Math 221 (Fall 2024)

Math 221 Course Webpage

Linear Algebra and Applications

Fall 2024, 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
      11:45 – 13:00, Physics Building 259

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
Canvas site: available to registered students via Duke NetID
Office hours: Tuesday, 13:00 – 14:15
                        Thursday, 13:00 – 14:15

Help Room

Thursdays, 19:00 - 22:00.
See here for more information

Emergency procedures

What to do in an emergency
Duke|ALERT
Downloadable classroom emergency checklist


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 video policies


Assignments

Policies regarding graded work Math 721 vs. Math 221: graduate coursework


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.)


#/Video       Date         Sections Topic Assignment due Thursday unless otherwise noted
  1. Tue 27 Aug 1.1 – 1.2 vectors  
  2. Thu 29 Aug 1.2 – 1.3 n-dimensional geometry  
  3. Tue   3 Sep 1.4 matrix multiplication  
  4. Thu   5 Sep 1.4 Gaussian elimination 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
  5. Tue 10 Sep 1.5 linear systems  
  6. Thu 12 Sep 1.5, 1.6.1 solving 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
  7. Tue 17 Sep 2.2 – 2.3 linear transformations  
  8. Thu 19 Sep 2.1 – 2.2 matrix algebra 1.5: 1, 2(a,b), 3(a,c), 4a, 6, 10, 12, 13, 14
1.6: 5, 7, 9, 11
  9. Tue 24 Sep 2.4 – 2.5 elementary matrices
transpose
 
10. Thu 26 Sep 3.1 – 3.2 linear subspaces 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
11. Tue   1 Oct 3.2 linear subspaces  
12. Thu   3 Oct 3.3 linear independence 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
13. Tue   8 Oct 3.3 – 3.4 bases; dimension  
Thu 10 Oct   FIRST MIDTERM EXAM Due Wed: 3.2: 1, 2(a,b), 10, 11
                  3.3: 1, 2, 8, 10, 11, 14, 15, 19, 21, 22
Tue 15 Oct   no class: Fall break  
14. Thu 17 Oct 3.4 bases; dimension  
15. Tue 22 Oct 3.6 abstract vector spaces  
16. Thu 24 Oct 3.6 – 4.1 inner products; projections 3.3: 5(a,b)
3.4: 3(a,b,d), 4, 8, 17, 20, 24
17. Tue 29 Oct 4.1 – 4.2 least squares; orthonormal bases; Gram-Schmidt  
18. Thu 31 Oct 4.4 abstract linear transformations 3.6: 1, 2(a,c,d), 3(a,c,f), 4, 6(a,b), 9, 13, 14(b,c), 15(a,b)
19. Tue  5 Nov 4.3 change of basis  
20. Thu  7 Nov 4.3 – 4.4 review of 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)
21. Tue 12 Nov 5.1 determinants  
22. Thu 14 Nov 5.2 formulas for 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
23. Tue 19 Nov 6.1 eigenvalues and eigenvectors  
Thu 21 Nov   SECOND MIDTERM EXAM Due Wed: 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
24. Tue 26 Nov 6.2 diagonalizability
spectral theorem
 
  Thu 28 Nov   no class: Thanksgiving Due Wed: 4.3: 18, 20, 21
                  6.1: 1 (do as many as you can stand!), 2, 3, 4, 6, 10, 12, 14
25. Tue   3 Dec 7.1; 6.4 Jordan form  
26. Thu   5 Dec 7.3 matrix exponentials; systems of ODE 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
  Thu 12 Dec   FINAL EXAM, 9:00 – 12:00 *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
Sun Sep 22 17:14:35 EDT 2024


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