Stony Brook University 3 credits MAT
Vector spaces: Cayley-Hamilton Theorem, Jordon normal form, bilinear forms, signature, tensor products, symmetric and exterior algebras. Homological algebra: categories and functors, universal and free objects, exact sequences, extensions. Representation theory for finite groups: irreducible representations and Shurβs Lemma, characters, orthogonality. Galois theory: splitting fields, finite fields, extension fields of various types, Galois polynomial and group, fundamental theorem of Galois theory, symmetric functions. 3 credits Prerequisite: MAT 534 Grading Letter graded (A, A-, B+, etc.)
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