UC Davis Math 167 -- Applied Linear Algebra
Summer Session II 2008

Basic information

Instructor: Brian Osserman Office:Mathematical Sciences Building (MSB) Room 3218 Office Hours: MW 2:00-3:00, starting 8/11 Email:
(Please include "MAT167" in your subject line.)
Lectures: MTW 12:10-1:50, Bainer 1128 CRN: 81066 Prerequisites: Math 22A or Math 67, and familiarity with Matlab

Welcome to Math 167, Applied Linear Algebra!

Announcements:

9/11: Final exam scores are now visible on Gradebook; the letter grade
ranges are the same as for the midterm.

9/10: I will be in my office Friday 1-2 if you want to look over your
graded final exam befores grades are posted.

9/7: I have posted a brief final exam study guide below.

9/2: I have added an extra office hour on Thursday, September 4, from 1-2.
You will also be able to pick up your graded Homework 4 during this hour.

8/25: Since Monday, September 1 is a holiday, my usual Monday office hours
are rescheduled to Tuesday that week.

8/22: Midterm scores are now visible on Gradebook, and a rough letter grade
breakdown is posted below.

I will be in Germany for a conference during the first week of classes;
lectures will be given by Fu Liu during that week. Obviously, I will not
have office hours while I am gone, but I will attempt to check email,
and Professor Liu has agreed to hold an office hour 2:00-3:00 on Wednesday,
August 7, in MSB 3220.

Important: this class will be on a very intensive schedule, so it is
important that you make sure to keep up from the very beginning, and not
miss any homework assignments.

Textbook and Syllabus:

The textbook for this course is Strang, Linear Algebra and its
Applications, 4th edition (I apologize for the outrageous price).
We will be covering a little more than half of the book, with a focus on
chapters 1, 2, 3, 5, and 6.
Note that we will be skipping many sections of the textbook -- that's
because this is not a self-contained linear algebra course, but rather
a course focusing on algorithms and applications, assuming a good base
of understanding of linear algebra (hence the prerequisites).

Grading:

Grades will be weighted as follows:

Homework, 30%

Midterm Exam, 30%

Final Exam, 40%

For people who do better on the final, an alternate weighting of
30%/20%/50% will be used.
Grading will be curved, but not strictly, meaning that I will not have
predetermined grade distribution for the course. For instance, if you all
do well enough, I will give all A's and B's.

To give you an idea of what the curve will look like, here is the
rough letter grade breakdown for the midterm and the final. The mean for
the midterm was 44.6%, and the median was 41%. The mean for the final
was 43.3%, and the median was 41%. The letter grade ranges for the
homework will be somewhat stricter.

60%-100%: A range
50%-60%: B range
35%-50%: C range
25%-35%: D range
0-25%: F

Exams:

There will be two in-class exams.
The exams will be given on Wednesday, August 20 (midterm), and Wednesday,
September 10 (final).

The midterm will be one hour long, starting at 12:50. It will cover
lecture material through Chapter 3, which includes all material from
lectures before the exam. However, most of Tuesday's lecture will be
devoted to review, and 12:10-12:50 on Wednesday will be an optional
additional question-and-answer session.

The final exam will fill the full time from 12:10-1:50. It will be
comprehensive, but will emphasize material from after the midterm.
Here is a brief study guide of topics and suggested problems from
the book for you to look at in order to prepare for the exam. This
is not comprehensive: topics from lecture not covered in the book like
database search may be on the exam, and some topics have too few problems
in the book to suggest new problems below. Also, these topics are not of
equal weight; the importance of each topic will roughly correspond to the
amount of class time we spent on it.

Gaussian elimination and LU factorization
Section 1.5 5, 15; Section 2.2 3, 5, 13, 42.

Incidence matrices of graphs
Section 2.5 1 (also look over rankings using least squares).

Fourier series and the discrete Fourier transform
Section 3.4 23; Section 3.5 3, 7.

Homework:

Homework assignments will be posted weekly on this page, starting
Monday, August 5. Due to our tight schedule, I will post homeworks
which include material not yet covered, so that a typical assignment
posted on Monday will cover through that Wednesday's material,
and will be due the following Monday. That way you can start work on the
homework problems for each lecture on the same day. There will be a
total of five homework assignments.

You can turn homeworks in after class, or you can drop them off in
the appropriate reader box on the first floor of MSB.

Because this course is focused on algorithms and applications, homework
will include occasional programming in Matlab. If you are not familiar
with Matlab, you should start looking it over as soon as possible.
Computer lab accounts are available to students in the class: go to
http://www.math.ucdavis.edu/comp/class-accts
to create the account.

Homework 1, due 8/11 by 5:00 PM: Section 1.3: 8, 10, 18;
Section 1.4: 10, 11, 20, 22, 32; Section 1.5: 11, 24, 28, 29;
Section 1.6: 2, 5, 6, 11, 29, 42.
Note the following typo in problem 11 of 1.5: "without multiplying
LU to find A" should read "without multiplying LU to find x".

Homework 3, due 8/25 by 5:00 PM: Section 3.3: 2, 4, 8, 10, 18, 41;
Section 3.4: 2, 10, 14, 16, 24. Also, do the following in MATLAB: download
this data file; it consists of many values for
the variables x and y. Find the least squares line best approximating all
the values (x,y). Plot all the values of (x,y) with the least
squares line superimposed over them, print out the plot, and include it
with the homework.

Homework 5, due 9/8 by 5:00 PM: Section 5.6: 2, 14, 36, 38; Section
2.5 6, 14 (ignore the comment on spanning trees); Section 3.5 2, 4, 8, 18,
20; Section 6.3 1, 2, 10, 18. Also, do the following in MATLAB: download
this data file; it contains a matrix X (to be
used as an image) and a colormap map. This can be displayed with the
commands "image(X); colormap(map)". Using the MATLAB function for
singular value decomposition, compute the SVD of X, and plot the singular
values using "plot(diag(S));". Using the singular value decomposition,
compute the approximated matrices X_{k} for k=1, 6, 11, 31, and
display the resulting images. Print the singular value plot and the images,
as well as the MATLAB commands you used, and submit them with your homework.
How many numbers need to be stored for X? What about for X_{1},
X_{6}, X_{11}, and X_{31}?

Students with disabilities:

Any student with a documented disability (e.g. physical, learning,
psychiatric, vision, hearing, etc.) who needs to arrange reasonable
accommodations must contact the Student Disability Center (SDC). Faculty
are authorized to provide only the accommodations requested by the SDC. If
you have any questions, please contact the SDC at (530)752-3184 or
sdc@ucdavis.edu.