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Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Introduces the basics of plasma physics, covering collective behavior, Debye length, and plasma conditions.

Introduces spatial scales, particle interactions, mass-energy equivalence, and momentum conservation in particle physics.

Explores the problem of a falling stone hitting the moon, focusing on gateways to the moon and local Floer homology.