Applied Linear Algebra

Class Time/Place: MWF 10:00am-10:50pm, CRUESS 107

Instructor: Jesus A. De Loera

virtual office hours!!

TA: Mr. Lang Mou

Course Description: This course aims to help you develop a solid useful understanding of linear algebra, in particular focusing on applied and computational aspects of the subject. Linear algebra is truly important because linear equations and eigenvalue problems appear everywhere in engineering and science. A growing area of application is data-mining or analytics. This will be my favorite application during the course.

Textbook: Matrix Methods in Data Mining and Pattern Recognition (Fundamentals of Algorithms), by Lars Elden, Published by SIAM ISBN-13: 978-0898716269

Note that this textbook has its official website: http://www.mai.liu.se/~laeld/matrix-methods/. Over there, you can find a lot of useful information. In particular, you should check out the currently known errata.

Other useful references I use in class C. Moler: Numerical Computing with MATLAB by Cleve Moler, SIAM 2004 (available freely online)

G. Strang: Linear Algebra and Its Applications, 4th Ed., Brooks/Cole, 2006.

P. Olver & C. Shakiban: Applied Linear Algebra, Pearson, 2006.

C. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2000.

Here are the key topics:

Quick Review of Vector Spaces, Subspaces, Linear Independence, Bases, Rank, Linear Transformations, Determinants. Review of MATLAB.
LU decomposition and Linear system solving, basic of numerical analysis.
Norms, Inner Products, Orthogonal Bases, Gram-Schmidt Orthogonalization, QR Factorization
Projections, Least Squares Problems, Data Fitting/Regression
Eigenvalues, Eigenvectors, Diagonalization, Positive Definite Matrices
Range-Nullspace Decomposition, Singular Value Decomposition
Applications to Statistics & Data Analysis, Web Search Engines & Network problems, Information processing (signal & images, error-correcting codes), others.

Prerequisite and Expectations

MAT 22A or MAT 67 (i.e., practical understanding of elementary linear algebra).
Basic knowledge of programming is required. Some experience in MATLAB is preferable, but MATLAB is very easy to learn. If you do not know how to use MATLAB, then you need to self-study using the MATLAB Primer and other material listed below.
Formal attendance will not be taken. However, whether you are able to attend class or not, you are responsible for all the material presented in class.
This is a 4 unit course! You are expected to work 3 hours at home for each hour of lecture. In other words, expect to have 10 hours of homework each week.

Grading:
The grades will be calculated using the average and standard deviation of the class. 100 points are possible which will be divided as follows:

Surprise quizzes online 10 points (about 7 quizzes of 2 points each, drop lowest scores, leaving top 5 scores)
Homeworks 20 points (5 homeworks of 5 points each, with the lowest score dropped),
Three midterm exams worth 20 points each (in class, Oct 24th, Nov 12, and Dec 10) with the lowest score dropped. Each exam will have 4 questions.
Final Project 25 points (Due December 19 at 12:30 pm) and
3 points awarded for participation in class, office hours, or on the online discussion forum.
2 points for the initial diagnostic exam

Some important rules will be followed:

It is very important that you think and discuss the material, that is why I will give point for participation. Valuable contribution to the discussion be done online, in our forum at SMARTSITE, in class, or during office hours.
The SMARTSITE online forum is a great way for all of us to work, collaborate, and discuss what you are learning. If you have to enter formulas, you can most likely paste them in from MATLAB OR you can follow MATLAB's code notation to express equations. I will check the online discussion every morning and evening. Students should comment or make suggestions if you see how to help some else figure the problem, but DO NOT POST STRAIGHT SOLUTIONS! Give hints not answers!
The homework and other material will be posted at bottom of the course web site. Homework is due at the beginning of class on the day the assignment is due. LATE HOMEWORK WILL NOT BE ACCEPTED.
Your work is not being graded solely from the final answer, I expect you to write neatly, justify your reasoning and show all missing details.
Each time, a subset of three homework problems will be graded. You will loose a point automatically if you did not work out all problems. The lowest two homework scores will be dropped when assessing your grade.
I will assign some HW problems that require you to use MATLAB.
All exams are closed book. No calculators or cell phones allowed.
There will be NO MAKE-UP EXAMS but I will drop the lowest score.
The final project should be done in a team of 2 or 3 students. The project will include writing MATLAB code to investigate one of the application topics presented in class (see first lecture). More details and rules will be stated after the first midterm.

SOFTWARE and other RESOURCES:

Create an account at the Math Department. Visit http://www.math.ucdavis.edu/comp/class-accts 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 one of the departmental servers, such as [point,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. 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.

The official MATLAB online "getting started guide" is available from MATLAB (it is free, but registration of an account is required).
MATLAB offers a very nice online video tutorial
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 7.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 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.

VIDEO LECTURES TO REVIEW LINEAR ALGEBRA, There are many useful resources in the internet! More than I can mention here! In particular world expert Prof. Gilbert Strang. Prof. Strang has posted During my lecture I plan to (1) go very quickly over the key points again, (2) add material (missing proofs, tricky details, interesting examples, correct mistakes, etc). More important (3) I plan to actively engage you to see how YOU are thinking about the topic! I will call on you, discuss your thoughts. Please be ready, I will call on you in class. Math is not an spectator sport!! You learn by doing it!

HOMEWORKS & HANDOUTS

Diagnostic EXAM Solve on your own as much as you can of the diagnostic test .
Solutions are due on Friday October 3rd in class by 10am. This exam has only 2 points of grade value,
but it will help me determine what you know already and it will help you remember it!!!

The computer slides announcing themes for final projects can be downloaded here .

Homework 1, due October 15th:
Homework 2, due October 27th:
practice midterm 1
Slides on least squares and QR
Homework 3, due November 5th:
IMPORTANT ANNOUNCEMENT: Details for final project are available here