Abstract Algebra: Theory and Applications

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.


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.


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