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.
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
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:
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 |
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ezramath.duke.edu
Thu Nov 12 04:47:05 EST 2020