# 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

 Paper Course Materials Objectives Students with Disabilities Schedule and Homework

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.

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.

 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.

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