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