Lectures related to Relations and Sequences: Well-ordered Sets and Geometric Series

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Explores strong induction as a proof method and demonstrates its application in proving a theorem about positive integers.

Introduces the properties and structure of real numbers, emphasizing completeness and the Archimedean property.

Covers the definition and properties of Markov chains, including transition matrix and examples.

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

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