Lectures related to Constructive proof

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

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

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

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.

Proofs: Contraposition vs. Contradiction

Covers the concepts of contraposition and contradiction in proofs.

Convergence in Law: Theorem and Proof

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

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.

Harmonic Forms: Main Theorem

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

Compression: Kraft Inequality

Explains compression and Kraft inequality in codes and sequences.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Coq Workshop: Introduction to Interactive Theorem Proving

Introduces Coq, an interactive theorem assistant based on the Curry-Howard isomorphism.

Fundamental Groups

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

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Functional Analysis I: November 18, 2021

Covers partially ordered sets, maximal elements, upper bounds, and the Zorn lemma in functional analysis.

Variational Formulation: Information Measures

Explores variational formulation for measuring information content and divergence between probability distributions.

Entanglement: Bell Inequalities

Covers entanglement, Bell inequalities, CSHS requirements, EPR paradox, and experimental verification in quantum mechanics.

Fundamental Solutions

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

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Prime Number Theorem

Explores the proof of the Prime Number Theorem and its implications in number theory.