By John Willard Milnor

This dependent e-book via amazing mathematician John Milnor, offers a transparent and succinct advent to at least one of crucial topics in sleek arithmetic. starting with simple thoughts corresponding to diffeomorphisms and tender manifolds, he is going directly to research tangent areas, orientated manifolds, and vector fields. Key recommendations similar to homotopy, the index variety of a map, and the Pontryagin development are mentioned. the writer provides proofs of Sard's theorem and the Hopf theorem.