Lectures related to Logical Structure: Choice and Bar Induction Principles

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

Philosophy of Mathematics: Ontology and Structures

Explores the existence of mathematical objects, truth of propositions, and knowledge about them, covering Platonism, Intuitionism, Structuralism, Nominalism, Logicism, and Formalism.

Set Theory: Introduction and Operations

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

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.

Numbers and Booleans

Introduces numbers and booleans in Python, covering numeric types, arithmetic operations, logical operations, and comparisons.

Formal Logic: Proofs and Sets

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

Proofs and Sets: Applications

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

Recursive Enumerability: Turing Machines and Undecidable Languages

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

Inductive Propositions: Reasoning and Evaluation Techniques

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

Propositional Calculus

Covers the basics of propositional calculus and its importance in computer science.

Predicate Logic: Sets Theory

Covers predicate logic and sets theory, explaining how to manipulate logical expressions.

Lifting properties and model categories

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Combinatorial Logic Circuits

Covers the basics of logical systems, Boolean algebra, logic gates, and coding in digital circuits.

Counting Basics: Set Theory and Permutations

Covers the main rules of counting for combinatorial objects and introduces various counting techniques.

Propositional Logic: Basics and Applications

Covers the basics of propositional logic, its history, language, and computing applications.

Dimension Theory: Vector Spaces and Bases

Explores dimension theory of vector spaces, covering bases, linear applications, and ranks.

Introduction & Propositional Logic

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

Automating First-Order Logic Proofs Using Resolution

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

Real Numbers: Sets and Operations

Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.