Course: MAT 167-001: Advanced Linear Algebra
CRN: 69752
Class: MWF 10:00am-10:50am, Cruess 107

Instructor: Naoki Saito 
Office: 675 Kerr 
Email: saito@math.ucdavis.edu
Office Hours: MW 11:00am-12:30pm

TA: Wei Yu
Office: 476 Kerr 
Email: yuwei@math.ucdavis.edu
Office Hours: Tu: noon-1:00pm, Th: noon-2:00pm

• To learn important concepts of linear algebra, such as vector spaces, basis, linear transformations, projections, least squares method, eigenvalues, and eigenvectors.
• To understand the importance of linear algebra and learn its applicability to practical problems, i.e., how the linear equations and eigenvalue problems appear in some practical applications.
• To enhance your understanding of the above concepts through MATLAB-based projects.

• Review of Gaussian Elimination, Row Echelon Forms, LU Factorization
• Review of Vector Spaces, Subspaces, Linear Independence, Bases, Rank, Linear Transformations
• Norms, Inner Products, Orthogonal Bases, Gram-Schmidt Orthogonalization, QR Factorization
• Range-Nullspace Decomposition, Singular Value Decomposition
• Projections, Least Squares Problems, Data Fitting/Regression
• Eigenvalues, Eigenvectors, Diagonalization, Positive Definite Matrices, Jordan Normal Form
• Discrete Fourier Transform, Applications to Image Processing, Statistics, and Inverse Problems

• The following textbook is required: Carl D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2000, ISBN: 0-89871-454-0.
• We will review Chapters 1, 2, 3, but our emphasis is on Chapters 4, 5, and 7. Exact coverage for the exams will be announced later.
• Note that this textbook has its official website: http://matrixanalysis.com/. Over there, you can find a lot of useful information.  In particular, you should check out the currently known errata for both the main textbook and the solution manual.

• MAT 22A (i.e., understanding of elementary linear algebra).
• Some experience in MATLAB is preferable.  If you do not know how to use MATLAB, then you need to self-study using the MATLAB Primer and other materials listed below.
  

Formal attendance will not be taken. However, I strongly encourage you to attend class regularly. I often talk about some of my own experiences and perspectives on linear algebra, which are not really written in the textbook.  Also, I plan to distribute handouts from time to time. Whether you are able to attend class or not, you are responsible for all the materials presented in class. While I will try to post class announcements via email or on the class web pages, it is your responsibility to find out what happened if you miss class.

I will maintain the Web pages for this course (one of which you are looking at now). All homework assignments and important announcements will be posted on these pages. Please check these pages regularly.
You can access the MAT 167 Home Page at https://www.math.ucdavis.edu/~saito/courses/167/ from which you can access to this Syllabus Page and Homework Page.

The MAT 167 Mailing List was created. I will use this list to announce some important information. You can also submit your emails (must be related to the class) to this mailing list. If you send your email to this list, then everyone will receive it. So, please use this wisely and politely. Once I had two students in the class who started discussing certain aspects of the exercise problem and sent back and forth about 10 emails to the mailing list in a few hours, and everyone else got fed up... The mailing list name is: mat167-s04@ucdavis.edu .

• 20% Homework
• 10% Computer Projects
  
• 25% Midterm Exam (in class, Wednesday, May 5, 2004)
• 45% Final Exam (1:30pm-3:30pm, Wednesday, June 16, 2004)

• I will assign homework problems after every class via Homework Page, so please check that page regularly. I strongly encourage you to do the homework on a regular basis. I will collect homework every Friday at the beginning of class. LATE HOMEWORK WILL NOT BE ACCEPTED.
• Staple your homework papers together, and write the due date and your name on the upper right corner of your paper.
• Please write neatly, accurately, and legibly.
• It is not enough to merely write the final answers. You must justify your answers by clearly stating your reasoning and showing your computation. This point is particularly important since the solution manual comes with the textbook.
• You are also encouraged to write in complete sentences. The reader has explicit instructions to penalize you if your work cannot be followed.
• A subset of these problems will be graded and returned on the following Friday at the end of class. I will not include the score of the worst performed homework when computing your grade.

