Syllabus

Date Notes Topics
Sep 6 1.1, 1.2 Fields, vector spaces
Sep 10 1.2–1.3 Properties of vector spaces, linear combinations
Sep 13 1.4, 1.5 Linear combinations, subspaces
Sep 17 1.5, 2.1 Direct sums, linear maps
Sep 20 2.2, 2.3 Kernel and image, vector spaces of linear maps
Sep 24 2.4, 3.1 Isomorphisms, spans
Sep 27 3.2, 3.3 Linear dependence/independence, finitely generated vector spaces
Oct 1 3.4 Basis and dimension
Oct 4 3.4, 3.5 Basis and dimension, the Dimension Theorem
Oct 11 3.5–3.7 The Dimension Theorem, dimensions of spaces of linear maps, dual spaces
Oct 15 3.7, 4.1 Dual spaces, the matrix of a linear map
Oct 18 4.1, 4.2 The matrix of a linear map, similar matrices
Oct 22–26 Reading week
Oct 29 4.3, 4.4 Gaussian elimination, the rank of a matrix
Nov 1 5.1, 5.2 Multilinear maps, the determinant
Nov 5 1.1–4.4 Midterm test
Nov 8 5.3, 5.4 Properties of the determinant
Nov 12 6.1 Inner product spaces
Nov 15 6.2 Orthogonality
Nov 19 6.3 Adjoints
Nov 22 TBA Eigenvectors and eigenvalues
Nov 26 TBA Diagonalization
Nov 29 TBA Diagonalization of symmetric matrices
Dec 3 TBA Diagonalization of symmetric matrices
Dec 5 N/A Review