Honors Linear Algebra — Mathematics 540
Detailed Syllabus and Homework Assignments
Brown University — Spring, 2012
Professor Joe Silverman

There will be some additional homework problems that are not in the text. They are labeled A.1, A.2, ... You can find them by following this link, or by clicking on the links provided below for each problem.

Click on the indicated links for solutions to selected homework problems.

For material on determinants, we will be using Chapter 3 of the book
       Linear Algebra Done Wrong by Sergei Treil.
(Yes, Professor Treil's title is adapted from Axler's title!) You can download the book for free by clicking the following link:
       Download Linear Algebra Done Wrong.
You can get further information about the book, including an errata sheet, at
       Home page of Linear Algebra Done Wrong.
In the reading and homework assignments, material from Treil's book will be denoted by LADW.

For the last few classes we will be using material from
       Additional Topics in Linear Algebra
which you should download by clicking the above link. In the reading and homework assignments, material from these notes will be denoted ATLA, and exercises are labeled C.1, C.2, etc.

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Homework Assignments for Math 540

Class # Date Topic Read HW Assignment HW Due
01 Wed Jan 23, 2013 Vector Spaces Pages 1–10 p. 19, # 1, 2, 3 Mon Jan 28
02 Fri Jan 25, 2013 Vector Spaces Pages 11–16 p. 19, # 4, 5, 6, 7, 8, 9 Weds Jan 30
03 Mon Jan 28, 2013 Finite Dim'l Vector Spaces Pages 16–18, 21–24 p. 35, # 1 and A.1
Solution to A.1 		Weds Jan 30
04 Wed Jan 30, 2013 Finite Dim'l Vector Spaces Pages 24–27 p. 35, # 2, 3, 4 Wed Feb 6
05 Fri Feb 1, 2013 Finite Dim'l Vector Spaces Pages 27–31 p. 35, # 6, 8, 9 Wed Feb 6
06 Mon Feb 4, 2013 Finite Dim'l Vector Spaces Pages 31–34 p. 35, # 10, 11 and A.2, A.3
Solution to A.2, A.3 		Wed Feb 6
07 Wed Feb 6, 2013 Linear Maps Pages 38–39 p. 35, # 13, 14, 16, 17 Wed Feb 13
08 Fri Feb 8, 2013 Class Canceled — Blizzard! — — —
09 Mon Feb 11, 2013 Linear Maps Pages 40–43 p. 59, # 1, 2, 3, 4
Solutions to #2 and #4 		Wed Feb 13
10 Wed Feb 13, 2013 Linear Maps Pages 44–47 p. 59, # 5, 6, 9, 10, 12, 14
Hint: 9 and 10 require little computation.
Bonus Problem: 16*
Solutions to 9, 10, 16 		Wed Feb 20
11 Fri Feb 15, 2013 Linear Maps Pages 48–53 p. 59, # 19 and A.4.
Solution to A.4 		Wed Feb 20
— Mon Feb 18, 2013 Brown closed — — —
12 Wed Feb 20, 2013 Linear Maps Pages 53–58 p. 59, # 22, 23, 24, 25 Wed Feb 27
13 Fri Feb 22, 2013 Linear Maps / Polynomials Pages 64–67 p. 59, # 18, 21, 26 and A.5 and A.6. Wed Feb 27
14 Mon Feb 25, 2013 Polynomials Pages 67–72 p. 73, # 1 Wed Feb 27
15 Wed Feb 27, 2013 First Hour Exam Solutions Covers up to page 50 and
up to HW due on Feb 20 		—
16 Fri Mar 1, 2013 Eigenvalues/Eigenvectors Pages 75–78 p. 73, # 4 and p. 94, # 2, 3, 4, 5, 6, 7 Wed Mar 6
17 Mon Mar 4, 2013 Eigenvalues/Eigenvectors Pages 79–82 p. 94, # 9, 10, 11, 12, 14 Web Mar 6
18 Wed Mar 6, 2013 Upper Triangular Matrices Pages 82–85 p. 94, # 13, 15, 17 Wed Mar 13
19 Fri Mar 8, 2013 More Matrix Stuff Pages 85–93 p. 94, # 18, 19, 20, 21 Wed Mar 13
