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Math 309,
Matrix Algebra
Section 1, Fall 2007
Note: Sections 1 and 2 of Math 309 use the same textbook and
will
cover nearly the same "core topics" that make up most of the
course. The sections may vary a bit in emphasis and on a few
optional topics. This
syllabus applies only to Section 1 .
Instructor: Professor Ron Freiwald
Office: Cupples I, Room 203A,
935-6737
Office Hours: (Beginning
week of
9/3) M 2:30-3:30, W
1:30-2:30, F 12:30-1:30 and by appointment
Class Time: M-W-F
10-11
a.m..
Location:
Cupples I, Room 113
Textbook & Related Resources
Linear Algebra and Its
Applications, by David Lay
This text is very well written and is a must-read as the course
moves along.
A copy of the Study Guide is
bundled with
your
textbook at the Campus Bookstore. The Study
Guide is a very valuable resource. I recommend that you
consistently use it as you work your way through the
course. In
particular, read carefully the note on How to Study Linear Algebra
at the beginning of the Study Guide. If you are purchasing your books through a different
source, the Study Guide,
though very useful, is optional.
There is some good
supplementary material at the Companion Web Site for the
course (http://www.laylinalgebra.com/). In particular, there's a
large collection review sheets and practice exams from
the author. (The practice exams may or may not be what our exams
look like, but they certainly provide a good self-test on some of the
material.)
You can also look at whatever
material is available at MyMathLab: registration material is included
with the textbook.
Homework
Each
week (beginning in week 2) I will post here a list
of assigned homework to be handed in. These assignments will
normally be due in class on Fridays. Late homeworks
usually will not be accepted unless
there is a special legitimate reason
such as illness. When
the problem list is first posted here it may not be
complete. However, the list of problems due the following
Friday
will always be complete by noon on the preceding Tuesday. Be sure
to check after Tuesday that you have the complete list of problems due
on Friday.
There will also be a longer list of recommended problems, not to be
handed in. You should be sure you can do them all and (even
better) try some others from the text book as well.
The hand-in homeworks should be written up on 8.5 x 11 paper
with "clean edges" (not torn out from a spiral bound notebook).
One goal in most upper level math courses is clear writing and
arguments, so the solution of each problem should be written up quite
clearly and legibly. (In particular,
check yourself
by reading aloud the words and symbols you wrote down, exactly
as written. The result should be smooth sounding English--or else
something is missing on paper!)
Talking with
other
students about homework
problems is a good way to
learn, but each student must write up his or her own
homework. Therefore, no solutions from two students
should look too much alike. After all, everybody says things in
their own way, makes up their own notation as needed, etc. A good
way to avoid "copying" even inadvertently from another student is to
talk about problems together without taking any notes away from
the conversation. This lets you share understanding and ideas,
but forces you to reconstruct your own understanding on paper.
A grader will assign a score to each homework. Each score will be
rescaled to a %, and the lowest two scores will be dropped. The
average of the remaining %'s will be your homework score, H.
Homework
Due Date
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Problems to Hand
In
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Other
Recommended
Problems
(not to hand in)
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Solutions
to
Hand-In Problems & Quizzes
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Friday,
September 7
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Sec 1.1: 18,22,34
Sec 1.2: 12,14,20, 28, 30
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Sec
1.1:
1,5,7,13,15,23,24,25,33
Sec 1.2: 3,13,15,21,22,23,29,31,
33
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Friday,
September 14
Reminder: short quiz in class Friday 9/14
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Sec
1.3: 12,14,18,
26,32
Sec 1.4: 8,14,18,20,
30,32
Sec 1.5: 6, 16, 28, 32
Sec 1.6: 12 (assume all the streets are one-way, so that traffic
must flow in the indicated directions)
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Sec
1.3:
5,7,9,23,24,25,27
Sec 1.4: 7,13,23,24,35
Sec 1.5: 13,23,24,31
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Friday, September 21
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Sec 1.7: 14,26,36,40
Sec 1.8: 6,10,26,32,34
Sec 1.9: 4,8,12,20,36
Section 1.10: 10
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Sec 1.7:
1,15,17,19, 21,22,23,27
Sec 1.8: 3,13,15,18,21,22,
27
Sec 1.9: 13,19,23,24,27
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Friday, September 28
Reminder: short
quiz in class Friday 9/28.
Typically, material on a quiz will go up through the sections/material
included in the homework due the same day.
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Sect 2.1: 6,10,24,34
Sec 2.2: 6, 14, 22, 24, 30, 32, 38
Sec 2.3: (Note the opening sentence for the exercise
set: "Unless otherwise
specified, ... " ) 2,4,8,14,18,34,38
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Sec 2.1: 11,13,15,16,17,19,23,25
Sec 2.2: 3,9,10,12
Sec 2.3: 11,12,17,21,37
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Friday, October 5
Reminder: Exam 1 in
class on Monday October 8
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Sec 2.6: 4
Sec 2.4: 4, 6 (in #6, assume that A ,C, X, and Z are square)
Sec 3.1: 8, 16 (see note in text preceding Problems 15-18)
, 42
Sec 3.2: 8, 14, 22, 26, 34
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Sec 3.1: 39,40
Sec 3.2: 15,17,19, 27,28, 33, 36
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Friday, October 12
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Sec 3.2: 36
Sec 3.3: 22,24,28,30
Sec 4.1: 2, 8, 20, 28, 30 (Hint: use #28)
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Sec 3.2: 35
Sec 3.3: 29
Sec 4.1: 1,5,6,25,26,27
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Since Friday, October 19 is Fall Break, the
homework that would normally be due then will be collected on
Monday,
October 22. I will try to have the complete assignment posted
here by
Monday, October 15.
