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