True Grit in Real Analysis

Abstract

SummaryFor far too many students, Real Analysis is a dreaded course that proceeds from unmotivated definitions to formal and impenetrable theorems with little sense of why the course unfolds as it does. This article describes the experience of a radically different approach that drew on the history of mathematics to confront students with the uncertainties and confusion that real mathematicians encounter as they explore new mathematical territory. The argument is made that such an historical approach enables students to appreciate the precise definitions that have evolved and the power of the theorems that are built upon them.