Overview
Instructor  Dr. Armin Straub
MSPB 313 straub@southalabama.edu (251) 4607262 (please use email whenever possible) 
Office hours  MWF, 911am, or by appointment
Held virtually using Zoom; please make an appointment by email at least 2 hours in advance. 
Class schedule  MWF, 8:008:55am, in MSPB 410
Due to COVID restrictions, you may only attend those meetings assigned to the cohort you signed up for. 
Midterm exams  The tentative dates for our two midterm exams are:
Friday, February 26 Monday, April 5 
Final exam  Monday, May 3 — 8:0010:00am 
Online grades 
Homework Scores
Exams: USAonline (Canvas) 
Syllabus  syllabus.pdf 
Assignments and course material
In order to be able to view the lecture recordings, you need to be logged into USAonline (Canvas). If you are still running into access issues, then please view the recordings through Panopto Video in our course page on Canvas.
Dates  Assignments and course material  

#1  01/20 01/22 01/25 
Assignments:
Homework Set 1 (due 2/1) Lecture notes:
Lecture recordings:
lecture011linearalgebra.mp4
(corresponding PDF)
lecture012linearalgebrapart2.mp4
(corresponding PDF)
lecture021gaussianelimination.mp4
(corresponding PDF)
lecture022ludecomposition.mp4
(corresponding PDF)
lecture03nullspace.mp4
(corresponding PDF)
Class schedule:
01/20: online using prerecorded lectures
01/22: inperson meeting 01/25: online using prerecorded lectures 
#2  01/27 01/29 02/01 
Assignments:
Homework Set 2 (due 2/8) Lecture notes:
Lecture recordings:
lecture041reviewdeterminants.mp4
(corresponding PDF)
lecture042revieweigenvectors.mp4
(corresponding PDF)
lecture043diagonalization.mp4
(corresponding PDF)
lecture051orthogonality.mp4
(corresponding PDF)
lecture052orthogonalcomplements.mp4
(corresponding PDF)
lecture06fundamentaltheorem.mp4
(corresponding PDF)
Class schedule:
01/27: inperson meeting
01/29: inperson meeting 02/01: online using prerecorded lectures 
#3  02/03 02/05 02/08 
Assignments:
Homework Set 3 (due 2/15) Lecture notes:
Lecture recordings:
lecture071consistency.mp4
(corresponding PDF)
lecture072leastsquares.mp4
(corresponding PDF)
lecture08leastsquareslines.mp4
(corresponding PDF)
lecture091leastsquaresdatafitting.mp4
(corresponding PDF)
lecture092orthogonalprojections.mp4
(corresponding PDF)
Class schedule:
02/03: inperson meeting
02/05: inperson meeting 02/08: online using prerecorded lectures 
#4  02/10 02/12 02/15 
Assignments:
Homework Set 4 (due 2/22) Lecture notes:
Lecture recordings:
lecture10projectionmatrices.mp4
(corresponding PDF)
lecture111orthogonalbases.mp4
(corresponding PDF)
lecture112orthogonalbasesexamples.mp4
(corresponding PDF)
lecture12gramschmidt.mp4
(corresponding PDF)
Class schedule:
02/10: inperson meeting
02/12: inperson meeting 02/15: online using prerecorded lectures 
#5  02/17 02/19 02/22 02/24 
Assignments:
Homework Set 5 (due 2/26) Lecture notes:
Lecture recordings:
lecture13qrdecomposition.mp4
(corresponding PDF)
lecture141orthogonalmatrices.mp4
(corresponding PDF)
lecture142diagonalizability.mp4
(corresponding PDF)
lecture15spectraltheorem.mp4
(corresponding PDF)
Class schedule:
02/17: inperson meeting
02/19: inperson meeting 02/22: online using prerecorded lectures 02/24: online via Zoom zoom0224.mp4
(corresponding PDF)

lectures0115.pdf (all lecture notes up to now in one big file)  
02/26 
Midterm Exam #1
Practice material:
Format of the exam:
 
