Lectures related to Formal Proofs: Checking Invariants and Bounded Model Checking

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

Explores encoding finite systems with boolean functions, propositional logic, inductive invariants, and formal proof systems.

Propositions and Proofs

Explores propositions, proofs, and contraposition in mathematical theory, emphasizing logical rules and proof methods.

Proofs: Logic, Mathematics & Algorithms

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

Concept of Proof in Mathematics

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

Coq: Introduction

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

Ordinary Differential Equations: Definitions and Methods

Explores ordinary differential equations, proof methods, and historical examples from Euclid, emphasizing logical reasoning and step-by-step derivations.

Propositional Logic: Translations and Equivalences

Covers translating natural language to propositional logic and proving tautologies.

Finite Systems Expressed with Formulas

Explores finite transition systems, propositional logic, truth interpretation, satisfiability, and boolean function representation with circuits.

Soundness and Completeness of a Propositional Proof System

Explores the importance of soundness and completeness in a propositional proof system.

Introduction to Categories

Introduces the concept of categories essential for understanding group theory.

Formal Logic: Proofs and Sets

Covers the basics of formal logic, focusing on logical expressions and mathematical proofs.

Automating First-Order Logic Proofs Using Resolution

Covers first-order logic syntax, semantics, and resolution for proving properties.

Optimal Transport: Theory and Applications

Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.

Linear Algebra: Implications and Equivalences

Explores implications and equivalences in linear algebra through examples and formal proofs.

WireGuard: Cryptographic Protocol for VPNs

Explores the WireGuard Protocol, a modern VPN replacement for IPsec and OpenVPN, focusing on encrypted tunnelling and security properties.

Jordan Curve Theorem

Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.

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.

Introduction & Propositional Logic

Covers the basics of propositional logic, logical connectives, truth tables, and compound propositions.

Hoare Logic: Foundations and Applications

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