Lax-Milgram: Variational Problems and Riesz's Theorem

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Explores trigonometric polynomials, emphasizing Fourier inversion and Plancherel formulas.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Explores RKHS, positive definite kernels, and the Moore-Aronszajn theorem in kernel methods.

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Covers the quantization of topological operators and Ising models on square lattices.

Introduces Hilbert space as a big place where quantum systems evolve with unitaries.