Minkowski-Weyl: Convexity and Separation Theorem

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Convexity: Functions and Global Minima

Explores convex functions, global minima, and their relationship with differentiability.

Cones of convex sets

Explores optimization on convex sets, including KKT points and tangent cones.

Conjugate Duality: Understanding Convex Optimization

Explores conjugate duality in convex optimization, covering weak and supporting hyperplanes, subgradients, duality gap, and strong duality conditions.

Compact Sets and Extreme Values

Explores compact sets, extreme values, and function theorems on bounded sets.

Cantor-Heine Theorem

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

Preparations for Surjection

Covers the fundamental group of a reattachment and surjection proofs with neighborhoods and cover overlays.

Diophantine Approximation: Minbowski's Theorem

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Setting up Experiments: Compactness, Isometries, Quasi-Isometry

Explains setting up experiments with compactness, isometries, and quasi-isometry.

Initial Problem Solutions

Covers the description of problem solutions and the concept of compactness and uniform continuity.