{"product_id":"9780387946559","title":"Graduate Texts in Mathematics","description":"\u003ch1\u003eGraduate Texts in Mathematics\u003c\/h1\u003e \u003ch2\u003eNathanson, Melvyn B.\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eMany classical problems in additive number theory are direct problems, in which one starts with a set \u003ci\u003eA\u003c\/i\u003e of natural numbers and an integer \u003ci\u003eH -\u0026gt; 2\u003c\/i\u003e, and tries to describe the structure of the sumset \u003ci\u003ehA\u003c\/i\u003e consisting of all sums of \u003ci\u003eh\u003c\/i\u003e elements of \u003ci\u003eA\u003c\/i\u003e. By contrast, in an inverse problem, one starts with a sumset \u003ci\u003ehA\u003c\/i\u003e, and attempts to describe the structure of the underlying set \u003ci\u003eA\u003c\/i\u003e. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an \u003ci\u003en\u003c\/i\u003e-dimensional arithmetic progression.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1996-08-22\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387946559\u003c\/p\u003e \u003cp\u003eDOI: \u003c\/p\u003e \u003cp\u003eDimensions: 234cm x156cm\u003c\/p\u003e \u003cp\u003ePages: 295\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":44499563282572,"sku":"9780387946559","price":89.1,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780387946559.jpg?v=1776434121","url":"https:\/\/lateknightbooks.com\/products\/9780387946559","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}