Concept

Proof theory

Related lectures (32)

Covers the proof of the convergence rate theorem, emphasizing the correction of a missing factor sqrt{pi_j} in the proof.

Inductive Propositions: Reasoning and Evaluation Techniques

Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Concept of Proof in Mathematics

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

Zig Zag Lemma

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: Logic, Mathematics & Algorithms

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

Central Limit Theorem: Proof

Presents the proof of the Central Limit Theorem using Lindeberg's principle.

Analysis IV: Measurable Sets and Properties

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

Convergence in Law: Theorem and Proof

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

Convergence in Induced Matrix

Covers convergence in induced matrices and advection-diffusion phenomena.

Fourier Inversion Formula

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Prime Number Theorem

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

Lebesgue Integral: Properties and Convergence

Covers the Lebesgue integral, properties, and convergence of functions.

Sequent Calculus: Basics and Applications

Covers the basics and applications of Sequent Calculus in Logic and Proof Theory, including Cut Elimination and practical proof analysis.

What is a Formal Proof?

Covers the concept of formal proof systems, their structure, and soundness.

Coupling of Markov Chains: Ergodic Theorem

Explores the coupling of Markov chains and the proof of the ergodic theorem, emphasizing distribution convergence and chain properties.

Proof Techniques: Examples

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

Entanglement: Bell Inequalities

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

Sparsest Cut: Bourgain's Theorem

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