Lectures related to Restriction, Prolongement et Graphe d'une Fonction

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.

Mathematical Analysis: Functions and Composition

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

Riemann Integral: Subdivisions and Volumes

Covers the concept of Riemann integral and volume calculation of closed pavements.

Graphical Definition: Level Sets and Domains

Covers the graphical definition of functions, focusing on level sets and domains.

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.

Tangent to Graph of a Function

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

Convex Functions

Covers the properties and operations of convex functions.

Optimal Transport: Cyclically Monotone Sets

Covers cyclically monotone sets in optimal transport theory and their properties.

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.

Functions and Integers

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

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Cayley Graphs: Properties and Applications

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

Graph Algorithms: Modeling and Traversal

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

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Stein Algorithm: Polynomial Identity Testing

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

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Shortest Path Algorithms: BFS and Dijkstra

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

Properties of X/G

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

Partial Derivatives: Understanding Tangents

Explores partial derivatives and their role in determining tangents to graphs.