  It is of course well known that the usual definitions of Riemann integration
and Riemann integrals are equivalent to simpler definitions which can be
expressed in terms of just one sequence of partitions, using dyadic intervals
or dyadic squares or dyadic cubes for univariate, double, or triple integrals
respectively. These lecture notes, intended mainly for undergraduates, present
and prove some basic standard results of Riemann integration in detail, taking
advantage of this simpler definition. The last section of the notes provides a
proof of the equivalence of this definition with the classical one. But the
implicit suggestion is that the classical definition need be the concern of
specialists only, and that regular students can probably do just about
everything that they need to do with Riemann integration by working only with
the simpler dyadic definition. This is a preliminary version of these notes
which will surely be updated later. It is very difficult to believe that there
do not exist any other documents which give a systematic treatment of Riemann
integration using this approach. The author would be very grateful for any
information about any such documents.
