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.
Name: Professor Ezra Miller
Address: Mathematics Department,
Duke University, Box 90320,
Durham, NC 277080320
Office: Physics 209
Phone: (919) 6602846
Email: ezramath.duke.edu
Webpage:
https://math.duke.edu/people/ezramiller
Course webpage: you're already
looking at it... but it's
https://services.math.duke.edu/~ezra/221/221.html
Office hours:
Tuesday 14:30 – 15:30 &
Friday 12:00 – 13:15, in Physics 209
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:
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 email me.
#  Date  Sections  Topic  Assignment due 

1.  Wed 30 Aug  1.1 – 1.2  vectors  
2.  Fri 1 Sep  1.2 – 1.3  ndimensional 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  inner products  3.3: 5(a,b) 3.4: 3(a, b, d), 4, 8, 17, 20, 24 
18.  Fri 27 Oct  4.1  projections; least squares  
19.  Wed 1 Nov  4.2  orthonormal bases; GramSchmidt algorithm  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  4.3  changes of basis  
21.  Wed 8 Nov  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) 
22.  Fri 10 Nov  4.3 – 4.4  review of change of basis  
23.  Wed 15 Nov  5.1  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  5.2  formulas for determinants  
26.  Fri 1 Dec  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 
27.  Wed 6 Dec  6.2  diagonalizability  
28.  Fri 8 Dec  6.4  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(ac) 
Sat 16 Dec  FINAL EXAM  FINAL EXAM, 19:00 – 22:00 
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ezramath.duke.edu
Wed Aug 30 22:26:21 EDT 2017