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A course of differential geometry and topology Aleksandr Sergeevich Mishchenko, A. Fomenko
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"This is a carefully written and wide-ranging textbook suitable mainly for graduate courses, although some advanced undergraduate courses may benefit from the early chapters. The book requires some very basic. But it's very short, very terse, and it has no exercises. Would it be better to do Topology and Differential Geometry in Maths, than to do undergraduate GR which would probably have less advanced Maths than the Differential Geometry course? It actually introduces point-set, algebraic, and differential topology as well as some differential geometry. Many of the basic notions used in analysis courses are described in n lab in the more general topological context if they belong there, e.g. I would really advise students to take courses in algebraic topology, differential geometry and so on. Below I list some such recent breakthroughs. Amazon.com: Basic Elements of Differential Geometry and Topology. Compact space, continuous map, compact-open topology and so on. Free Mathematics Video Courses (Includes discrete mathematics, algebra, linear algebra, mathematics problems, differential equations, math methods for engineers); More Mathematics and Theoretical Computer and chaos, computer musings (by Knuth) and other Donald E. 133 Algebraic Geometry: A First Course, Joe Harris 47 Geometric Topology in Dimensions 2 and 3, Edwin E. Many of the aspects of For example the synthetic differential geometry of Lawvere and Kock (more in next paragraph) and the nonstandard analysis of Robinson, and its variant, internal set theory of Nelson are some of the principal examples.