Lectures related to Propositional Calculus

Concept of Proof in Mathematics

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

Formal Logic: Proofs and Sets

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

Recursive Enumerability: Turing Machines and Undecidable Languages

Covers recursively enumerable languages, Turing machines, and the construction of undecidable languages.

Linear Algebra: Propositions and Sets

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

Introduction & Propositional Logic

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

Propositions and Proofs

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

Complexity & Induction: Algorithms & Proofs

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Coq: Introduction

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

Proofs and Computations: A Journey Through Mathematical Theory

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

Hoare Logic: Foundations and Applications

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

Automated Reasoning: Formal Verification with LISA

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

Computational Complexity: Theory and Applications

Explores computational complexity, NP-completeness, and polynomial reductions in theoretical computer science.

Proofs and Sets: Applications

Covers the basics of proofs, defining sets, and applications between sets.

Complex Systems: Critical Phenomena

Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.

Formal Proofs: Checking Invariants and Bounded Model Checking

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

Injective Functions: Properties and Examples

Covers the properties of injective functions and demonstrates their proofs through examples and visual aids.

Understanding Equivalence Relations and Integer Construction

Covers the construction of integers through equivalence relations and their properties in mathematics.

Discrete Mathematics: Logic, Structures, Algorithms

Covers the basics of discrete mathematics, focusing on logic, structures, and algorithms for computer systems.

Set Theory: Introduction and Operations

Covers the foundation of mathematics through set theory concepts like membership and unions.

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.