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Other titles in the Graduate Texts in Mathematics series:
Graduate Texts in Mathematics #0153: Algebraic Topology: A First Courseby William Fulton
Synopses & ReviewsPublisher Comments:Reformer, rancher, conservationist, hunter, historian, police commissioner, soldier, the youngest man ever to serve as president of the United Statesno other American public figure has led as vigorous and varied a life as Theodore Roosevelt. This volume brings together two fascinating autobiographical works. The Rough Riders (1899) is the story of the 1st U.S. Volunteer Cavalry, the regiment Roosevelt led to enduring fame during the SpanishAmerican War. With his characteristic elan Roosevelt recounts how these grim hunters of the mountains, these wild rough riders of the plains, endured the heat, hunger, rain, mud, and malaria of the Cuban campaign to charge triumphantly up the San Juan Heights during the Battle of Santiago. In An Autobiography (1913), Roosevelt describes his life in politics and the emergence of his progressive ideas. Surveying his career as a state legislator, civil service reformer, New York City police commissioner, assistant secretary of the navy, governor, and president, Roosevelt writes of his battles against corruption, his role in establishing America as a world power, his passionate commitment to conservation, and his growing conviction that only a strong national government and an energetic presidency could protect the public against the rapacious greed of modern corporations.
Synopsis:This book introduces the important ideas of algebraic topology by emphasizing the relation of these ideas with other areas of mathematics. Rather than choosing one point of view of modern topology (homotropy theory, axiomatic homology, or differential topology, say) the author concentrates on concrete problems in spaces with a few dimensions, introducing only as much algebraic machinery as necessary for the problems encountered. This makes it possible to see a wider variety of important features in the subject than is common in introductory texts; it is also in harmony with the historical development of the subject. The book is aimed at students who do not necessarily intend on specializing in algebraic topology.
Table of Contentsx Introduction x Part I: Calculus in the Plane x Path Integrals x Angles and Deformations x Part II: Winding Numbers x The Winding Number x Applications of Winding Numbers x Part III: Cohomology and Homology, I x De Rham Cohomology and the Jordan Curve Theorem x Homology x Part IV: Vector Fields x Indices of Vector Fields x Vector Fields on Surfaces x Part V: Cohomology and Homology, II x Holes and Integrals x MayerVietoris x Part VI: Covering Spaces and Fundamental Groups, I x Covering Spaces x The Fundamental Group x Part VII: Covering Spaces and Fundamental Groups, II x The Fundamental Group and Covering Spaces x The Van Kampen Theorem x Part VIII: Cohomology and Homology, III x Cohomology x Variations x Part IX: Topology of Surfaces x The Topology of Surfaces x Cohomology of Surfaces x Part X: Riemann Surfaces x Riemann Surfaces x Riemann Surfaces and Algebraic Curves x The RiemannRoch Theorem x Part XI: Higher Dimensions x Toward Higher Dimensions x Higher Homology x Duality x Appendices: x A. Point Set Theory x B. Analysis x C. Algebra x D. On Surfaces x E. Proof of Borsuk's Theorem x Hints and Answers x References What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
Other books you might likeRelated SubjectsScience and Mathematics » Mathematics » Algebra » General Science and Mathematics » Mathematics » Differential Equations Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry Science and Mathematics » Mathematics » History Science and Mathematics » Mathematics » Topology 

