Polynomial Identity Testing

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Related lectures (29)

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Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Interlacing Families and Ramanujan Graphs

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

Graphical Models: Representing Probabilistic Distributions

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

Matroids: Matroid Intersection

Covers the concept of matroids, focusing on matroid intersection and the properties of subsets of a ground set.

Interlacing Families and Ramanujan Graphs

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

Differentiable Functions and Lagrange Multipliers

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

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Unweighted Bipartite Matching

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.

Building Ramanujan Graphs

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