Proper Actions and Quotients

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Covers the fundamentals of group theory in physics, focusing on symmetries and transformations leaving physical equations unchanged.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.

Explores subsets and subgroups related to group actions on sets.

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Explores irreducible representations of the rotations group and their mathematical properties.