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1. Infinite dimensional vector spaces: Banach and Hilbert spaces. 2. Geometry of Hilbert spaces. 3. Orthonormal bases and Fourier analysis. 4. The problem of best approximation and other applications. 5. Linear operators on Hilbert spaces. 6. Self-adoint and unitary operators on Hilbert spaces: The Fourier transform. 7. The spectral theorem. 8. Applications to signal theory: sampling. 9. Applications to physical theories: quantum mechanics. 10. Applications to numerical analysis: Sobolev spaces.
Get a Flight Credit worth up to $1,000 when you apply with code* by September 12, 2025