Lectures related to Partial Ordering: Relations, Sequences, Summation

Introduces the theory of categories through examples and discusses the product of categories.

Covers the combination of lattice elements, partial orders, complete lattices, and Tarski's Fixed Point theorem.

Explores inverse limits, profinite completions, and Hausdorff topologies in group theory and topology.

Introduces binary relations, functions, and various types of relations in sets.

Explores entropy theory, compression without loss, and the efficiency of the Shannon-Fano algorithm in data compression.

Covers fundamental concepts related to integers, including properties of well-ordered sets and the principle of induction.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Introduces posets, Hasse diagrams, and equivalence relations on sets.