Math 22
Linear algebra with applications
Last updated August 18, 2014

## Syllabus

The following is a tentative syllabus for the course.
It will be updated as the class proceeds to reflect the actual progress we cover as well as the homework that will be assigned daily after class and due every friday at 12:00 PM.

Actual syllabus
Lectures Sections in Text Brief Description Practice homework Turn-in homework
6/20 1.1 Linear systems. 1.1: 5,6,8,14,16,19,20; App: 33,34 1.1: 7,13,21,25 (due 6/27)
6/21 (special time 8:00am) 1.2 Row reduction. 1.2: 1,2,5,9,10,12,14 1.2: 11,13
6/23 1.3
1.4
Vectors, linear combinations
Ax=b
1.3: 12,13,14; App: 29,30;
1.4: 6,8,11,12,14
1.3: 26;
1.4: 10,25
6/25 1.4
1.5
Matrix equations
Solutions to homogeneous and non-homogeneous systems
1.4: 17,18,19,20
1.5: 1,2,4,6,11,18,33

1.5: 3,12
6/27 1.6 Applications 1.6: 2, 3 (a,b), 4 (a), 7,8,9,14,15 1.6: 12 (due 7/4)
6/30 1.7 Linear dependence 1.7: 11,12,14,15,16,17,18,19,31 1.7: 13,32
7/2 1.8 Linear transformations. 1.8: 4,5,10,12,32 1.8: 7,9,11,17,19,20,33
7/3 (x-hour) 1.9 The Matrix of a linear transformation 1.9: 1,4,5,15,16,18,20 1.9: 3,17,19,25,27 (due 7/11)
7/7 2.1 Matrix algebra 2.1: 6,7,8,9,12,28 2.1: 5,10,27
7/9 2.2 Inverse of a matrix 2.2: 2,4,7,8,33,34 2.2: 30,32,35
7/10 (x-hour) 2.3 Invertible matrix theorem; review 2.3: 1,2,3,5,15,16,17,18,22 2.3: 6,8 (due 7/18)
7/11 1.10, 2.4, 2.5, 2.6, 2.7 Applications (not an exam topic) See extra credit HW
7/14 2.8 Subspaces of Rn and bases. 2.8: 1,2,3,4,5,11,13,23,25 2.8: 12,18,24,26
7/16 2.9
3.1
Coordinates and dimension
Determinants
2.9: 3,5,9,11,13,16
3.1: 1-6
2.9: 4,6,10,12,14,15
7/18 3.1
3.2
3.3
Determinants
Properties
Applications
3.1: 7,9,11,13
3.2: 5,7,9,11,13,21,23,25
3.3: 1,3,5,11,13
3.1: 10,12,14 (due 7/25)
3.2: 22
7/21 5.1 Eigenvalues 5.1: 3,4,6-12,15-20 5.1: 2,5,13,14
7/23 5.2 Characteristic equation 5.2: 3-5, 7-10, 12-17, 25 5.2: 6, 11
7/25 5.3 Diagonalization 5.3: 2,6,7,8,15,16,17,19,20 5.3: 1,3,4,5,9,10,11,12,13,14 (due 8/1)
7/28 4.4, 4.7, 5.4 Change of basis 4.7: 9,10
5.4: 13-17
Review complex numbers (Appendix B)
7/30 5.5
Off book
Complex eigenvalues
Jordan form
5.5: 1-20
Extra credit homework 3 (to be posted)
Skim through the PageRank papers found here
8/1 4.9

5.8
Markov chains.
PageRank.
Power method.
4.9: 1-14
Extra credit #3
5.8: 1-6
Review dot product and length for R2, R3 (see old calc books)
8/4 6.1
6.2
Geometry in Rn
Orthogonal sets
6.1 :1-10, 12,13,15,16
6.2 :1-4,6-9, 17-20
6.1 :11, 14, 17,18
6.2 :5,10,21
8/6 6.2, 6.3 Projections 6.2: 11-13,16
6.3: 1-5,7,8,10,11,13-16
6.2:14,15
6.3: 6,9,12
8/7 (x-hour) 6.5 Least squares 6.5: 1,3,5-10,12,14 6.5: 2,4,11,13 (due 8/15)
8/8 6.6
7.1
Regression
Orthogonal diagonalization
6.6: 8a, 9a, 10a
7.1: 1-16,18,20-22
6.6: 3,4,7a
7.1: 17,19
8/11 No class
8/13 7.2 Quadratic forms 7.2: 1-6 7.2: 8
8/14 (x-hour) 7.3 Contrained optimization 7.2: 9-14
7.3: 1-4, 7-10
7.3: 5,6 (note: any homework from now on is not to be turned in)
8/15 7.4 SVD 7.4: 1-6,8,10,12 7.4: 7,9,11
8/18 7.5 Applications of the SVD 7.5: 2,4,8 7.5: 1,3,7,9
8/20 Review

Tentative syllabus
Lectures Sections in Text Brief Description Practice homework Turn-in homework

Nicolas Petit
Last updated August 18, 2014