Instructor: John Voight
Course on canvas.dartmouth.edu.⇗
Syllabus
Course Summary: Date Details Mon Sep 12 Finite-dimensional vector spaces Tue Sep 13 Matrices, change of basis Wed Sep 14 Bases, sums and direct sums, free vector spaces Fri Sep 16 Quotients, factors through, rank-nullity Mon Sep 19 Exact sequences, splitting Wed Sep 21 Duals, pullback Fri Sep 23 Annihilators, bilinear forms Mon Sep 26 Kernels, symmetric bilinear forms, orthogonal group Wed Sep 28 Diagonalization, adjoints, real inner product spaces Fri Sep 30 Sesquilinear forms, unitary, Hermitian, complex inner product spaces Mon Oct 3 Diagonalizability, upper triangularizability Tue Oct 4 SVD, matrix factorizations Wed Oct 5 Normal operators, spectral theorem Mon Oct 10 Tensor products Wed Oct 12 Multilinear forms, symmetric and exterior powers, determinants Fri Oct 14 Algebras Mon Oct 17 Categories, functors Wed Oct 19 Natural transformations Mon Oct 24 Universal properties, modules Wed Oct 26 Free modules, quotients, exact sequences, splitting Fri Oct 28 Projective modules Mon Oct 31 Modules over PIDs Wed Nov 2 Canonical forms Fri Nov 4 Linear representations, decomposable, Maschke's theorem Mon Nov 7 Operations on linear representations Wed Nov 9 Characters, Schur's lemma Fri Nov 11 Character tables, orthogonality Mon Nov 14 Wrap up