Permutation group

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Explores the Symmetric group, cycle notation, multiplication, the sign of a permutation, and the Alternating group.

Explores the reasons behind the abundance of saddle points in deep learning optimization, emphasizing statistical and geometric arguments.

Explores group actions on lattices, emphasizing GL₂(Q) and GL₂(Ag) compatibility and alternative formulations.

Explores the algebraic properties of the cross product and its linearity.

Introduces algebraic structures essential for understanding mathematical objects used in science and engineering.

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.