Lectures related to Proof of Convergence Rate Theorem

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Zig Zag Lemma

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Harmonic Forms: Main Theorem

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

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

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Proof Techniques: Examples

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

Implicit Functions: Unique Solutions and Class C Functions

Covers the proof of the theorem of implicit functions and the concept of class C functions.

The Languages of Isabelle: Isar, ML, and Scala

Explores the languages of Isabelle, focusing on Isar, ML, and Scala, covering proof schemes, Natural Deduction rules, inductive definitions, and the LCF approach.

Convergence of Fourier Series

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Sparsest Cut: Bourgain's Theorem

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Convergence in Law: Theorem and Proof

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Compression: Kraft Inequality

Explains compression and Kraft inequality in codes and sequences.

Geodesic Convexity: Theory and Applications

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Relative Homology: Exact Sequence

Covers the long exact sequence of relative homology groups and chain complexes.

Harmonic Forms and Riemann Surfaces

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

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Concept of Proof in Mathematics

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.