Math 221 Course Webpage

Linear Algebra and Applications

Fall 2021, Duke University


General information | Course description | Lecture and covid policies | Assignments | Homework and lecture schedule | Grading | Links | Fine print

General information

Goal: Students will become proficient in both using and understanding the theory and algorithms of linear algebra and will learn how to write rigorous mathematical arguments.

Lectures: Tuesdays and Thursdays
      12:00 – 13:15, Physics Building 119 (Section 02)

Text: Linear Algebra: A Geometric Approach, by Ted Shifrin and Malcolm Adams, second edition.
In past semesters, this textbook has been available for 3-hour checkout at the Duke Libraries; search the Libraries' Top Textbooks program.

Contact information for the Instructor

Name: Professor Ezra Miller
Address: Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320
Office: Physics 209
Phone: (919) 660-2846
Email: ezramath.duke.edu   —   this is the primary mode of contacting me!
Zoom: https://duke.zoom.us/my/ezra.miller
Webpage: https://math.duke.edu/people/ezra-miller
Course webpage: you're already looking at it... but it's https://services.math.duke.edu/~ezra/221/221.html
Office hours: Monday, 16:15 – 17:15
                        Thursday, 13:15 – 14:30

Help Room

Mondays and Thursdays, 19:00 - 22:00 and other times.
See here for more information

Emergency procedures

What to do in an emergency
Duke|ALERT


Course description

Goal: Students will become proficient in both using and understanding the theory and algorithms of linear algebra, and they will learn how to write rigorous mathematical arguments.

Course content: Chapters 1 – 7 of the course text, by Shifrin & Adams
Most items constitute one lecture each; some fill two lectures:

Prerequisite: Second-semester calculus (Math 122, 112L, or 122L)


Lecture and covid policies

Policies regarding covid


Assignments

Policies regarding graded work


Homework and lecture schedule

This schedule reflects the current plan, but it is subject to change. The exam schedule, however, is fixed.

If a lecture or assignment hasn't been posted, and you think it should have been, then please do email me. Sometimes I encounter problems (such as, for example, the department's servers going down) while posting assignments; other times, I might simply have forgotten to copy the updated files into the appropriate directory, or to set the permissions properly.

Read and study the text carefully before attempting the assignments. Make sure you fully understand the given proofs and examples. Note that there are examples in the text similar to most of the homework problems. The material in gray shaded boxes consists of definitions; learn them precisely. (Often when students say they do not know how to do a problem it is because they don't know the definitions of the terms in the problem.) The material in blue shaded boxes introduces points of logic and techniques of proof that you will find helpful in writing your arguments. If you have trouble understanding something in the text after working on it for a while, then see me in office hours or e-mail me.

Lecture notes

You can download all lectures in one PDF file.
Alternatively, for notes on an individual lecture, click on the date in the table.

Lecture videos

You can view all of the lecture videos on one webpage.
Alternatively, for an individual lecture video, click on the lecture # in the table.
(Note: there are no videos for Lectures 25 and 26, since the pandemic semester was one week shorter than usual.)


