Math 221 Course Webpage

Linear Algebra and Applications

Fall 2020, Duke University


General information | Course description | Lecture and video policies | Assignments | Homework 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
      13:45 – 15:00, LSRC B101 "Love Auditorium" (Section 01)
      13:45 – 15:00, online (Section 02)

Discussion sections (mandatory): depends on your selection at registration
      Mondays 12:00 – 12:50 (Section 01D), Prof. Hain
      Mondays 13:45 – 14:35 (Section 02D), Prof. Hain
      Mondays 15:30 – 16:20 (Section 03D), Prof. Hain
        Days and times TBD    (Section 04D), Prof. Myer

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: Tuesdays and Thursdays, 15:00 – 16:30, by Zoom

Help Room

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

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 video policies


Assignments

Policies regarding graded work


Homework 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.

# Date Sections Topic Assignment due
  1. Tue 18 Aug 1.1 – 1.2 vectors  
  2. Thu 20 Aug 1.2 – 1.3 n-dimensional geometry  
  3. Tue 25 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 27 Aug 1.4 Gaussian elimination  
  5. Tue   1 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   3 Sep 1.5, 1.6.1 solving linear systems  
  7. Tue   8 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 10 Sep 2.1 – 2.2 matrix algebra  
  9. Tue 15 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 17 Sep 3.1 – 3.2 linear subspaces  
11. Tue 22 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
12. Thu 24 Sep 3.3 linear independence
Tue 29 Sep   FIRST MIDTERM EXAM 3.2: 1, 2(a,b), 10, 11
13. Thu   1 Oct 3.3 – 3.4 bases; dimension  
14. Tue   6 Oct 3.4 bases; dimension 3.3 1, 2, 5(a,b), 8, 10, 11, 14, 15, 19, 21, 22
15. Thu   8 Oct 3.6 abstract vector spaces  
16. Tue 13 Oct 3.6 – 4.1 inner products; projections 3.4: 3(a, b, d), 4, 8, 17, 20, 24
3.6: 1, 2(a, c, d), 3(a, c, f), 4, 6(a, b), 9, 13, 14(b, c), 15(a, b)
17. Thu 15 Oct 4.1 – 4.2 least squares; orthonormal bases; Gram-Schmidt  
18. Tue 20 Oct 4.4 abstract linear transformations 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)
19. Thu 22 Oct 4.4 change of basis  
20. Tue 27 Oct 4.3 more change of basis 4.4: 2, 5, 8, 11, 13, 14, 16, 22(a,b), additional problems 1–9
21. Thu 29 Oct 5.1 determinants  
22. Tue  3 Nov 5.2 formulas for determinants 4.3: 3, 7, 9, 12, 18, 19, 20, 21, additional problems 1–3
5.1: 1(a, b, c), 2, 3, 4, 7, 9(a), 10, 11
23. Thu  5 Nov 6.1 eigenvalues and eigenvectors  
Tue 10 Nov   SECOND MIDTERM EXAM 5.2: 1a, 3, 4, 5(a,c,f), 7, 8, 10
6.1: 1 (do as many as you can stand!), 2, 3, 4, 6, 10, 12, 14
24. Thu 12 Nov 6.2, 6.4 diagonalizability; spectral theorem  
25. Mon 16 Nov (7.1, 7.3) (perhaps: Jordan form; ODE systems) 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
  Sun 22 Nov   FINAL EXAM, 14:00 – 17:00 *optional* 7.1: 4, 6, 7, 8, 14, 16                
*optional* 7.3: 1, 4, 5, 8, 9, 10, 13, 14       


Grading scheme

Final course grades: Quizzes and attendance at office hours can contribute additional credit to your Homework score.
Participation in class discussion can contribute additional credit to your Discussion score.


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
Thu Nov 12 04:47:05 EST 2020


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