The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

## Tag: equivalence relations

## Make Your Own Magical Rules

When people go about making their own magical “systems”, there tend to be two popular routes they take: making their own magical language without formalizing their ontology or they create random sigils. The problem, though, is that those two popular methods alone technically don’t create a magical system. A magical system is an abstraction comprised of a body of axioms, rules, and operations. If you were to look at classical and historical “magical systems”, you will see a formally articulated set of axioms and rules; an example of this is Western occultism. The problem with informally creating your own magical Read More

## Harmonically Bridging The Future

My fiancé is a genius! He used his intuitive knowledge as a singer to help me figure out how to make manipulation of reality through manipulation of probable futures consistent. Temporal histories and probabilities are basically a set of harmonics, according to Physics. Time is less like a line and more like a collection of superimposed sinusoidal waves. You can see this if you look at how you can use Fourier Transformation (FT) to turn instances of time-dependent objects into frequency spectrums. Since the intervals of edges of concepts are “like” time in a lot of ways, you can apply Read More

## Telling Time on a Torus

What shape do you most associate with a standard analog clock? Your reflex answer might be a circle, but a more natural answer is actually a torus. Surprised? Then stick around.

## Times Tables, Mandelbrot and the Heart of Mathematics

The good old times tables lead a very exciting secret life involving the infamous Mandelbrot set, the ubiquitous cardioid and a myriad of hidden beautiful patterns. Time for the Mathologer to go on a serious fact-finding mission.