This exploration explores group theory at the university level, but is uniquely motivated through symmetries, applications, and challenging problems. For example, before diving into the technical axioms, we'll explore their motivation through geometric symmetries. And after some formalism, we'll explore games like the Rubik's cube through the lens of group theory. You'll be left with a deep understanding of how group theory works and why it matters.
An introduction to Group Theory through the beauty of symmetry.
The axioms, subgroups, abelian groups, homomorphisms, and quotient groups.
Number theory, the 15-puzzle, peg solitaire, the Rubik's cube, and more!
From the isomorphism theorems to conjugacy classes and symmetric groups.
Burnside's Lemma, semidirect products, and Sylow's Theorems.
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