This first volume of a three-part series introduces modern geometry, focusing on its applications in mathematics and theoretical physics. It covers tensors, differential calculus, and geometric field theory, presented in clear language suitable for physicists. The second edition features significant revisions.
This book discusses the evolution of university-level geometry education, highlighting the shift from classical differential geometry to the inclusion of Riemannian geometry and topology. It outlines the development of a modernized curriculum at Moscow State University, emphasizing essential topics like tensor theory and geodesics for practical applications in mathematics.
Fomenko's work emphasizes the importance of visualization in understanding geometry and topology, highlighting how visual representations can illuminate complex mathematical concepts. The book progresses from classical topology to modern advancements in Hamiltonian geometry, focusing on intuitive explanations rather than abstract calculations. It features numerous illustrations created by the author, which serve to clarify mathematical ideas and methods. This accessible narrative is designed to engage not only mathematicians but also students and professionals from natural sciences and the arts.