Note: This is a 4 unit course! In practical terms, that means you are expected to work 3 hours at home for each hour of lecture. In other words, expect to have 9 to 10 hours of homework each week.

I will also assign a set of projects using MATLAB, once in April and once in May. These will become invaluable experience for you. Your understanding of linear algebra will deepen by doing these projects. See Computer Projects Page and the MATLAB Access section below.

There will be one midterm and a final examination. The midterm is scheduled for Wednesday, May 5 in class. The final exam will be 1:30pm-3:30pm, Wednesday, June 16 at Cruess 107. Also, be sure to note the following policies:
• All exams are closed book. You may not use the textbook, crib sheets, notes, or any other outside material. Do not bring your own scratch paper. Do not bring blue books.
• There will be no calculators/laptop computers for the exam. The exam is to test whether you know the material.
• Everyone works on their own exams. Any suspicions of collaboration, copying, or otherwise violating the Student Code of Conduct will be forwarded to the Student Judicial Board.
• The final exam is cumulative, i.e., it covers the whole course material, although more emphasis is on the topics that were not covered by the midterm.
• There will be NO MAKE-UP MIDTERM EXAM. If you miss the midterm exam due to catastrophic events such as serious illness of yourself or death of your immediate family, you must provide me with a written proof (e.g., a report or a letter written by a medical doctor with signature). Only then I will readjust the weight (e.g., Homework 25%; Computer Projects 15%; Final 60%).
• If you miss the final exam due to catastrophic events such as serious illness of yourself or death of your immediate family, you will receive "Incomplete" grade, provided that you give me a written proof (e.g., a report or a letter written by a medical doctor with signature). Then you must take a make-up exam in the following quarter to receive a letter grade.

To use MATLAB, there are a few options:
• Create an account at the Math Department. Visit https://www.math.ucdavis.edu/~saito/courses/howto451.html and follow the instructions. It is important to create your account before you come to the Lab for the first time. You can then work either at the Undergraduate Computer Lab (451 Kerr) or from any other lab in the campus or even from your home PC by remotely connecting to one of the three departmental servers [cosine,sine,tangent].math.ucdavis.edu. The lab is open 9am-5pm on weekdays.
• Use your own account at your own department if your department has the MATLAB license. This is the case for most of the engineering departments.
• Buy a Student Version of MATLAB at UCD Bookstore (costs about $100).
• Install Octave system on your own PC, which is free software and emulates MATLAB. Caution: Most likely you can do all the lab exercises, but I have not tested all the exercises yet. In fact, if you decide to use octave and notify me whether you can do the projects with octave or not, I would greatly appreciate it! Visit the official web site of Octave at http://www.octave.org for downloading and installing information.

For those who have never used MATLAB before or need to brush up their MATLAB knowledge, please take a look at the following highly useful MATLAB primers and tutorials.
• A Practical Introduction to MATLAB by Mark S. Gockenbach.
• MATLAB Primer by Kermit Sigmon. This publicly available version was written for older version of MATLAB 3.5, but still useful. (Our current version of MATLAB is 6.x.)
• MATLAB Tutorial at MIT. This is the shortest one, tailored to the linear algebra context.
• Numerical Computing with MATLAB by Cleve Moler. This is a soon-to-be-published book by the creator of MATLAB. I highly recommend to read Chapter 1: Introduction to MATLAB as well as Chapter 2: Linear Equations, Chapter 5: Least Squares, and Chapter 10: Eigenvalues and Singular Values.
• For the details, the official MATLAB manual is available from MATLAB Online Help Desk (for web) and MATLAB Online Manuals (in PDF).
• To view PDF files, you need acroread from Adobe Systems Inc .