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

## Elegant Thaumaturgy

An arbitrary and random collection of symbols is not enough to create a consistent magical system. An issue with creating a magical system from random symbols is that there is no formal ontological framework. Consistent magical ontological frameworks can emerge from magical languages, and people can create magical languages through ordered and logical methods. A magical system is an abstraction comprised of a tuple of symbols and strings. Those strings encapsulate magical sigils, axioms, rules, and operations that relate sigils and entities. In classical, western, occult “magical systems”, there are formally articulated sets of axioms and rules. The dilemma of 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.