{"product_id":"mapping-degree-theory-9780821887141","title":"Mapping Degree Theory","description":"\u003cp\u003e • Author(s): Enrique Outerelo, Jesús M Ruiz\u003cbr\u003e • Publisher: Orient Blackswan Pvt Ltd\u003cbr\u003e • Publisher Imprint: Orient Blackswan Pvt Ltd\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis textbook treats the classical parts of mapping degree theory, with a detailed account of its history traced back to the first half of the 18th century. After a historical first chapter, the remaining four chapters develop the mathematics. An effort is made to use only elementary methods, resulting in a self-contained presentation. Even so, the book arrives at some truly outstanding theorems: the classification of homotopy classes for spheres and the Poincaré-Hopf Index Theorem, as well as the proofs of the original formulations by Cauchy, Poincaré, and others.\u003c\/p\u003e \u003cp\u003eAlthough the \u003cstrong\u003emapping degree theory\u003c\/strong\u003e you will discover in this book is a classical subject, the treatment is refreshing for its simple and direct style. The straightforward exposition is accented by the appearance of several uncommon topics: tubular neighborhoods without metrics, differences between class 1 and class 2 mappings, Jordan Separation with neither compactness nor cohomology, explicit constructions of homotopy classes of spheres, and the direct computation of the Hopf invariant of the first Hopf fibration.\u003c\/p\u003e \u003cp\u003eThe book is suitable for a one-semester graduate course. There are 180 exercises and problems of different scope and difficulty.\u003c\/p\u003e","brand":"Orient Blackswan Pvt Ltd","offers":[{"title":"Paperback","offer_id":45616520298647,"sku":"9780821887141","price":1179.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780821887141.webp?v=1769295011","url":"https:\/\/atlanticbooks.com\/products\/mapping-degree-theory-9780821887141","provider":"Atlantic Books","version":"1.0","type":"link"}