Lectures related to Ordinal number

Covers strings, countable sets, cardinality, and the concept of countability, exploring the countability of various sets and Cantor diagonalization.

Explores the Euclidean norm properties, special cases, and applications of the Cauchy-Schwarz inequality.

Explains the definitions and properties of maximum, minimum, supremum, and infimum in real numbers.

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Covers the relations between the ideal class group and proper fractional ideals.

Covers proofs by mathematical induction and the number of subsets of a finite set.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Explores counting infinite sets and decision problems, showcasing the limits of computation in solving certain undecidable problems.