Apprentice Program, Summer 2011 REU
Linear Algebra and Combinatorics

Instructor: László Babai

Home | What's New? | Synopsis | Problem sets | Notes | Further reading

What's New?

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The apprentice problem sets have been consolidated into a single file and separated from the class notes (see below).

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The course will develop the usual topics of linear algebra and illustrate them on highly unusual and often striking applications to combinatorics, discrete geometry, and discrete probability. Emphasis will be on creative problem solving and discovery.

The basic topics include permutations, determinants, linear transformations, the characteristic polynomial, Euclidean spaces, orthogonalization, the Spectral Theorem, linear algebra over finite fields. Application areas to be highlighted include, time permitting, extremal set theory, the spectral theory of graphs (expansion, mixing of random walks, independence number, Shannon capacity, etc.), k-wise independence of events, counting zero-patterns of polynomial maps, and more.

Class notes, problem sets

The online class notes (continually updated): Apprentice Problems (separated from class notes):

Prior years' notes.

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Further reading

REU 2011 Home

László Babai's home page

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