#6  03/01 03/03 03/05 
Assignments:
Homework Set 6 (due 3/14) Lecture notes:
Lecture recordings:
lecture16powersofmatrices.mp4
(corresponding PDF)
lecture17markovchains.mp4
(corresponding PDF)
lecture18pagerankalgorithm.mp4
(corresponding PDF)
Class schedule:
03/01: online using prerecorded lectures
03/03: inperson meeting 03/05: inperson meeting 
#7  03/08 03/10 03/12 03/15 
Assignments:
Homework Set 7 (due 3/22) Lecture notes:
Lecture recordings:
lecture19recurrenceequations.mp4
(corresponding PDF)
lecture20solvingrecurrences.mp4
(corresponding PDF)
lecture21projectionmatricesagain.mp4
(corresponding PDF)
Class schedule:
03/08: online using prerecorded lectures
03/10: student holiday 03/12: inperson meeting 03/15: online using prerecorded lectures 
#8  03/17 03/19 03/22 
Assignments:
Lecture notes:
Lecture recordings:
lecture22reflections.mp4
(corresponding PDF)
lecture22exponential.mp4
(corresponding PDF)
lecture231systemsofdiffeqs.mp4
(corresponding PDF)
lecture232solvingsystemofdiffeqs.mp4
(corresponding PDF)
lecture24detosystem.mp4
(corresponding PDF)
lecture24jnf1.mp4
(corresponding PDF)
Class schedule:
03/17: inperson meeting
03/19: inperson meeting 03/22: online using prerecorded lectures 
#9  03/24 03/26 03/29 03/31 04/02 
Assignments:
Lecture notes:
Lecture recordings:
lecture25jnf2.mp4
(corresponding PDF)
lecture25jnf3.mp4
(corresponding PDF)
lecture26dejnf.mp4
(corresponding PDF)
lecture27rotations.mp4
(corresponding PDF)
lecture27complex.mp4
(corresponding PDF)
Class schedule:
03/24: inperson meeting
03/26: inperson meeting 03/29: online using prerecorded lectures 03/31: inperson meeting 04/02: online via Zoom zoom0402.mp4
(corresponding PDF)

lectures1628.pdf (all lecture notes since the previous exam in one big file)  
04/05 
Midterm Exam #2
Practice material:
 
#10  04/07 04/09 04/12 
Assignments:
Lecture notes:
Lecture recordings:
Class schedule:
04/07: inperson meeting
04/09: inperson meeting 04/12: online using prerecorded lectures 
#11  04/14 04/16 04/19 
Assignments:
Lecture notes:
Lecture recordings:
lecture32pseudoinverse1.mp4
(corresponding PDF)
lecture32pseudoinverse2.mp4
(corresponding PDF)
lecture33matrixapproximation.mp4
(corresponding PDF)
lecture34functionspaces.mp4
(corresponding PDF)
Class schedule:
04/14: inperson meeting
04/16: inperson meeting 04/19: online using prerecorded lectures 
#12  04/21 04/23 04/26 04/28 04/30 
Assignments:
Lecture notes:
Lecture recordings:
lecture35functionapproximation.mp4
(corresponding PDF)
lecture37fourierseries.mp4
(corresponding PDF)
Class schedule:
04/21: inperson meeting
04/23: inperson meeting 04/26: online using prerecorded lectures 04/28: inperson meeting 04/30: online via Zoom zoom0430.mp4
(corresponding PDF)

lectures2938.pdf (all lecture notes since the previous exam in one big file)  
05/03 
Final Exam
Practice material:

About the homework
 Homework problems are posted for each unit. Homework is submitted online, and you have an unlimited number of attempts. Only the best score is used for your grade.
Most problems have a random component (which allows you to continue practicing throughout the semester without putting your scores at risk).
 Aim to complete the problems well before the posted due date.
A 15% penalty applies if homework is submitted late.
 Collect a bonus point for each mathematical typo you find in the lecture notes (that is not yet fixed online), or by reporting mistakes in the homework system. Each bonus point is worth 1% towards a midterm exam.
The homework system is written by myself in the hope that you find it beneficial. Please help make it as useful as possible by letting me know about any issues!
Sage
As part of this course, we will explore the opensource free computer algebra system Sage to assist with more involved calculations.
If you just want to run a handful quick computations (without saving your work), you can use the text box below.
An easy way to use Sage more seriously is https://cocalc.com. This free cloud service does not require you to make an account or to install anything: select View Your CoCalc Projects..., followed by New and Sage worksheet and start computing. (To save your work for later, you can create a free account.)
Here are some other things to try:
 Sage makes solving least squares problems pleasant. For instance, to solve Example 45 in Lecture 8:
A = matrix([[1,2],[1,5],[1,7],[1,8]]); b = vector([1,2,3,3]) (A.transpose()*A).solve_right(A.transpose()*b)
 Sage can compute QR decompositions. For instance, we can have it do Example 70 in Lecture 13 for us:
A = matrix(QQbar, [[0,2,1],[3,1,1],[0,0,1],[0,0,1]]) A.QR(full=false)
The result is a tuple of the two matrices Q and R. If that is too much at once,A.QR(full=false)[0]
will produce Q, andA.QR(full=false)[1]
will produce R. (Can you figure out what happens if you omit thefull=false
? Check out the comment under "Variations" for the QR decomposition in the lecture sketch. On the other hand, theQQbar
is telling Sage to compute with algebraic numbers (instead of just rational numbers); if omitted, it would complain that square roots are not available.)