# Website activity diary 2018

Differentiate polynomials

Explored the gradients of chords to show how an algebraically formulated deriviative matches my latest reformulation of how to do differentiation. Explored several other details (e.g. multinomials, particularly homogenous ones) in support of that.

Permutations

Began describing one of the tools that shows up repeatedly all over mathematics.

Natural arithmetic
I began examining the consequences of applying general arithmetic to the natural numbers, starting with a look at unique prime factorisation.
Another look at polynomials
Now contrasting their formal treatment, as lists of coefficients under a contrived arithmetic, with their interpretation as functions from a ringlet to itself.
Began describing differentiation
Introducing it in the context of linear spaces, rather than reals, using simplices to generalise chords and provide gradients. I've had this in mind for many years.
Reworked positive ordering
A clarification of earlier work on when arithmetic itself induces order on its values.
Earlier history
2017, 2016, 2011–2015, 2010, 2009, 2008, 2007, 2006.
Written by Eddy.