Notes on Galois Theory

Or, with apologies to any French readers Réflexions sur la résolution des articles mathématiques incompréhensibles par blog posts. Since the year 2013, seemingly every springtime I become interested in the theory of algebraic equations / polynomials / Galois theory. Ever since I was a teenager I have really really wanted to understand why the general … Continue reading Notes on Galois Theory


Values, Diffs and Functions

We awaken in a world of "things" (e.g. points, states, versions). We call these values. From any ordered pair of values (a, b) we can form a diff from the first to the second. We write this as a→b, pronounced "a to b". (A better terminology could perhaps be simply absolutes and relatives, or abses … Continue reading Values, Diffs and Functions

Notes on the Differences Between Things

This series will deal with the following truly widespread concept: the absolute "state", and the relative "change between states". Some examples: Points and Vectors Certain areas of mathematics (e.g. homogenous co-ordinates in computer graphics) distinguish between points -- i.e. multiple origins -- and vectors, the "displacements between points". You can't really do any operations on … Continue reading Notes on the Differences Between Things