Lectures related to Binary Relations and Cartesian Products

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

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

Explains binary relations on a set and their properties with illustrative examples.

Explains binary relations, reflexive, symmetric, antisymmetric, and transitive relations on a set.

Covers logical expressions, sets, elements, and equivalence relations.

Covers equivalence relations, classes, and partitions of a set.

Covers the Cartesian product of sets and binary relations with detailed examples and graphical representations.

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

Explores properties of operations, equivalence relations, and logic basics.

Explores automorphisms of graphs, focusing on automorphism groups, Cayley-Abels graphs, and quasi-isometry.

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Explores the diagonalization of matrices and the conditions for exact diagonalization, with examples demonstrating the process.

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.

Explores Belief Propagation in graphical models, factor graphs, spin glass examples, Boltzmann distributions, and graph coloring properties.

Covers graph properties, representations, and traversal algorithms using BFS and DFS.

Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.

Covers the analysis of functions, composition, and mathematical induction.

Explores automorphism groups in trees and graphs, focusing on ends and types of automorphisms.