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M11 · Measure, Functional Analysis and High-Dimensional Probability

A free, illustrated L4 course of 10 modules in the Mathematics track. Modules include: Sigma-algebras and measures; Lebesgue integration; Measure-theoretic probability.

M11 L4 · Expert 10 modules · about 40 lessons Planned · Ring 4

Part of the Mathematics track. Ships in Ring 4 (Expert) of the roadmap.

Modules

1. Sigma-algebras and measures
2. Lebesgue integration
3. Measure-theoretic probability
4. Normed, Banach and Hilbert spaces
5. Reproducing kernel Hilbert spaces
6. High-dimensional geometry and concentration of measure
7. Sub-Gaussian and sub-exponential variables
8. Random matrices and their spectra
9. Optimal transport and Wasserstein distances
10. Information geometry

Signature illustrations

The pictures a learner should still see in their head a year later:

Riemann versus Lebesgue slicing, mass concentrating in the shell of a high-dimensional sphere, kernel feature-map lift, transport-plan heatmaps.

Status

This course is planned, not written yet. It ships with Ring 4 (Expert).

Every lesson will follow the same twelve-part blueprint with at least three purpose-made figures. Watch the repository to hear when modules ship, or help write and review it.