Lectures related to Cayley Graphs: Properties and Applications

Mathematical Analysis: Functions and Composition

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

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Graph Algorithms: Modeling and Traversal

Covers graph algorithms, modeling relationships between objects, and traversal techniques like BFS and DFS.

Shortest Path Algorithms: BFS and Dijkstra

Explores Breadth-First Search and Dijkstra's algorithm for finding shortest paths in graphs.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Graph and Diagonal

Discusses the graph of a relation and the concept of separation.

Real Functions of Two Real Variables

Explores real functions of two real variables, illustrating domains, images, and graphs.

Restriction, Prolongement et Graphe d'une Fonction

Explains the relationship between two functions through restriction and prolongation, emphasizing the importance of defining a function by its graph.

Minimum Spanning Trees: Prim's Algorithm

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Graphical Models: Representing Probabilistic Distributions

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

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Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Fixed Points in Graph Theory

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Properties of X/G

Explores the properties of the quotient space X/G when X is compact and sometimes separated.

Derivative: Application Examples

Explores examples of using derivatives to find tangent lines and points on graphs.

Functions and Integers

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

Automorphism groups of trees and graphs

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

Graphs in Deep Learning: Applications and Techniques

Explores the role of graphs in deep learning, focusing on their structure, applications, and techniques for processing graph data.

Expander Graphs: Properties and Eigenvalues

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

Graphs: Properties and Representations

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