Understanding Analysis – Stephen Abbott – 1st Edition


Understanding outlines an elementary; one-semester course designed to expose to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real .

The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this is to focus attention on the questions that give analysis its inherent fascination.

Does the Cantor set contain any irrational ? Can the set of points where a function is discontinuous be arbitrary? Are derivatives continuous? Are derivatives integrable? Is an infinitely differentiable function necessarily the limit of its series? In giving these topics center stage; the hard work of a rigorous study is justified by the fact that they are inaccessible without it.

Table of Contents

The Real Numbers
Sequences and Series
Basic Topology of R
Functional Limits and Continuity
The Derivative
Sequences and Series of Functions
The Riemann Integral
Additional Topics
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