At the start of October 2024, I agreed to rework an introductory real analysis manuscript for CRC Press. Yesterday I delivered the manuscript. Details will follow in coming weeks as they become available.
If you teach introductory/intermediate real analysis, or are a school teacher looking for a friendly desk reference, please do consider the book. It relies systematically on adversarial games to explain the definitions of analysis: limits, continuity and uniform continuity, integrability, compactness,.... There are over 630 exercises, many with answers/solutions in the back. A complete solution manual will be available to instructors.
The book starts with chapters on the language of mathematics and on the natural numbers, then gives axioms for the reals and works its way through the fundamental theorems of calculus, construction of elementary functions, metric spaces, and a sampling of approximation theorems (including construction of the reals as a completion of the rationals). Everything (except sets and elements) is defined, and aside from the division algorithm for integers, everything is proved. There are fun destinations, including transcendentality of \(e\), an analytic definition of \(\pi\), the many faces of exponentiation, the product-of-chord-lengths theorem in the unit circle, irrational windings on a square torus, and the evaluation of \(\zeta(2n)\) for positive integer \(n\).
I took considerable care with self-containment and internal consistency, logical structuring, simplicity and expository clarity, navigability, and other matters. Whether my intentions succeeded, naturally, is up to you, the reader.
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