Lectures related to Hilbert's axioms

Covers the concept of sigma fields and their role in probability theory.

Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.

Introduces the axioms of connection in Euclidean geometry, emphasizing unique lines and non-collinear points.

Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.

Explores the significance of types in programming and discusses unsound type systems and inductively defined relations.

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

Explores the Euclidean algorithm, Bézout's identity, extended Euclid algorithm, and commutative groups in mathematics.

Introduces informal proofs, explores practical applications, and explains theorem proofs using direct and indirect methods.

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