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Created by:

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Last updated:

September 23, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This course covers a collection of geometric techniques that apply broadly in modern algorithm design.

Course Curriculum

    • Linear algebra review Unlimited
    • Properties of the Laplacian Unlimited
    • Courant-Fischer and Rayleigh quotients Unlimited
    • (Lazy) random walks Unlimited
    • Monte Carlo methods continued Unlimited
    • Diameters and eigenvalues, expander graphs Unlimited
    • Nonblocking routing networks Unlimited
    • Local and almost-linear time clustering Unlimited
    • Sparsification (combinatorial and spectral) Unlimited
    • Spectral sparsification (cont.), introduction to convex geometry Unlimited
    • Polar of a convex body, separating Unlimited
    • Separating hyperplanes (cont.) Unlimited
    • Brunn-Minkowski inequality (cont.) Unlimited
    • Approximating the volume of a convex body Unlimited
    • Random sampling from a convex body (cont.) Unlimited
    • Concentration of measure and the isoperimetric inequality Unlimited
    • Johnson-Lindenstrauss theorem (cont.) Unlimited
    • Lattices, fundamental parallelepiped and dual of a lattice Unlimited
    • Minkowski’s theorem, shortest/closest vector problem Unlimited
    • LLL algorithm for lattice basis reduction Unlimited
    • Iterative methods to solve linear systems, steepest descent Unlimited
    • Convergence analysis of steepest descent and conjugate gradients Unlimited
    • Preconditioning on Laplacians, ultra-sparsifiers Unlimited
    • Multiplicative weights Unlimited
    • Multiplicative weights and applications to zero-sum games Unlimited

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Massachusetts Institute of Technology
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