Lectures related to Exponential Family

Mathematical Analysis: Functions and Composition

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

Convex Functions

Covers the properties and operations of convex functions.

Connectivity in Graph Theory

Covers the fundamentals of connectivity in graph theory, including paths, cycles, and spanning trees.

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.

Graphical Models: Representing Probabilistic Distributions

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

Graph Theory: Connectivity and Properties

Explores the properties of undirected and directed graphs, emphasizing connectivity and network topology modeling.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Functions and Integers

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

Transformations Affines

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

Terminologie: Functions Graph Discussion

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

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.

Sparsest Cut and Concurrent Flow

Covers sparsest cut, NP-completeness, Bougains Theorem, and concurrent flow in graphs.

Graph Algorithms: Modeling and Traversal

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

Laplacian Matrix: Properties and Examples

Explores the Laplacian matrix, time-varying consensus theorems, and balanced graphs in networked control systems.

Model Selection and Local Geometry

Explores model selection challenges in causal models and the impact of local geometry on statistical inference.

Tangent to Graph of a Function

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

Networked Control Systems: Laplacian Matrix and Consensus in Continuous Time

Explores the Laplacian matrix properties and consensus in continuous time.

Laplacian Matrix in Networked Control Systems

Explores the Laplacian matrix in electric and mechanical networks, consensus, and properties of Laplacian matrices in networked control systems.

Networked Control Systems: Coordination Among Agents

Explores coordination among agents in networked control systems through graph theory and real-world examples.