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.
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.
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.
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.
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.
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.