MTH 513 Linear Algebra
Spring 2010 - Course Webpage
James Baglama Office: Lippitt Hall 101A
Department of Mathematics
Phone: 401.874.4412 Email: jbaglama@math.uri.edu

Final Exam Chapters 4, 5, 6 will be a take home. I will post the final exam in Sakai on Tuesday May 4 in the assignment tool section of our class website. Sharing or discussing solutions with other students will result in a failing grade. I will not give hints or answer questions about the exam. Do not ask, is this correct? You may hand write your solutions to the exam, however it MUST be neat. The exam is due in one week, by 11:55p.m. Tuesday May 11. You may upload your exam to Sakai or hand it in to me or place it in my mailbox before the due date. No late exams will be accepted. Again sharing of answers or ideas for a take home exam is considered cheating.

Course Material
Text:
Linear Algebra, 4/E
Authors: Friedberg, Insel, and Spence
ISBN-10: 0130084514
ISBN-13: 9780130084514

I suggest using amazon or another online book dealer to get the book. Please have the book before the start of the semester.

Additional texts:
Good reference books for this course.

Linear Algebra with Applications by Steve Leon
Linear Algebra by David Lay
Matrix Analysis by Horn and Johnson

Prerequisites:
Mathematical maturity and a basic knowledge of linear algebra, e.g. solving linear
systems, matrices, rank, computing determinants, orthogonality, vector spaces, and
linear transformations.

Objectives
The primary aim of MTH 513 is to gain an in depth knowledge of linear
algebra. You will be introduced to basic concepts and facts of linear
algebra. You will learn the terminology, fundamental principles, and
common methods used in linear algebra. This course will prepare you
to understand the abstract concepts behind linear algebra.
We will study vector spaces, linear transformations,
matrices, determinants, linear equations, eigenvalues,
canonical forms, and inner product spaces.

Exams and Grade Evaluation
2 Exams 200 pts
Homework 0pts - 200pts
Paper 100 pts
Total points 300pts - 500pts

Grade is determined by summing up your points and dividing by the total
number of points.
A .. 100-92
A- .. 91-90
B+ .. 89-87
B .. 86-82
B- .. 81-80
C+ .. 79-77
C .. 76-72
C- or lower is considered failing in a 500 level course

Homework
Mathematics is learned by doing mathematics i.e. by working on problems.
Thus doing your homework is the most important part of this class. One of the goals of
the course is to improve your ability to think and write mathematics. Every homework
assignment

must have your name and list of problems assigned at the top,
must be typed and written logically. Very little tolerance is given to
to homework that I cannot follow. State all of your steps in a logical, easy to follow
manner,
and do NOT email your homework to me! You must handin your homework.
I will not accept ANY late or incomplete homework assignments.
Remarks: I will be happy to give you hints if you are stuck with your homework.
However, I will NOT answer the problem for you. I encourage you to discuss homework
problems with other students in the class. If you become stuck on a problem, fresh ideas from
someone else might provide you with some new angles to try.
Feel free to use any book to help with homework. Avoid the Internet! There are many
wrong answers, incorrect methods, and hand waving proofs floating around in cyberspace.
Finally, you must write up the solutions by yourself. (In practice,
this means that you should not be looking at other people's solutions as you write your
own.) If identical homework sets are handed in, all of the identical copies will received 0
points. A word-by-word copy of a solution from another source (including the internet) is
not acceptable and will also receive 0 points. Suspicious homework may require
additional explanation in person.

Paper
The paper is worth 100 points.
The due date Monday April 19 2010.
Do not wait until the last minute!

A common feature of virtually all large linear problems
is that they cannot be solved directly by existing computers.
Many of these large linear problems require solutions that
involve hundreds of thousands of unknowns.
For such problems, approximation techniques are used
to find solutions.
This is commonly done by finding a problem of much smaller
dimension which can be solved directly and whose solution
can be used to generate an acceptable approximation of the
original problem. Important collections of techniques of
this kind are called Krylov subspace methods .

Each paper should contain the following:
A description and history of Krylov subspaces and how they are used
to solve large linear problems.
A more indepth description of a specific Krylov subspace method
and how it is used to solve either an eigenvalue problem or a linear system.
Some specific Krylov subspace methods:
Arnoldi, Lanczos, GMRES, CG, MINRES, LSQR.
Description of a real world application.
List of references. You must use more than one source. I
will not accept a website as a reference.

Each paper must
have your name and title at the top,
be typed and written logically,
be more than one page,
be double spaced, font size 12 pts, with one inch margins.
be submitted via Assignment tool in Sakai. Do NOT email your paper to me!
I will not accept ANY late papers.

Some articles and books to get you started:
J. Demmel, Applied Numerical Linear Algebra, SIAM Philadelphia PA, 1997.
G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. John Hopkins 1996.
I. C. F. Ipsen and C. D. Meyer, ``The idea behind krylov methods'', The American Mathematical
Monthly, Vol. 105, No. 10 pp 889-899, December 1998. Click here
for the paper.
Y. Saad, Iterative Methods for Sparse Linear Systems, PWS 1996.
Y. Saad, Numerical Methods for Large Eigenvalue Problems, Manchester Univ. Press 1992.
A copy is avaiable on Saad's website
http://www-users.cs.umn.edu/~saad/books.html .

Sakai
Sakai is being used in part to teach this course.
That means you should become familiar with using Sakai.
You can access Sakai at the following web address:
https://sakai.uri.edu/portal/
Use your e-campus id or your 9-digit URI student number and your @mail.uri.edu email password.

H1N1 Flu
Illness Due to Flu:
The H1N1 Flu Pandemic may impact classes this semester. If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class. Notify your instructor by phone or by email of your status. Your instructor will communicate by email or by phone with you. In this way you and your instructor will work together to ensure that course instruction and work is completed for the semester.
The Centers for Disease Control and Prevention have posted simple methods to avoid transmission of illness. These include: covering your mouth and nose with a tissue when coughing or sneezing; frequently washing your hands to protect from germs; avoiding touching your eyes, nose and mouth; and staying home when you are sick. For more information, please view
http://www.cdc.gov/flu/protect/habits.htm
URI information on the H1N1 will be posted on the URI website at
http://www.uri.edu/news/h1n1 , with links to the
http://www.cdc.gov site .

Students with Disabilities
Any student with a documented disability should contact your instructor early in the semester so that he or she may work out reasonable accommodations with you to support your success in this course. Students should also contact Disability Services for Students: Office of Student Life, 330 Memorial Union, 874-2098. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.