Graph Theory Courses

Graph Neural Networks - Architectures and Message Passing - Lecture 5

Explore graph neural networks, their connections to MLPs and CNNs, message passing algorithms, and theoretical limitations on expressive power with practical implications.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Approximation Theory - Lecture 3

Explore how deep neural networks approximate functions through universal approximation theorems, Barron's theorem, and the role of depth in expressivity.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

Generalization Theory - Overparameterization, Double Descent, and Inductive Biases - Lecture 6

Explore overparameterization, double descent, and VC dimension limitations while understanding how inductive biases shape deep learning generalization.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Representation Learning - Theory - Lecture 13

Explore the theoretical foundations of representation learning, examining architectural inductive biases and neural network connections to Gaussian processes.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Basic Group Theory - Lecture 11

Explore fundamental group theory concepts including group definitions, subgroups, cosets, and Lagrange's theorem, culminating in a proof of Fermat's little theorem.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Search Theory and Price Dispersion - Lecture 9

Explore search theory, including search costs and price dispersion, in this industrial organization lecture by Glenn Ellison at MIT.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Threshold for a Random Graph to Contain a Triangle - MIT 18.226

Explore probabilistic methods to determine when random graphs develop triangles, using first and second moment analysis techniques in combinatorial mathematics.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Extremal Set Theory - Sperner's Theorem

Explore the fascinating world of Sperner's Theorem and learn how to determine the maximum number of subsets possible in an n-element set without subset containment.

• YouTube
• 13 minutes
• Self-Paced
• Free Video

Extremal Set Theory - Intersecting Families and the Erdős-Ko-Rado Theorem

Explore the probabilistic method in combinatorics through intersecting families of sets, featuring the Erdős-Ko-Rado theorem and its applications in extremal set theory.

• YouTube
• 17 minutes
• Self-Paced
• Free Video

Production Theory - Lecture 5

Explore the fundamentals of production theory, including production functions, short and long-run production, returns to scale, and productivity in this MIT microeconomics lecture.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Divisibility - Number Theory and Applications Through GCD and Extended Euclidean Algorithm - Lecture 8

Explore number theory fundamentals through divisibility, greatest common divisor (GCD), and the Extended Euclidean Algorithm in this MIT mathematics lecture.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Graph Matching - Maximum Weight, Stable, and Bipartite Matching - Lecture 12

Explore graph matching theory including maximum weight matching, stable matching, and bipartite/non-bipartite graph algorithms in this MIT mathematics lecture.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Introduction to Nonequilibrium Theory: Onsager Reciprocity and Maximum Entropy Production - Lecture 21

Delve into advanced thermodynamics concepts including Onsager reciprocity, thermal conductivity tensors, and nonequilibrium theory through detailed mathematical derivations and practical applications.

• YouTube
• 1 hour 39 minutes
• Self-Paced
• Free Video

Principles of Microeconomics: Producer Theory and Cost Analysis - Lecture 6

Explore producer theory fundamentals, including short-run and long-run cost curves, supply curve origins, and cost measurement techniques in microeconomics.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Production Theory - Lecture 5

Explore production theory concepts including production functions, short and long-run production, returns to scale, and productivity with Prof. Gruber in this microeconomics lecture.

• YouTube
• 48 minutes
• Self-Paced
• Free Video