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Sec 4.2: 6,12,14,22,32,34
( in #34, C[0,1] is the vector space of all continuous functions
defined on the closed interval [0,1] )
Sec 4.3: 8,14,16,20,26,32 (#32 should also say "T is linear
"), 34
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Sec 4.2: 2,10,11,19,
25,26
Sec 4.3: 1,3,5,11,21,22, 29, 30,33
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Friday,
October 26
Quiz in Class Friday, October 26
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Sec 4.4: 8,14,30,32
Supplementary
Problems
based on the handout Introduction
to Diagonalization |
Sec 4.4: 3,5,10,15,16
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Friday,
November 2
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Sec
4.5: 6,12,14,16,22,24
Sec 4.6: 4,12,14,24
Sec 4.9: 4,14
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Sec
4.5: 3,19,20,28
Sec 4.6: 17,18,27
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Friday,
November 9
(Quiz in class Friday
November 9)
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Sec
5.1: 8,16,20,24,36
Sec 5.2: 14,18,20,24 ("algebraic multiplicity" is what I
called "multiplicity" in class; sometimes the dimension of the
eigenspace is called the "geometric multiplicity" of the eigenvalue.)
Sec 5.3: 4, 6, 8, 12 (The eigenvalues for #12 are given just
before
#7, at the bottom right corner of p. 325)
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Sec
5.1: 1,3,7,21,22,35
Sec 5.2: 5,7,21,22,25
Sec 5.3: 3,21,22
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Friday,
November 16
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Sec
5.4: 4,10,16, 26 ( use 25 )
Sec 5.5: 6, 8,12,16
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Sec
5.4: 3,15,25
Sec 5.5: 25
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Friday,
November 30
Quiz in Class Friday, December
7 (not November 30, as advertsied earlier)
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Sec
5.6: 2, 6,10
Sec 6.1: 14,18,24,26,28
Sec 6.2: 10,14,16,20,22,28
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Sec 5.6:
1,18 (if you have access to Matlab or a similar tool to assist)
Sec 6.1: 9,11,19,20,31
Sec 6.2: 1,5,23,24
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Friday,
December 7
Quiz in Class
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Sec
6.3: 10,16,20,24
Sec 6.4: 4,8,12
Sec 6.5: 4,8,12,14,24
Sec 6.6: 4, 8a,10a,14
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Sec 6.3:
5,21,22
Sec 6.4: 17,18
Sec 6.5: 17,18,25
Sec 6.6: 7, 9. It's nice to do 8b and 10b if you can have
Matlab or some other program help with the computations.
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These
problems are recommended for practice, but no more homework is to
be
handed in.
Sec 7.1: 10,12,15,19 (notice that the eigenvalues are given in the
paragraph preceding Problem 13), 25,26,33,35
Sec 7.2: 3,5,7,11,13,19
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Quizzes
In alternate weeks
(unless there is a holiday or exam that week) there will be a short
quiz, no more than 15 minutes, given toward the end of the class.
This means there will be about six quizzes during the semester.
The first will be on Friday, September 14. These quizzes will contain one or
more questions requiring you to do a
very simple calculation, interpret a calculation, give a definition,
state a theorem, or answer some true/false questions. There will
be no make-up quizzes The quiz scores
will be rescaled as a %, and the lowest score
dropped. The remaining scores will be averaged together to
produce your quiz score, Q.
Tests
There will be
two exams (E1, E2) in
class during the semester. The dates of these exams will be
announced at least 1 week in advance, but the dates will probably be in
late September and late October.
After E2, there
will be an optional Exam 3 (E3) given in the
late afternoon or evening, probably in late November.
(See
details under "Grading" below.)
The final exam (F)
will be held at the
time
scheduled in the Course Listings book:
Tuesday,
December 18, 2007, 10:30-12:30 in the regular classroom, Cupples I,
room 113
Information about each
exam
will be posted
in the table below when available.
Course
Grade
Your grade will
be based on T, your Total Score (%),
computed as follows:
1) if you do not
take
the
optional Exam
3: T = (1/5) * (E1 + E2 + F + Q + H )
(so exams, quizzes and homework scores are all equally
weighted)
2) if you do take the optional Exam 3, then your T will
be the larger of
T = (2/11) * (E1 + E2
+ F + Q + H) + (1/11) * E3
T = (2/12) * (E1 + E2 + E3 + F + Q + H )
(so if you choose to take E3,
you have
to take it seriously:
the score will count and it could hurt your Total T.
However
if
E3 doesn't go well, it will carry only half the weight of the other
exams; if it helps you, it will count the full weight of the
other two exams.)
I will base
grades on the number T, rounded up to the nearest
integer.
I
will
not make up a grading scale until the end of the course, but it
is guaranteed that the grading will be no more severe than:
90-100
A
(possibly +/-)
80-89
B
(possibly +/-)
65-79
C
(possibly +/-)
50-64
D
<
50 F
If you are taking the course on a
CR/NCR
(=pass/fail) basis, then you will need a T score value to a C-
or
better to
earn a "CR"
Course Evaluations Online Course Evaluations will
be available toward the end of the semester. I urge all of you to
participate. Thoughtful and accurate feedback is valuable to both
the instructor and to your fellow students.
Academic
Integrity This link gives the general policies of the
University on academic integrity. Please also see the
comments,
above, about homework collaboration.
Anonymous
Feedback to Professor Freiwald. Of course, I'd really
prefer open
feedback and
discussion about the course at any time. However,
this link is provided as a way for students to offer suggestions and
comments anonymously. I'll keep this link here as long as it's
constructively
used. (I can't
respond, of course, to your
anonymous e-mail.)
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