SES #	TOPICS	KEY DATES
1	The geometry of linear equations
2	Elimination with matrices
3	Matrix operations and inverses
4	LU and LDU factorization
5	Transposes and permutations	Problem set 1 due
6	Vector spaces and subspaces
7	The nullspace: Solving Ax = 0
8	Rectangular PA = LU and Ax = b	Problem set 2 due
9	Row reduced echelon form
10	Basis and dimension
11	The four fundamental subspaces	Problem set 3 due
12	Exam 1: Chapters 1 to 3.4
13	Graphs and networks
14	Orthogonality	Problem set 4 due
15	Projections and subspaces
16	Least squares approximations
17	Gram-Schmidt and A = QR	Problem set 5 due
18	Properties of determinants
19	Formulas for determinants
20	Applications of determinants	Problem set 6 due
21	Eigenvalues and eigenvectors
22	Diagonalization
23	Markov matrices	Problem set 7 due
24	Review for exam 2
25	Exam 2: Chapters 1-5, 6.1-6.2, 8.2
26	Differential equations
27	Symmetric matrices
28	Positive definite matrices
29	Matrices in engineering	Problem set 8 due
30	Similar matrices
31	Singular value decomposition	Problem set 9 due
32	Fourier series, FFT, complex matrices
33	Linear transformations
34	Choice of basis	Problem set 10 due
35	Linear programming
36	Course review
37	Exam 3: Chapters 1-8 (8.1, 2, 3, 5)
38	Numerical linear algebra
39	Computational science
40	Final exam