**Course:** MAT 167 Applied Linear Algebra

**CRN:** 78139

**Credit Units:** 4

**Class:** MWF 3:10pm-4:00pm, ART 217

**Instructor:** Naoki Saito

**Office:** 2142 Math. Sci. Building

**Email:** saito@math.ucdavis.edu

**Office Hours:** MW 4:10pm-5:30pm

**TA1: ** Bohan Zhou (for students whose last name starts from A to J)

**Office:** 3131 Math. Sci. Building

**Email: ** bhzhou@ucdavis.edu

**Office Hours:** F 2pm-3pm

**TA2: ** Yunshen Zhou (for students whose last name starts from K to Z)

**Office:** 3131 Math. Sci. Building

**Email: ** yszhou@math.ucdavis.edu

**Office Hours:** R 3pm-4pm

**Course Objectives:**

- To understand the importance of linear algebra and learn its applicability to practical problems, in particular, applications in machine learning/pattern recognition, data mining/search engines, and signal/image processing.
- To learn important concepts of linear algebra, such as linear transformations, bases, projections, least squares method, various matrix decompositions such as LU, QR, eigenvalue, and
*SVD (singular value decomposition)*. - To enhance your understanding of the above concepts through the use of MATLAB.

**Textbook:**

- The following textbook is
*required*: - Lars Eldén:
*Matrix Methods in Data Mining and Pattern Recognition*, SIAM, 2007, ISBN: 978-0-898716-26-9. Note that this textbook has its official website: http://users.mai.liu.se/larel04/matrix-methods/. Over there, you can find a lot of useful information. In particular, you should check out the currently known errata. - In addition, I would like to mention that the following textbooks are
*optional*: - Carl D. Meyer:
*Matrix Analysis and Applied Linear Algebra*, SIAM, 2000, ISBN: 0-89871-454-0. - You can read the whole book online by downloading pdf files from http://matrixanalysis.com/DownloadChapters.html>. Check out the currently known errata for both the main textbook and the solution manual.
- Lloyd N. Trefethen & David Bau, III:
*Numerical Linear Algebra*, SIAM, 1997, ISBN: 0-89871-361-7. - Check its book website: http://people.maths.ox.ac.uk/trefethen/text.html for postscript files of the first five lectures.
- David Skillicorn:
*Understanding Complex Datasets: Data Mining with Matrix Decompositions*, Chapman & Hall/CRC, 2007, ISBN: 1-58488-832-6. - Michael W. Berry & Murray Browne:
*Understanding Search Engines: Mathematical Modeling and Text Retrieval*, 2nd Ed., SIAM, 2005, ISBN: 0-89871-581-4. - John MacCormick:
*9 Algorithms That Changed The Future: The Ingenious Ideas That Drive Today's Computers*, Princeton Univ. Press, 2012, ISBN: 978-0-691-14714-7.

**Prerequisite:**

- MAT 22A or MAT 67 (i.e., understanding of elementary linear algebra).
- Some experience in MATLAB is mandatory. If you do not know how to use MATLAB, then you need to self-study using the MATLAB Primer and other materials listed below.

If you have never programed in MATLAB or feel uneasy about your ability to do so, get in contact with your TAs, by Friday April 7, 2017. In the Subject Line, please say: Student of Math 167 seeking HELP with MATLAB.

If you are reasonably comfortable with MATLAB, please email them with the Subject Line: Student in Math 167 with REASONABLE MATLAB SKILLS. The more frequent and meaningful contact you have with me (Professor Saito), your TAs, and your fellow students, the better able you will be to succeed in this course.

**Topics:**

I plan to cover the following topics in the textbook:

- Motivation: Vector/Matrix Representation of Datasets (Chap. 1)
- Review of Vectors & Matrices (Chap. 2)
- Linear Systems & Least Squares (Chap. 3)
- Orthogonality (Chap. 4)
- QR Decomposition (Chap. 5)
- Singular Value Decomposition (Chap. 6)
- Clustering & Nonnegative Matrix Factorization (Chap. 9)
- Classification of Handwritten Digits (Chap. 10)
- Text Mining (Chap. 11)
- Page Ranking for a Web Search Engine (Chap. 12)

**Attendance:**

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.

As soon as you know you are going to miss class, send your TA an email indicating which class you will/have miss(ed). Be sure to ask your TA how you can get a hold of the information you need. We may ask you to meet us in our office hours or to contact one of your classmates. However, please stay in contact with us so that we can best help you succeed!

**Class Web Page:**

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://canvas.ucdavis.edu/courses/102487 from which you can access to this Syllabus Page and Homework Assignment Page.

**Discussions/Chat Room in canvas:**

We will use the announcements and notification functions of canvas to communicate important information regarding this course. It is your responsibility to check your email/text messages. In addition, we highly recommend that you communicate with your fellow students about the course material. In order to assist you in this process, the canvas page for this course has both a chat room and a discussion/forum page. Please use these resources to discuss the content with your peers. Finally, while electronic communications are very convenient, they should not suffice. Please make it a priority to come to the office hours I offer as well as those that my TAs will be offering. If you cannot make these office hours, contact us to make an appointment. The more frequent and meaningful discussions you have about this material, the better!

**Grading Scheme:**

- 40% Homework
- 20% Midterm Exam (in class, Monday May 8, 2017)
- 40% Final Exam (6pm-8pm, Monday, June 12, 2017)

**Homework:**

- I will assign homework problems after each Friday lecture, which can be seen at Homework Assignment Page.
**The due date of each homework set is Monday (i.e., 10 days from the assigned date)**(except on university holidays; see the Homework Page above for the details). So, I will collect the homework at each Monday lecture starting on April 17. 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 Monday at the end of class.
*I will not include the score of the worst performed homework when computing your grade.* - Occasionally, I will assign HW problems that require to use MATLAB. These will become invaluable experience for you. Your understanding of linear algebra will deepen by doing these projects.
- 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.

**Exams:**

There will be one midterm and a final examination. The midterm is scheduled for **Monday, May 8 in class**. The final exam will be **6pm-8pm, Monday, June 12 (the location will be announced later)**. 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.
- You are not allowed to use calculators/laptop computers/cell phones in 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 45%; Final 55%).
- 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.

**MATLAB Access:**

To use MATLAB, there are a few options:

- Create an account at the Math Department. Visit http://www.math.ucdavis.edu/~saito/courses/howtolab.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 (2118 Math. Sci. Bldg.) or from any other lab in the campus or even from your home PC by remotely connecting to the departmental server round.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 using Octave 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. - If you wish, you can use the other high-level programming languages such as R or julia, both of which are open source and freely downloadable. However, we will not provide HW answers using R or julia. Also, julia is rapidly being developed and sometimes has version conflicts of various packages; hence use it at your own risk.

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.

- MATLAB Onramp. These video tutorials cover the basics of importing data, manipulating arrays, creating visualizations, and more.
- 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 9.x.)
- A Practical Introduction to MATLAB by Mark S. Gockenbach.
- MATLAB Tutorial at MIT. This is the shortest one, tailored to the linear algebra context.
- Numerical Computing with MATLAB by Cleve Moler. This is an online 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).

Please email me if you have any comments or questions!

Go back to MAT 167 Home Page