How We Got from There to Here: A Story of Real Analysis
A Story of Real Analysis - Table of Contents
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
5. Joseph Fourier: The Man Who Broke Calculus
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
What You Will Learn in A Story of Real Analysis
"How We Got from There to Here: A Story of Real Analysis" by "Eugene Boman and Robert Rogers" is an engaging and approachable textbook that teaches real analysis through the "historical development" of its ideas. Instead of starting with abstract definitions, the book shows how concepts such as limits, sequences, series, continuity, and convergence evolved over time. By following this historical narrative, students gain a deeper understanding of "why" rigorous definitions and proofs are structured the way they are, making the subject more intuitive and meaningful.
The book covers standard "real analysis" topics while highlighting the historical challenges and motivations behind each concept. Key sections focus on sequences and series, limits and continuity, differentiation and integration, and the evolution of proof techniques. Problems and exercises are integrated into the narrative to reinforce learning and encourage students to actively engage with the material. This approach helps readers build strong "conceptual understanding" alongside formal mathematical skills.
A major advantage of this textbook is that it is an "open access textbook", freely available under a Creative Commons license. It is well suited for undergraduate students, self-learners, and instructors seeking a more narrative-driven approach to real analysis. Overall, "How We Got from There to Here" combines rigorous mathematics with historical context, making it a unique and valuable resource for developing "proof-based reasoning" and appreciation of the subject’s evolution.
Book Details & Specifications
Title:
How We Got from There to Here: A Story of Real Analysis
Publisher:
Lulu.com
Year:
2013
Pages:
220
Type:
PDF
Language:
English
ISBN-10 #:
1312348690
ISBN-13 #:
978-1312348691
License:
CC BY-NC-SA 3.0
Amazon:
Amazon
About the Author: Eugene Boman and Robert Rogers
The author
Eugene Boman and Robert Rogers
are mathematicians and educators known for their innovative approach to "Real Analysis". Boman teaches at "Pennsylvania State University", while Rogers is a professor at "SUNY Fredonia". Both are recognized for clear explanations and excellence in "Mathematics Education". Their book "How We Got from There to Here" introduces analysis concepts through a "Historical Approach", showing how ideas developed over time. By blending rigorous theory with engaging stories and problem-based learning, it helps students build a deeper understanding of proofs, sequences, and functions, making advanced topics accessible and meaningful for learners.
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