Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly. On the other hand, the weekly syllabus contained in on Canvas will always be accurate.

Lecture Date Sections in Text Brief Description
1 1/3 1.1, 6.1 Systems of linear equations; vectors (part 1)
2 1/5 1.2 Row reduction and echelon forms
3 1/8 1.2, 1.3 Reduced row echelon form; Vector equations
4 1/10 1.3, 1.4, 1.5 Vector equations; Matrix equations, the matrix equation Ax=b and its solutions
5 1/12 1.5, 1.7 Homogeneous systems, general solutions, particular solution, linear Independence
1/15 No class (MLK Day)
6 1/17 1.8 Introduction to linear transformations
7 1/18 (x-hour) 1.9 The matrix of a linear transformation
8 1/19 2.1 Matrix operations
9 1/22 2.2 Inverse of a matrix
10 1/24 2.3 Invertible Matrix Theorem
1/25 Exam 1
11 1/26 4.1, 4.2 Introduction to Vector Spaces, null space, column space, notion of a linear transformation
12 1/29 4.3 Linearly independent sets; bases
13 1/31 4.4 Coordinate systems
14 2/2 4.5, 4.6 Dimension; Rank
15 2/4 4.7, 5.4 Change of coordinates matrix and composition of linear transformations
16 2/7 3.1, 3.2 Determinants and properties of determinants
17 2/9 5.1, 5.2 Eigenvalues and the characteristic equation
18 2/12 5.2, 5.3 The characteristic equation, diagonalization
19 2/14 5.3, 5.4 Diagonalization and linear transformations
2/15 Exam 2
20 2/16 4.9, 5.8 Markov chains; Iteration method for eigenvalues; Google's page rank
21 2/19 6.1, 6.2 Inner products and orthogonality
22 2/21 6.3, 6.4 Projections; Gram-Schmidt process
23 2/23 6.5 Least-squares problems
24 2/26 7.1 Diagonalization of symmetric matrices
25 2/28 7.4 Application: Singular value decomposition (SVD)
26 3/1 7.5 Principal component analysis (PCA) and eigenfaces
27 3/4 Review for the final exam