000			03186nam a2200361 4500
001			OTLid0000200
003			MnU
005			20201105133304.0
006			m o d s
008			180907s2014 mnu o 0 0 eng d
020			_a9781312348691
040			_aMnU _beng _cMnU
050		4	_aQA1
100	1		_aRogers, Robert _eauthor
245	0	0	_aHow We Got from There to Here _bA Story of Real Analysis _cRobert Rogers
264		2	_bOpen Textbook Library
264		1	_bOpen SUNY
300			_a1 online resource
490	0		_aOpen textbook library.
505	0		_a1 Numbers, Real (R) and Rational (Q) -- 2 Calculus in the 17th and 18th Centuries -- 3 Questions Concerning Power Series -- 4 Convergence of Sequences and Series -- 5 Convergence of the Taylor Series: A "Tayl" of Three Remainders -- 6 Continuity: What It Isn't and What It Is -- 7 Intermediate and Extreme Values -- 8 Back to Power Series -- 9 Back to the Real Numbers
520	0		_aThe typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis. This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context. This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.
542	1		_fAttribution-NonCommercial-ShareAlike
546			_aIn English.
588	0		_aDescription based on print resource
650		0	_aMathematics _vTextbooks
700	1		_aBoman, Eugene _eauthor
710	2		_aOpen Textbook Library _edistributor
856	4	0	_uhttps://open.umn.edu/opentextbooks/textbooks/200 _zAccess online version
999			_c19608 _d19608