Instructor: John Voight

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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