Lectures related to Graph (discrete mathematics)

Exponential Family

Covers the concept of the exponential family and discusses forward and backward maps, expensive computations, parameters, functions, and convexity.

Minimum Spanning Trees: Prim's Algorithm

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

Graph Algorithms: Modeling and Traversal

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

Mathematical Analysis: Functions and Composition

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

Shortest Path Algorithms: BFS and Dijkstra

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

Graph Theory and Network Flows

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

Connectivity in Graph Theory

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

Graphical Models: Representing Probabilistic Distributions

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

Networked Control Systems: Opportunities

Explores coordination in networked control systems, graph theory, and consensus algorithms.

Graph Algorithms: Modeling and Representation

Covers the basics of graph algorithms, focusing on modeling and representation of graphs in memory.

Fixed Points in Graph Theory

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

Differentiable Functions and Lagrange Multipliers

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

Max Flav-Min Cut in Directed Graphs

Covers the concept of maximum flow-minimum cut in directed graphs with capacity constraints.

Szemerédi Regularity Lemma

Explores the Szemerédi Regularity Lemma, e-regularity in bipartite graphs, supergraph structure, and induction techniques.

Graph Theory Fundamentals

Covers the fundamentals of graph theory, including vertices, edges, degrees, walks, connected graphs, cycles, and trees, with a focus on the number of edges in a tree.

Graph Algorithms II: Traversal and Paths

Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.

Interlacing Families and Ramanujan Graphs

Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.

Model Selection and Local Geometry

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

Sparsest Cut and Concurrent Flow

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

Consensus Algorithms: Weight Assignment and Applications

Explores the design of graph weights for consensus and applications in sensor networks.