Math 221 Course Webpage

Linear Algebra and Applications

Fall 2017, Duke University


General information | Course description | 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: Wednesday and Friday, 13:25 – 14:40, Physics Building 119

Text: Linear Algebra: A Geometric Approach, by Ted Shifrin and Malcolm Adams, second edition.

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
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: Tuesday 14:00 – 15:00 & Wednesday 12:00 – 13:15, in Physics 209

Help Room

Mondays and Thursdays, 7:00 - 10:00 in Carr 137, from September 4th to December 11th.
See here for more information.


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 – 6 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)


Assignments

Policies regarding graded work


Homework schedule

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 nas, 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. Wed 30 Aug 1.1 – 1.2 vectors  
  2.    Fri   1 Sep 1.2 – 1.3 n-dimensional geometry  
  3. Wed   6 Sep 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.    Fri   8 Sep 1.4 Gaussian elimination  
  5. Wed 13 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.    Fri 15 Sep 1.5, 1.6.1 solving linear systems  
  7. Wed 20 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.    Fri 22 Sep 2.1 – 2.2 matrix algebra  
  9. Wed 27 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, 16
10.    Fri 29 Sep 3.1 – 3.2 linear subspaces  
11. Wed   4 Oct   FIRST MIDTERM EXAM 2.4: 7, 12
2.5: 1(a,f,j), 4, 8, 9, 12, 15, 19(a,b), 22, 23
12.    Fri   6 Oct 3.2 linear subspaces  
13. Wed 11 Oct 3.3 linear independence 3.1: 1, 2(a,c,d), 6, 9(b,c), 10, 12, 13, 14
14.    Fri 13 Oct 3.3 – 3.4 bases; dimension  
15. Wed 18 Oct 3.4 bases; dimension 3.2: 1, 2(a,b), 10, 11
3.3 1, 2, 8, 10, 11, 14, 15, 19, 21, 22
16.    Fri 20 Oct 3.6 abstract vector spaces  
17. Wed 25 Oct 3.6 – 4.1 inner products; projections 3.3: 5(a,b)
3.4: 3(a, b, d), 4, 8, 17, 20, 24
18.    Fri 27 Oct 4.1 – 4.2 least squares; orthonormal bases; Gram-Schmidt  
19. Wed  1 Nov 4.3 change of basis 3.6: 1, 2(a, c, d), 3(a, c, f), 4, 6(a, b), 9, 13, 14(b, c), 15(a, b)
20.    Fri  3 Nov 4.4 abstract linear transformations  
21. Wed  8 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)
22.    Fri 10 Nov 5.1 determinants  
23. Wed 15 Nov 5.2 formulas for determinants 4.3: 3, 7, 9, 12, 18, 19, 20, 21
4.4: 2, 5, 7, 8, 11, 13, 14
24.    Fri 17 Nov   SECOND MIDTERM EXAM SECOND MIDTERM EXAM
  Wed 22 Nov   no class: Thanksgiving  
     Fri 24 Nov   no class: Thanksgiving  
25. Wed 29 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
26.    Fri  1 Dec 6.2 diagonalizability  
27. Wed  6 Dec 7.1; 6.4 Jordan form; spectral theorem 6.1: 1 (do as many as you can stand!), 2, 3, 4, 6, 10, 12, 14
6.2: 1 (do as many as you can stand!), 3, 4, 6, 11, 16(a-c)
28.    Fri  8 Dec 7.3 matrix exponentials; systems of ODE  
   Sat 16 Dec   FINAL EXAM FINAL EXAM, 19:00 – 22:00


Grading scheme

Final course grades: Quizzes and participation in class discussion can contribute to your homework 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
Fri Oct 27 02:01:29 EDT 2017


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