How We Got from There to Here: A Story of Real Analysis by Eugene Boman, Robert Rogers

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About this book :-
This book is an introductory real analysis textbook, presented through the lens of history. That is, it proposes that an effective way to motivate the highly non-intuitive definitions and theorems encountered in an introductory, college level 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. The 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.

Book Detail :-
This book has following details information.
Title: How We Got from There to Here: A Story of Real Analysis by Eugene Boman, Robert Rogers by NA
Publisher: Lulu.com
Series: eBookDirectory, FreeBookCentre
Year: 2013
Pages: 220
Type: PDF
Language: English
ISBN-10 #: 1312348690
ISBN-13 #: 978-1312348691
Country: Pakistan
License: CC BY-NC-SA 3.0
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
Part-I In Which We Raise A Number Of Questions 1. Prologue: Three Lessons Before We Begin 2. Numbers, Real (R) and Rational (Q) 3. Calculus in the 17th and 18th Centuries 4. Questions Concerning Power Series Part-II Interregnum 5. Joseph Fourier: The Man Who Broke Calculus Part-III In Which We Find (Some) Answers 6. Convergence of Sequences and Series 7. A “Tayl” of Three Remainders 8. Continuity: What It Isn’t and What It Is 9. Intermediate and Extreme Values 10. Back to Power Series 11. Back to the Real Number 12. Epilogues

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