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Lecture
Stein Algorithm: Polynomial Identity Testing
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Polynomials, Division, and Ideals
Explores polynomials, their operations, and the concept of ideals in polynomial rings.
Polynomials: Operations and Properties
Explores polynomial operations, properties, and subspaces in vector spaces.
Shortest Path Algorithms: BFS and Dijkstra
Explores Breadth-First Search and Dijkstra's algorithm for finding shortest paths in graphs.
Polynomials: Rings and Operations
Covers the basics of polynomials, focusing on rings, operations, and properties.
Graphical Models: Probability Distributions and Factor Graphs
Covers graphical models for probability distributions and factor graphs representation.
Linear Combinations and Vector Spaces
Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.
Linear Transformations: Matrices and Kernels
Covers linear transformations, matrices, kernels, and properties of invertible matrices.
Master Theorem: Time Complexity Analysis
Introduces the Master Theorem for analyzing algorithm time complexity through problem subdivision and formula application.
Complex Roots and Polynomials
Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.