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Arbitrarily Close: An Introduction to Real Analysis is geared towards the curious student who prefers thorough explanations and an abundance of detail beyond what the current canon on analysis generally offers. Concepts are built from a formal definition for “arbitrarily close” to parse introductions to the core and notoriously difficult concepts of convergence, compactness, continuity, limits, derivatives, integrals, uniform convergence, and series.
The overall structure here follows a definition-example/theorem/lemma-scratch work-proof pattern. In particular, scratch work is used to motivate, comment upon, and provide preliminary work for proofs. Included are approximately 150 figures and 20 QR codes with links to dynamic Desmos and GeoGebra activities, all designed to help the reader find their own intuition for real analysis. Color is used in figures and to differentiate definitions, examples, theorems, remarks, and scratch work in order to aid with organization and the ability to reference material quickly.
John A. Rock is a professor in the Department of Mathematics and Statistics at Cal Poly Pomona. He earned his PhD in Mathematics from the University of California, Riverside, under the guidance of Michel L. Lapidus, in 2007. His publications are largely in the area of fractal geometry, but his current research interests focus on pedagogy. A couple publications cover the usefulness of a tabular method cover for integration by parts called “row integration by parts”. John spends his spare time hanging out in Hyrule with Link in Tears of the Kingdom.
The overall structure here follows a definition-example/theorem/lemma-scratch work-proof pattern. In particular, scratch work is used to motivate, comment upon, and provide preliminary work for proofs. Included are approximately 150 figures and 20 QR codes with links to dynamic Desmos and GeoGebra activities, all designed to help the reader find their own intuition for real analysis. Color is used in figures and to differentiate definitions, examples, theorems, remarks, and scratch work in order to aid with organization and the ability to reference material quickly.
John A. Rock is a professor in the Department of Mathematics and Statistics at Cal Poly Pomona. He earned his PhD in Mathematics from the University of California, Riverside, under the guidance of Michel L. Lapidus, in 2007. His publications are largely in the area of fractal geometry, but his current research interests focus on pedagogy. A couple publications cover the usefulness of a tabular method cover for integration by parts called “row integration by parts”. John spends his spare time hanging out in Hyrule with Link in Tears of the Kingdom.
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