A Note on Teaching the Riemann Integral

Summary

There are alternative definitions for the Riemann integral, many of which avoid some of the unpleasant computations that arise when using Riemann sums. In this version a simple distance function for step functions is used and the Riemann integral is defined and developed by employing exclusively “convergent” sequences of step functions. While only modestly different from the standard presentation it might have some extra intuitive appeal. This is a common device in advanced theories of integration and can be introduced at this elementary level.

Additional information

Notes on contributors

Brian S. Thomson

Brian S. Thomson ([email protected]) received his mathematical training at the University of Toronto and the University of Waterloo. In 1968 he joined the faculty of the newly-created Simon Fraser University on the west coast of Canada. He has served on the editorial boards of the Real Analysis Exchange and the Journal of Mathematical Analysis and Applications. In 2021 he was the recipient of the MAA Halmos-Ford Award for an article he published in the monthly.