Lectures related to The Languages of Isabelle: Isar, ML, and Scala

Coq Workshop: Introduction to Interactive Theorem Proving

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

Concept of Proof in Mathematics

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

Inductive Propositions: Reasoning and Evaluation Techniques

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

Proofs: Logic, Mathematics & Algorithms

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

Introduction to Coq: Arithmetic Expressions and Evaluators

Covers the basics of Coq, focusing on arithmetic expressions, evaluation, and proof techniques.

Hoare Logic: Foundations and Applications

Covers Hoare Logic, its foundations, applications, and significance in program verification.

Inductive Propositions: Understanding Evaluation in Coq

Covers inductive propositions in Coq, focusing on evaluation rules for arithmetic expressions and their applications in defining partial and non-deterministic functions.

Coq: Overview

Introduces Coq and focuses on proving the theorem and_comm step by step.

Coq Workshop: Inductive Data Types and Proofs

Covers the definition of an inductive data type in Coq and how to build proofs interactively using tactics.

Analysis IV: Measurable Sets and Properties

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

Big-step semantics: Defining arithmetic expressions and commands

Covers the definition of a simple programming language and its big-step semantics, including arithmetic expressions and imperative commands.

Coq: Introduction

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Zig Zag Lemma

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

Proofs and Logic: Introduction

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

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.

Harmonic Forms: Main Theorem

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

Fourier Inversion Formula

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

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.