{"product_id":"a-combinatorial-introduction-to-topology-revised-dover-books-on-mathematics","title":"A Combinatorial Introduction to Topology (Revised) (Dover Books on Mathematics)","description":"\n\u003ctable align=\"center\" border=\"0\" cellpadding=\"2\" cellspacing=\"0\" width=\"100%\"\u003e\n\u003ctr\u003e\n\u003ctd class=\"productDetailSmallElements\"\u003e\n\u003cp\u003e\n\u003cstrong\u003eMarc Notes\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tOriginally published: San Franciso: W.H. Freeman, 1979.;Includes bibliographical references (p. [303]-304) and index.\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eTable of Contents\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tChapter One Basic Concepts \n\u003cbr\u003e1 The Combinatorial Method \n\u003cbr\u003e2 Continuous Transformations in the Plane \n\u003cbr\u003e3 Compactness and Connectedness \n\u003cbr\u003e4 Abstract Point Set Topology \n\u003cbr\u003eChapter Two Vector Fields \n\u003cbr\u003e5 A Link Between Analysis and Topology \n\u003cbr\u003e6 Sperner's Lemma and the Brouwer Fixed Point Theorem \n\u003cbr\u003e7 Phase Portraits and the Index Lemma \n\u003cbr\u003e8 Winding Numbers \n\u003cbr\u003e9 Isolated Critical Points \n\u003cbr\u003e10 The Poincaré Index Theorem \n\u003cbr\u003e11 Closed Integral Paths \n\u003cbr\u003e12 Further Results and Applications \n\u003cbr\u003eChapter Three Plane Homology and Jordan Curve Theorem \n\u003cbr\u003e13 Polygonal Chains \n\u003cbr\u003e14 The Algebra of Chains on a Grating \n\u003cbr\u003e15 The Boundary Operator \n\u003cbr\u003e16 The Fundamental Lemma \n\u003cbr\u003e17 Alexander's Lemma \n\u003cbr\u003e18 Proof of the Jordan Curve Theorem \n\u003cbr\u003eChapter Four Surfaces \n\u003cbr\u003e19 Examples of Surfaces \n\u003cbr\u003e20 The Combinatorial Definition of a Surface \n\u003cbr\u003e21 The Classification Theorem \n\u003cbr\u003e22 Surfaces with Boundary \n\u003cbr\u003eChapter Five Homology of Complexes \n\u003cbr\u003e23 Complexes \n\u003cbr\u003e24 Homology Groups of a Complex \n\u003cbr\u003e25 Invariance \n\u003cbr\u003e26 Betti Numbers and the Euler Characteristic \n\u003cbr\u003e27 Map Coloring and Regular Complexes \n\u003cbr\u003e28 Gradient Vector Fields \n\u003cbr\u003e29 Integral Homology \n\u003cbr\u003e30 Torsion and Orientability \n\u003cbr\u003e31 The Poincaré Index Theorem Again \n\u003cbr\u003eChapter Six Continuous Transformations \n\u003cbr\u003e32 Covering Spaces \n\u003cbr\u003e33 Simplicial Transformations \n\u003cbr\u003e34 Invariance Again \n\u003cbr\u003e35 Matrixes \n\u003cbr\u003e36 The Lefschetz Fixed Point Theorem \n\u003cbr\u003e37 Homotopy \n\u003cbr\u003e38 Other Homologies \n\u003cbr\u003eSupplement Topics in Point Set Topology \n\u003cbr\u003e39 Cryptomorphic Versions of Topology \n\u003cbr\u003e40 A Bouquet of Topological Properties \n\u003cbr\u003e41 Compactness Again \n\u003cbr\u003e42 Compact Metric Spaces \n\u003cbr\u003eHints and Answers for Selected Problems \n\u003cbr\u003eSuggestions for Further Reading \n\u003cbr\u003eBibliography \n\u003cbr\u003eIndex\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eBrief Description\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tExcellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required. Bibliography. 1979 edition.\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003ePublisher Marketing\u003c\/strong\u003e:\u003cbr\u003e\n\u003c\/p\u003e\n\u003cp\u003eThe creation of algebraic topology is a major accomplishment of 20th-century mathematics. The goal of this book is to show how geometric and algebraic ideas met and grew together into an important branch of mathematics in the recent past. The book also conveys the fun and adventure that can be part of a mathematical investigation.\u003cbr\u003eCombinatorial topology has a wealth of applications, many of which result from connections with the theory of differential equations. As the author points out, \"Combinatorial topology is uniquely the subject where students of mathematics below graduate level can see the three major divisions of mathematics -- analysis, geometry, and algebra -- working together amicably on important problems.\"\u003cbr\u003eTo facilitate understanding, Professor Henle has deliberately restricted the subject matter of this volume, focusing especially on surfaces because the theorems can be easily visualized there, encouraging geometric intuition. In addition, this area presents many interesting applications arising from systems of differential equations. To illuminate the interaction of geometry and algebra, a single important algebraic tool -- homology -- is developed in detail.\u003cbr\u003eWritten for upper-level undergraduate and graduate students, this book requires no previous acquaintance with topology or algebra. Point set topology and group theory are developed as they are needed. In addition, a supplement surveying point set topology is included for the interested student and for the instructor who wishes to teach a mixture of point set and algebraic topology. A rich selection of problems, some with solutions, are integrated into the text.\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\n\n\u003cbr\u003e\n\u003cbr\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":46581129314435,"sku":"SPTM-9780486679662","price":14.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0564\/6830\/8099\/files\/9780486679662_spiral_c9ec857e-0443-4917-b8c1-e3daf75612a5.png?v=1770802698","url":"https:\/\/sebink.com\/products\/a-combinatorial-introduction-to-topology-revised-dover-books-on-mathematics","provider":"Sebink","version":"1.0","type":"link"}