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.
  • Abstract vector spaces, bases, and linear transformations
    Section 2.1 1, 7, 21; Section 2.3 5, 12, 35, 42; Section 2.6 1, 7, 15.
  • Orthogonality, Gram-Schmidt, and the QR factorization
    Section 3.1 1, 7, 25; Section 3.4 9, 13, 29.
  • Eigenvectors, diagonalization, and Jordan form
    Section 5.1 5, 23, 29; Section 5.2 1, 7, 25; Section 5.5 13, 19; Section 5.6 5, 35, 41.
  • Singular value decomposition and applications
    Section 6.3 5, 15, 17 (also look over image processing, etc).
  • Projections, least squares and weighted least squares
    Section 3.2 7, 17; Section 3.3 3, 7, 23 (also look over smallest length least squares from SVD).
  • Difference and differential equations
    Section 5.3 11, 17, 23; Section 5.4 1, 2, 9, 23.
  • 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 2, due 8/18 by 5:00 PM: Section 2.1: 2, 8; Section 2.2: 2, 6, 10, 12, 38; Section 2.3: 6, 14, 20; Section 2.6: 4, 8, 22, 40; Section 3.1: 2, 4, 6, 30, 34; Section 3.2: 4, 16, 18, 26.

  • 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 4, due 9/2 by 5:00 PM: Section 5.1: 4, 6, 12, 26; Section 5.2: 4, 6, 22, 28, 30, 32; Section 5.3: 4, 8, 12, 24; Section 5.4: 4, 6, 8, 12; Section 5.5: 12, 14, 18, 20.

  • 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 Xk 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 X1, X6, X11, and X31?

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.