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Understanding analysis / St...
Introduction to the Problems in Analysis outlines an elementary, one semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Can the rational numbers be written as a countable intersection of open sets? Is an infinitely differentiable function necessarily the limit of its Taylor series? Giving these topics center stage, the motivation for a rigorous approach is justified by the fact that they are inaccessible without it
Monografía
monografia Rebiun35537192 https://catalogo.rebiun.org/rebiun/record/Rebiun35537192 m o d cr cn||||||||| 100929s2001 nyua ob 001 0 eng d 00058308 231581405 814270207 834401578 1044186982 1056356959 1060839639 1073049245 1113070388 1113622158 1360064002 9781441928665 electronic bk.) 1441928669 electronic bk.) 9780387215068 electronic bk.) 0387215069 electronic bk.) 1280189681 9781280189685 6610189684 9786610189687 0387950605 9780387950600 10.1007/978-0-387-21506-8 doi AU@ 000051742550 NLGGC 401200078 NZ1 14977640 NZ1 15300836 IDEBK eng pn IDEBK MNU OCLCQ SINTU OCLCO GW5XE OCLCF OCLCQ COO OCLCQ UAB EBLCP STF OCLCQ CEF U3W AU@ OCLCO LEAUB OCLCQ UKBTH OCLCQ UKAHL YDX OCLCQ OCLCO N$T OCLCQ INARC OCLCO OCLCL QA lcco PBKB bicssc MAT034000. bisacsh MAT037000. bisacsh Abbott, Stephen 1964-) https://id.oclc.org/worldcat/entity/E39PCjvFJFvKYkh7kBfcBYbdpP Understanding analysis Stephen Abbott New York Springer 2001 New York New York Springer 1 online resource (xii, 257 pages) illustrations 1 online resource (xii, 257 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF Undergraduate texts in mathematics Includes bibliographical references (pages 251-252) and index The real numbers -- Sequences and series -- Basic topology of R -- functional limits and continuity -- The derivative -- Sequences and series of functions -- The Riemann Integral -- Additional topics Introduction to the Problems in Analysis outlines an elementary, one semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Can the rational numbers be written as a countable intersection of open sets? Is an infinitely differentiable function necessarily the limit of its Taylor series? Giving these topics center stage, the motivation for a rigorous approach is justified by the fact that they are inaccessible without it English Mathematical analysis Analyse mathématique Mathematical analysis. Reelle Analysis. Analyse (wiskunde) Cálculo diferencial e integral (textos intermediários) Print version Abbott, Stephen, 1964-. Understanding analysis. New York : Springer, 2001 9780387950600 (DLC) 00058308 (OCoLC)44592777 Undergraduate texts in mathematics