# epub Topology from the Differentiable Viewpoint (Princeton Landmarks in Mathematics and Physics) Author John Milnor – Andy-palmer.co.uk

My boyfriend bought this book for his favorite class in college The condition of the book is great, Of course, it s brand new and I think he really love the contents and I think it s interesting too, through his explanation. This Elegant Book By Distinguished Mathematician John Milnor, Provides A Clear And Succinct Introduction To One Of The Most Important Subjects In Modern Mathematics Beginning With Basic Concepts Such As Diffeomorphisms And Smooth Manifolds, He Goes On To Examine Tangent Spaces, Oriented Manifolds, And Vector Fields Key Concepts Such As Homotopy, The Index Number Of A Map, And The Pontryagin Construction Are Discussed The Author Presents Proofs Of Sard S Theorem And The Hopf Theorem Very interesting little book. Milnor s Topology from the Differentiable Viewpoint is a brief sketch of differential topology, well written, as are all books by Milnor, with clear, concise explanations For students who wish to learn the subject, it should be read as a companion to a substantive text, such as Guillemin Differential Topologyor Hirsch sDifferential Topology, as too much of the material is left out for this to be adequate as a textbook OTOH, it does make for good bedtime reading.While this book is highly regarded among mathematicians, it is not without its faults, namely, it fails to cover many topics of importance, such as transversality only mentioned in an exercise , embeddings, differential forms, integration, Morse theory, and the intersection form it only cites some theorems without proving them, or it leaves the proofs to the reader it offers proofs of many theorems that are really only sketches without all the details manifolds are only defined as subsets of Euclidean spaces there is only 1 collection of 17 problems at the end of the book, which are used to introduce important concepts and it probably moves too quickly for true beginners, packing a lot into only 51 pages.So don t buy this as your only, or even first, book on differential topology Oddly, many of the faults that I listed above are simultaneously strengths, in that it can be read very quickly, with relatively little effort and a high rate of retention Milnor really emphasizes the topology of the subject, giving applications such as the fundamental theorem of algebra, Brouwer s fixed point theorem, the hairy ball theorem, the Poincare Hopf theorem, and Hopf s theorem Most of the book focuses on degree theory, but there is also a nice introduction to framed cobordism, which is rare for an elementary book Guillemin Pollack s book was based in large part on this one, and could be read together, with G P giving elementary explanations and additional topics, while Milnor s book provides a proof of the Sard theorem and the Pontrjagin Thom construction The exercises, though not particularly difficult, do provide a good opportunity to practice proving theorems in the subject, as there are no hints for them, as one would find in many other differential topology books, and they are not separated by chapter. An excellent accompaniment to the vid.eo lectures available on linbe To find them simply Google John Milnpr, diffddrential gopology lectures, a sdries of three 60 90 minute lectures. This is a fantastic book on intro to differential topology Milnor is amazing.