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Topology from the Differentiable Viewpoint

1997-12-14 Mathematics
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Release : 1997-12-14
Genre : Mathematics
Kind : eBook
Book Rating : 338/5 ( reviews)

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Book Synopsis Topology from the Differentiable Viewpoint by : John Willard Milnor

Download or read book Topology from the Differentiable Viewpoint written by John Willard Milnor. This book was released on 1997-12-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Differential Topology

2010 Mathematics
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Release : 2010
Genre : Mathematics
Kind : eBook
Book Rating : 934/5 ( reviews)

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Book Synopsis Differential Topology by : Victor Guillemin

Download or read book Differential Topology written by Victor Guillemin. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.

Geometry from a Differentiable Viewpoint

2013 Mathematics
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Release : 2013
Genre : Mathematics
Kind : eBook
Book Rating : 074/5 ( reviews)

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Book Synopsis Geometry from a Differentiable Viewpoint by : John McCleary

Download or read book Geometry from a Differentiable Viewpoint written by John McCleary. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.

Differential Topology

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 49X/5 ( reviews)

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Book Synopsis Differential Topology by : Morris W. Hirsch

Download or read book Differential Topology written by Morris W. Hirsch. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: "A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS

Introduction to Differential Topology

1982-09-16 Mathematics
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Release : 1982-09-16
Genre : Mathematics
Kind : eBook
Book Rating : 707/5 ( reviews)

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Book Synopsis Introduction to Differential Topology by : Theodor Bröcker

Download or read book Introduction to Differential Topology written by Theodor Bröcker. This book was released on 1982-09-16. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an elementary introduction to differential manifolds. The authors concentrate on the intuitive geometric aspects and explain not only the basic properties but also teach how to do the basic geometrical constructions. An integral part of the work are the many diagrams which illustrate the proofs. The text is liberally supplied with exercises and will be welcomed by students with some basic knowledge of analysis and topology.

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