Stony Brook University 3 credits MAT
Groups: normal subgroups, quotient groups, Lagrange’s theorem, class formula, finite p-groups and solvable groups, Sylow’s theorems, finitely generated abelian groups. Rings and modules: subrings, fields, prime and maximal ideals, quotient rings, ID’s, PID’s, UFD’s, polynomial rings, field of fractions, the Wedderburn theorem, Hilbert basis theorem, finitely generated modules over a PID. Vector spaces: basis, linear maps and matrices, dual spaces, determinants, eigenvalues and vectors, inner products, spectral theorem for normal operators. 3 credits Prerequisite: Mathematics PhD student or completion of MAT 524 or equivalent course with departmental permission. Grading Letter graded (A, A-, B+, etc.)
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