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MATH-467: Probabilistic methods in combinatorics

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Lectures in this course (56)

Expander Graphs: Properties and Eigenvalues Log in to Mediaspace to watch this video

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Ramanujan Graphs: Generating Functions and Expander Graphs Log in to Mediaspace to watch this video

Explores Ramanujan graphs, generating functions, non-backtracking walks, and expander graphs in relation to NP-hard problems.

Building Ramanujan Graphs Log in to Mediaspace to watch this video

Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.

Polynomial Averaging: Root Pairing Log in to Mediaspace to watch this video

Delves into the concept of averaging polynomials and the significance of pairing up roots.

Interlacing Polynomials Log in to Mediaspace to watch this video

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

Interlacing Families and Ramanujan Graphs Log in to Mediaspace to watch this video

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Interlacing Families and Ramanujan Graphs Log in to Mediaspace to watch this video

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

Ramanujan Graphs: Constructions and Similarities Log in to Mediaspace to watch this video

Explores Ramanujan graphs' constructions, matching polynomials, perfect matchings, and universal covers, along with quantitation and qualitative aspects.

Markov's Inequality and Hoeffding's Lemma Log in to Mediaspace to watch this video

Introduces Markov's inequality and Hoeffding's lemma to analyze random variables' behavior.

Reformulating Problems: Tools and Intuition Log in to Mediaspace to watch this video

Focuses on open problems and the importance of reformulating problems with better tools and intuition.

Partial Differential Equations Log in to Mediaspace to watch this video

Covers the basics of Partial Differential Equations, including the Laplace equation, heat equation, and wave equation.

Linearity of Expectation: First Moment Method Log in to Mediaspace to watch this video

Introduces Linearity of Expectation and the First Moment Method, explores probability theory problems like Buffon's Needle, and discusses transitive tournaments and Ham paths.

Stirling's Formula: Applications and Embeddings Log in to Mediaspace to watch this video

Explores Stirling's formula applications, polarization in vectors, and graph embeddings in Euclidean space.

Graph Theory Basics Log in to Mediaspace to watch this video

Introduces graph theory basics, Ramsey theory, and graph coloring concepts.

Graph Theory Fundamentals Log in to Mediaspace to watch this video

Explores fundamental graph theory concepts, Erdős' results, Chromatic Lemma, and Union Bound theorem in graph theory.

Second Moment Method Log in to Mediaspace to watch this video

Explores the Second Moment Method and variance of random variables, including covariance and independence.

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