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Description

A Contextual Introduction to Real Analysis: How We Got From There to Here is an innovative introduction to real analysis that presents the subject through the historical development of its key ideas. Rather than introducing rigorous definitions as isolated abstractions, the text shows how concepts such as limits, continuity, convergence, differentiation, and integration emerged in response to specific mathematical challenges. Historical context is woven into the structure of the book, helping students understand both the motivation and necessity behind modern analysis.

The second edition expands the book's coverage with new material on the Fundamental Theorem of Calculus, the Cauchy, Riemann, and Darboux integrals, and an introduction to Cantor's set-theoretic framework, measure theory, and the Lebesgue integral. Designed for undergraduate real analysis courses, the text combines historical narrative, guided proof development, and integrated exercises to help students transition from intuitive reasoning to rigorous mathematics. By connecting the evolution of mathematical ideas with modern theory, the book offers a distinctive and engaging pathway into one of mathematics' most challenging subjects.

ISBN

978-1-956862-31-7

Publication Date

11-12-2026

Publisher

Milne Open Textbooks

City

Geneseo

Keywords

Real analysis, calculus, history

Disciplines

Analysis | Mathematics | Other Mathematics

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.

A Contextual Introduction to Real Analysis: How We Got From There to Here

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