Functional analysis is a branch of mathematical analysis that studies vector spaces with limit-related structures and linear functions defined on them. It has its roots in the study of spaces of functions and transformations of functions, and is useful for the study of differential and integral equations. It is also used to extend theories of measure, integration, and probability to infinite dimensional spaces.
Stanford University
Autumn 2022
The course addresses both classic and recent developments in counting and sampling. It covers counting complexity, exact counting via determinants, sampling via Markov chains, and high-dimensional expanders.
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