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This course covers a collection of geometric techniques that apply broadly in modern algorithm design.
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English
English [CC]
FREE
- Learn basic syntax that can apply to any language.
- Learn what is a programming language and the basic concepts for beginners.
- Understand what is Javascript in it's truest form.
- Know the basic syntax of Javascript.
- Know some hidden quirks in Javascript.
Description
Course content
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- 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
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- 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
- Multiplicative weights Unlimited
- Multiplicative weights and applications to zero-sum games Unlimited
Instructor
Massachusetts Institute of Technology
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1916
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