Understanding Analysis Undergraduate Texts in Mathematics by Stephen Abbott

Understanding Analysis Undergraduate Texts in Mathematics by Stephen AbbottISBN 978144I928665, 9780387215068My primary goal in writing Understanding Analysis was to create an elementaryone-semester book that exposes students to the rich rewards inherent intaking a mathematically rigorous approach to the study of functions of a realvariable. The aim of a course in real analysis should be to challenge and improvemathematical intuition rather than to verify it. There is a tendency,however, to center an introductory course too closely around the familiar theoremsof the standard calculus sequence. Producing a rigorous argument thatpolynomials are continuous is good evidence for a well-chosen definition of continuity,but it is not the reason the subject was created and certainly not thereason it should be required study. By shifting the focus to topics where anuntrained intuition is severely disadvantaged (e.g., rearrangements of infiniteseries, nowhere-differentiable continuous functions, Fourier series), my intentis to restore an intellectual liveliness to this course by offering the beginningstudent access to some truly significant achievements of the subject.