Real Mathematical Analysis
Resource Information
The work Real Mathematical Analysis represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Real Mathematical Analysis
Resource Information
The work Real Mathematical Analysis represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Real Mathematical Analysis
 Statement of responsibility
 by Charles Chapman Pugh
 Language

 eng
 eng
 Summary
 Based 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, fourdimensional visualization, basic pointset 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. New to the second edition of Real Mathematical Analysis 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 oneline/onepicture proof of Fubini's theorem from Cavalieri’s Principle, and, in many cases, the ability to see 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
 Dewey number
 515.42
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 GMIctvU1_E
 Image bit depth
 0
 Language note
 English
 LC call number
 QA312312.5
 Literary form
 non fiction
 Series statement
 Undergraduate Texts in Mathematics,
Context
Context of Real Mathematical AnalysisWork of
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