Probabilistic Methods Courses and Certifications

Centre International de Rencontres Mathématiques

Probabilistic Methods - Entropy Compression

Explore probabilistic methods and entropy compression in mathematics through an in-depth lecture by František Kardoš at CIRM's ALEA days conference.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Stanford CS109 - Future of Probability - Lecture 28

Explore the future of probability in computer science with Stanford's expert insights, covering advanced concepts and their applications in emerging technologies.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Existence of Graphs with High Girth and High Chromatic Number

Delve into probabilistic methods in combinatorics, exploring Erdős's groundbreaking proof of graphs with high girth and chromatic number through elegant mathematical reasoning.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Lower Bounds to Ramsey Numbers - MIT 18.226 Probabilistic Methods in Combinatorics

Delve into probabilistic methods in combinatorics, exploring Ramsey numbers through alteration techniques and the Lovász Local Lemma for advanced mathematical problem-solving.

• YouTube
• 43 minutes
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Markov, Chebyshev, and Chernoff Inequalities in Probabilistic Analysis

Master fundamental probabilistic inequalities - Markov, Chebyshev, and Chernoff - and their applications in combinatorial analysis through clear mathematical explanations and examples.

• YouTube
• 17 minutes
• On-Demand
• 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
• On-Demand
• Free Video

Crossing Number Inequality in Graph Theory and Combinatorics

Explore the probabilistic method in combinatorics and its application to graph theory, focusing on proving the crossing number inequality in graph drawings.

• YouTube
• 18 minutes
• On-Demand
• Free Video

Independent Sets and Turán's Theorem

Explore the probabilistic method in combinatorics through graph theory, focusing on independent sets, cliques, and the fundamental principles behind Turán's theorem.

• YouTube
• 15 minutes
• On-Demand
• Free Video

IEEE

Stochastic Weighted Matching - 1-Epsilon Approximation

Explore stochastic weighted matching algorithms, including Monte Carlo analysis, vertex-independent matching, and greedy approaches for efficient approximation solutions.

• YouTube
• 29 minutes
• On-Demand
• Conference Talk

Simons Institute

On Perfectly Friendly Bisections of Random Graphs

Explores vertex-isoperimetry expansion in random graphs, using boolean function tools to prove equipartition results with specific neighbor distribution properties across partitions.

• YouTube
• 57 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Probabilistic Methods in Data Science - Lecture by Aurélien Garivier

Exploration des méthodes probabilistes et d'optimisation en science des données, mettant l'accent sur les techniques analytiques et algorithmiques pour traiter efficacement les grands volumes de données.

• YouTube
• 1 hour 50 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Graph Alignment: Informational and Computational Limits - Lecture 2

Explore graph alignment challenges, focusing on informational and computational limits. Gain insights into probabilistic and optimization methods for data science applications.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Graph Alignment: Informational and Computational Limits - Lecture 1

Explore graph alignment challenges, focusing on informational and computational limits in data science. Gain insights into probabilistic methods for analyzing complex network structures.

• YouTube
• 1 hour
• On-Demand
• Free Video