# Date Sections Topic Assignment due
  1. Tue 24 Aug 1.1 – 1.2 vectors  
  2. Thu 26 Aug 1.2 – 1.3 n-dimensional geometry  
  3. Tue 31 Aug 1.4 matrix multiplication 1.1: 6(a,c,g), 7, 8, 9, 21, 22, 23, 25, 29
1.2: 1(b,d,g), 2(b,d,g), 4, 9, 11, 13 (no geometric interpretation necessary), 16, 18
  4. Thu   2 Sep 1.4 Gaussian elimination  
  5. Tue   7 Sep 1.5 linear systems 1.3: 1(a,c,f), 3(a,d,e), 5, 8, 10, 12
1.4: 1, 3(a–f), 4(d,f), 10, 11, 12, 13, 15
  6. Thu   9 Sep 1.5, 1.6.1 solving linear systems  
  7. Tue 14 Sep 2.2 – 2.3 linear transformations 1.5: 1, 2(a,b), 3(a,c), 4a, 6, 10, 12, 13, 14
1.6: 5, 7, 9, 11
  8. Thu 16 Sep 2.1 – 2.2 matrix algebra  
  9. Tue 21 Sep 2.4 – 2.5 elementary matrices
transpose
2.1: 1(a,c,f), 2, 5, 6, 7, 8, 12(a,b,d), 14
2.2: 5, 7, 8
2.3: 1(b,d,f), 2(a,c,d), 4, 8, 11, 13(a,b,c), 16
10. Thu 23 Sep 3.1 – 3.2 linear subspaces  
11. Tue 28 Sep 3.2 linear subspaces 2.4: 7, 12
2.5: 1(a,f,j), 4, 8, 9, 12, 15, 19(a,b), 22, 23
3.1: 1, 2(a,c,d), 6, 9(b,c), 10, 12, 13, 14
Thu 30 Sep   FIRST MIDTERM EXAM  
Tue   5 Oct   no class: Fall break  
12. Thu   7 Oct 3.3 linear independence
13. Tue 12 Oct 3.3 – 3.4 bases; dimension 3.2: 1, 2(a,b), 10, 11
3.3 1, 2, 8, 10, 11, 14, 15, 19, 21, 22
14. Thu 14 Oct 3.4 bases; dimension  
15. Tue 19 Oct 3.6 abstract vector spaces 3.3: 5(a,b)
3.4: 3(a,b,d), 4, 8, 17, 20, 24
16. Thu 21 Oct 3.6 – 4.1 inner products; projections  
17. Tue 26 Oct 4.1 – 4.2 least squares; orthonormal bases; Gram-Schmidt 3.6: 1, 2(a,c,d), 3(a,c,f), 4, 6(a,b), 9, 13, 14(b,c), 15(a,b)
18. Thu 28 Oct 4.4 abstract linear transformations  
19. Tue  2 Nov 4.3 change of basis 4.1: 1(a,b), 3, 6, 7, 9, 11, 13, 15
4.2: 2(b,c), 3, 6, 7(a,b), 8a, 9a, 11, 12(a,b)
20. Thu  4 Nov 4.3 – 4.4 review of change of basis  
21. Tue  9 Nov 5.1 determinants 4.4: 2, 5, 8, 14, 16, 22(a,b), additional problems 1–9
4.3: 3, 9, 12, 19, additional problems 1–3
22. Thu 11 Nov 5.2 formulas for determinants  
23. Tue 16 Nov 6.1 eigenvalues and eigenvectors 5.1: 1(a,b,c), 2, 3, 4, 7, 9(a), 10, 11
5.2: 1a, 3, 4, 5(a,c,f), 7, 8, 10
Thu 18 Nov   SECOND MIDTERM EXAM  
24. Tue 23 Nov 6.2 diagonalizability
spectral theorem
4.3: 18, 20, 21
6.1: 1 (do as many as you can stand!), 2, 3, 4, 6, 10, 12, 14
  Thu 25 Nov   no class: Thanksgiving  
25. Tue 30 Nov 7.1; 6.4 Jordan form 6.2: 1 (do as many as you can stand!), 3, 4, 6, 11, 16(a-c)
6.4: 1, 2, 3, 4, 5, 8, 10, 11, 13
26.  Thu  2 Dec 7.3 matrix exponentials; systems of ODE  
  Mon 13 Dec   FINAL EXAM, 14:00 – 17:00 *optional* 7.1: 4, 6, 7, 8, 14, 16                 (but you will be
*optional* 7.3: 1, 4, 5, 8, 9, 10, 13, 14       tested on this material)


Grading scheme

Final course grades: Quizzes, participation in class discussion, and attendance at office hours can contribute additional credit to your Homework score. In particular, students who regularly attend office hours often jump up over a gradeline simply due to the earned participation points.


Links

University academic links Departmental links


The fine print

I will do my best to keep this web page for Math 221 current, but this web page is not intended to be a substitute for attendance. Students are held responsible for all announcements and all course content delivered in class.
Many thanks are due to Jeremy Martin and Vic Reiner, who provided templates for this webpage many years ago.


The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Duke University.

ezramath.duke.edu
Wed Dec 1 18:52:13 EST 2021


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