Lectures related to Properties of X/G

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

Mathematical Analysis: Functions and Composition

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

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

Tangent to Graph of a Function

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

Implicit Functions Theorem

Explores the implicit functions theorem and the equation of the tangent plane in a graph.

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Real Functions of Two Real Variables

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

Cayley Graphs: Properties and Applications

Explores the properties and applications of Cayley graphs in group theory and network analysis.

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Stein Algorithm: Polynomial Identity Testing

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

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.

Shortest Path Algorithms: BFS and Dijkstra

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

Rolle's Theorem: Applications and Examples

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

Separation Conditions: Graph and Saturations

Discusses separation conditions, graph, and saturations in equivalence relations on a space.

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Graph Algorithms: Modeling and Traversal

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

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.

Derivative: Application Examples

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

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Extreme Points and Function Extrema

Explores finding extrema of functions over compact sets and edge parametrization.