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.

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

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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