20 Mon Mar 11, 2013 Determinants LADW Pages 79–82** LADW p. 85, # 3.1, 3.2, 3.3 Wed Mar 13
21 Wed Mar 13, 2013 Determinants — — Wed Mar 20
22 Fri Mar 15, 2013 Determinants LADW Pages 82–87 p. 244, #2, 20, 21 and
LADW p. 85, # 3.4, 3.5, 3.6		 Wed Mar 20
23 Mon Mar 18, 2013 Determinants LADW Pages 89–94 LADW p. 94, # 5.1, 5.2, 5.3
Bonus Problem: LADW p. 94, # 5.5* 		Wed Mar 20
24 Wed Mar 20, 2013 Determinants — p. 244, #1 and
LADW p. 96, # 7.2, 7.3 and A.7. 		Wed Apr 3
25 Fri Mar 22, 2013 Inner Product Spaces Pages 97–103 p. 122, # 1, 2, 6 Wed Apr 3
— Mon Mar 25, 2013 Spring Break — — —
— Wed Mar 27, 2013 Spring Break — — —
— Fri Mar 29, 2013 Spring Break — — —
26 Mon Apr 1, 2013 Inner Product Spaces Pages 104–109 p. 122, # 3 Wed Apr 3
27 Wed Apr 3, 2013 Second Hour Exam Solutions Covers Chapters 1–5 and LADW pages 75–94
and up to HW assigned on Mar 20 		—
28 Fri Apr 5, 2013 Inner Product Spaces Pages 109–114 p. 122, # 9, 10, 11, 13, 15, 16 and A.8 Wed Apr 10
29 Mon Apr 8, 2013 Inner Product Spaces Pages 117–121 p. 122, # 24, 25, 26, 27, 28 Wed Apr 10
30 Wed Apr 10, 2013 Operators on Inner Product Spaces Pages 127–130 p. 125, # 29, 30(a), 31 and p. 158, # 1, 2 Wed Apr 17
31 Fri Apr 12, 2013 Operators on Inner Product Spaces Pages 130–134 p. 158, # 5, 6, 7, 9, 11 Wed Apr 17
32 Mon Apr 15, 2013 Operators on Inner Product Spaces Pages 144–147 p. 158, # 14, 17, 18, 19 Wed Apr 17
33 Wed Apr 17, 2013 Operators on Inner Product Spaces Pages 147–150 p. 158, # 20, 21, 22 Wed Apr 24
34 Fri Apr 19, 2013 Operators on Inner Product Spaces Pages 147–150, 152–157 p. 158, # 23, 26, 28 Wed Apr 24
35 Mon Apr 22, 2013 Operators on Inner Product Spaces Pages 147–150, 152–157 p. 158, # 30, 31, 32, 33 Wed Apr 24
36 Wed Apr 24, 2013 Jordan Normal Form ATLA Pages 5–10 *** ATLA p. 13, # C.2, C.4, C.6
Solutions to C.1–C10 		Wed May 1
37 Fri Apr 26, 2013
(Reading period starts)		 The Cayley-Hamilton Theorem
Linear Recursions 		ATLA Pages 10–13, 15–19 ATLA p. 13, # C.1, C.3, C.5 and
ATLA p. 24, # C.7
Solutions to C.1–C10 		Wed May 1
38 Mon Apr 29, 2013 Linear Recursions ATLA Pages 19–23 ATLA p. 24, # C.8(a,d,f), C.9(a,c), C.10
Solutions to C.1–C10 		Wed May 1
39 Wed May 1, 2013 Linear Recursions ATLA Pages 23–24 There is no additional homework
ATLA p. 23 §5 will not be on the final exam. 		—
— Fri May 3, 2013 Review and Q & A Session — — —
  Weds, May 8, 2013 Final Exam — 2:00–5:00pm
Location: Kassar–Foxboro 		Solutions The final exam is comprehsensive. It may
include all material covered in class, in
homework, and in assigned readings. 		 

*Note on Bonus Problems: Bonus problems are for those who enjoy working on challenging problems for the sake of working on challenging problems. They will not get you much extra credit, but doing them will earn you a warm sense of satisfaction at having done a hard problem.

**LADW: These readings and problems refer to Linear Algebra Done Wrong by Sergei Treil. (Click on the link to download a free copy.)

***ATLA: These readings and problems refer to Additional Topics in Linear Algebra. (Click on the link to download a free copy.)

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