modern Geometry: Methods and Applications (First Volume) Geometric Surfaces, Transformation Groups, and Fields (Fifth Edition)

Author: (Russia) Dubrovink, (Russia) Novikov, (Russia) Fominko, translated by Xu Ming
Publisher:
Publish Date: 2006-06-16
Features: This book is the result of the modernization reform of the geometry course at the Department of Mathematics and Mechanics of Moscow State University. Novikov, one of the authors, is a recipient of the Fields Medal in 1970 and the Wolf Prize in 2005. The book strives to explain the material from an intuitive and physical perspective, making it a rare and excellent resource on modern geometry. It covers topics such as tensor analysis, geometry of curves and surfaces, one-dimensional and multidimensional variational methods (Volume), the topology and geometry of smooth manifolds (Volume 2), and homology and cohomology theory (Volume 3). This book can be used as a teaching text for senior undergraduate and graduate students in mathematics and theoretical physics, and is also highly valuable for researchers working in geometry and topology.