Shows that the notion of what a derivative is -- NOT what one learns in first year calculus -- that it is the "best" linear approximation to a function.

This idea allows us to extend the derivative beyond what one sees in first year calculus; meaning, extending the idea of derivative to higher dimensional functions.

In fact, it can be used in an "infinite" dimensional setting to derive equations of motion in physics.

A new geometric proof of the result that for primitive Pythagorean triples:

c is odd

one of the legs is divisible by 4

the other leg is odd.

Conjectures that partition the set of primitive Pythagorean hypotenuses into two sets.

Conjectures that try to examine the complexity of these two partitioning sets.

Derives recursive computational formulas for EMA and its standard deviation.

Derives formulas for computing higher unbiased moments.

The general theme is to show that the differencing and summing oof sequences of numbers are inverse operations in some sense. This is easy to do and helps us understand the continuous analogs of these; namely, differentiation and integration.

Goes further and examines difference equations and relates them to the continuous notion of differential equations. Once again, it uses the easier discrete problem to help understand the continuous one.

Places supporting concepts to the appendices. These include:

• Functions, Formulas, Graphs, and Notation..
• Straight Line Functions.
• Infinite Sequences and Limits.
• Mathematical Induction.
• Taylor's Theorem.