{"product_id":"real-mathematical-analysis-paperback","title":"Real Mathematical Analysis - Paperback","description":"\u003cp\u003eby \u003cb\u003eCharles Chapman Pugh\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eElucidates abstract concepts and salient points in proofs with over 150 detailed illustrations\u003c\/p\u003e\u003cp\u003eTreats the rigorous foundations of both single and multivariable Calculus\u003c\/p\u003e\u003cp\u003eGives an intuitive presentation of Lebesgue integration using the undergraph approach of Burkill\u003c\/p\u003e\u003cp\u003eIncludes over 500 exercises that are interesting and thought-provoking, not merely routine\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eBased on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis.\u003cbr\u003e\u003cbr\u003eNew to the second edition of \u003ci\u003eReal Mathematical Analysis\u003c\/i\u003e is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line\/one-picture proof of Fubini's theorem from Cavalieri's Principle, and, in many cases, the ability to \u003ci\u003esee\u003c\/i\u003e an integral result from measure theory. The presentation includes Vitali's Covering Lemma, density points -- which are rarely treated in books at this level -- and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003eCharles C. Pugh is Professor Emeritus at the University of California, Berkeley. His research interests include geometry and topology, dynamical systems, and normal hyperbolicity.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 478\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.99 x 10 x 7 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 15, 2016\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42105764446343,"sku":"9783319330426","price":89.08,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0601\/2623\/2711\/files\/df0a72b0b558e43442f243bfb0d519e6.webp?v=1732437577","url":"https:\/\/booksby.splitshops.com\/products\/real-mathematical-analysis-paperback","provider":"Books by splitShops","version":"1.0","type":"link"}