The mathematics of calculus when h is not removed by limiting it to zero.
Back in 2001 I wrote this project while studying Mathematics at university. I never finished it, and I hoped one day to work on it more. However, life filled up with other things.
Rather than sit on it, I wanted to share it for others that may be interested.
In this paper I present a calculus where h is not removed by limiting it to zero, rather h is kept in the equations as an extra dimension to the calculus. This creates a whole new dimension to the mathematics of calculus, whereby present-day calculus can be seen as a special case of the more general form by tending h -> 0. However, it turns out by not taking the limit as h tends to 0, many fascinating results can be deduced. The most interesting and pertinent of these are those that seem to tie closely with number theory and the Riemann Zeta Function.
It is my hope that by studying this broader, discrete calculus, inroads may be made into solving the Riemann Hypothesis.
Please feel free to contact me if you are interested in this topic, I would love to hear from anybody that is as interested in this topic as me.
Peter Moore Jan 2016