Lectures related to Linear Algebra: Implications and Equivalences

WireGuard: Cryptographic Protocol for VPNs

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

Formal Proofs: Checking Invariants and Bounded Model Checking

Explores formal proofs, satisfiability problems, and inductive invariants using SAT queries in sequential circuits.

Optimal Transport: Theory and Applications

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

Linear Algebra: Equivalence and Calculations

Explains equivalence in linear algebra and set calculations with illustrative examples.

Coq: Introduction

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

Formal Logic: Proofs and Sets

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

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Linear Algebra: Properties and Operations

Explores subset properties, contraposition, and equivalence in linear algebra.

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What is a Formal Proof?

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

Finite Systems Expressed with Formulas

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

Linear Algebra: Reciprocity and Equivalence

Explores reciprocity, equivalence, and proof techniques in linear algebra, emphasizing logical reasoning and mathematical rigor.

Finite Automata: Recap

Covers the fundamentals of finite automata and formal languages.

Linear Similarities and Similitudes

Explores linear similarities and similitudes, demonstrating their properties and applications in geometry.

Automated Reasoning: Formal Verification with LISA

Explores formal verification using the LISA proof assistant and the OCBSL Equivalence Checker.

Proofs and Computations: A Journey Through Mathematical Theory

Explores historical mathematical proofs, decision problems, deductive systems, probabilistic and quantum proofs, and interactive proof systems.

Analysis IV: Measurable Sets and Properties

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

Coq: Overview

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

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.

Linear Algebra: Propositions and Sets

Covers propositions indexed by vectors, proof by induction, and Cartesian products of sets.