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Christopher Hammond, Professor of Mathematics at Connecticut College, has written an introductory textbook in real analysis. This resource is freely available for anyone to use, either individually or in a classroom setting.
The primary innovation of this text is a new perspective on teaching the theory of integration. Most introductory analysis courses focus initially on the Riemann integral, with other definitions discussed later (if at all). The paradigm being proposed is that the Riemann integral and the “generalized Riemann integral” should be considered simultaneously, not separately – in the same manner as uniform continuity and continuity. Riemann integrability is simply a special case of integrability, with particular properties that are worth noting. This point of view has implications for the treatment of other topics, particularly continuity and differentiability.
This work is published under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Open Educational Resources, real analysis, continuity, differentiation, integration, sequences, series
Analysis | Mathematics
Hammond, Christopher, "The Art of Analysis" (2022). Open Educational Resources. 3.