Lectures related to Untitled | EPFL Graph Search

Tangent to Graph of a Function

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

Mathematical Analysis: Functions and Composition

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

Real Functions of Two Real Variables

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

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.

Cayley Graphs: Properties and Applications

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

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Functions and Integers

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

Shortest Path Algorithms: BFS and Dijkstra

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

Terminologie: Functions Graph Discussion

Covers the terminology related to the graph of a function and intervals.

Transformations Affines

Covers the concept of affine transformations in functions, including shifting and compressing functions.

Graphical Definition: Level Sets and Domains

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

Graph Algorithms: Modeling and Traversal

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

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.

Equation of Tangent Hyperplane

Explores finding the equation of a tangent hyperplane to a function and its implications.

Real Functions: Graphs and Properties

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

An Example: Graph of a Function

Analyzes a function's graph, discussing local and global extrema and concavity intervals.