How We Got from There to Here:
A Story of Real Analysis

 Robert Rogers and Eugene Boman

Digital versions	PDF
Latex source	No
Exercises	Yes
Solutions	No
License	Creative Commons Attribution-NonCommercial-ShareAlike 3.0

• Published by SUNY Open Textbooks
• Printed version for $20 from Lulu or $30 from Amazon
• 220 page text with 9 chapters and supplements
• 221 problems
• MAA Review of the book
• For more information and to download

This text for a semester course portrays real analysis in the context of its historical development. It is written in a direct style aimed at students and not instructors. A student using the book is guided to understand and prove much of the actual mathematical content through the more than 200 problems that are embedded within the narrative and not placed at the end of sections as in most textbooks. For a course taught in the inquiry based learning mode this book should work better than standard texts. On the other hand, with the instructor offering more guidance it should also work well with a more traditional classroom style.

Contents

1. Numbers, Real and Rational
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
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