Math 321 - Linear Algebra

### MATH 321 - Linear Algebra

This class is listed as:

• Math 321-002 - Call #18697 - Linear Algebra
• Schedule: Tue-Th 2:00-3:15pm Room DSH 229

Textbook: Linear Algebra by S.H. Friedberg, A.J. Insel, L.E. Spence, Fourth Edition. Prentice Hall, 2003.
We will cover most of the material in Chapters 1-6, and time permitting some of the material in Chapter 7. There are many other introductory books in linear algebra. Reading from other sources is always very valuable. We recommend Linear Algebra Done Right by Sheldon Axler, Second Edition, Springer, 1997; and Introduction to Linear Algebra by Gilbert Strang, Fourth Edition, Wellesley Cambridge Press, 2009.

Course Content: This is a course on linear algebra. We will study

• Vector Spaces: various examples beyond two and three dimensional spaces encountered in a Multivariable Calculus course such us Math 264, vector subspaces, concepts of linear dependence (and independence), dimension and bases.
• Linear Transformations: associated vector spaces (null space and range), and their dimensions (nullity and rank), representations in different bases, matrix representation, basic operations (sum, scalar multiplication, composition), invertible linear transformations, change of co-ordinates.
• Systems of linear equations and how to solve them using elementary matrix operations. Rank of a matrix and inverse of a matrix, computational methods: Gaussian elimination. Determinants and Cramer's rule.
• Diagonalization: eigenvalues, eigenvectors, eigenspaces, similar matrices, characteristic polynomial. Time permitting we will explore the canonical Jordan Form.
• Inner product vector spaces: inner product, orthogonality, orthonormal basis, Gram-Schmidt orthogonalization process, orthogonal complements, orthogonal projections. normal and self-adjoint operators, Spectral theorem. Singular value decomposition (SVD).
The emphasis in this course is theoretical, including abstract proof-type questions in the homework and in the exams. For most of these questions, a relevant sequence of equations arranged in an intelligent and logical order, accompanied by a few words of explanation at the critical steps, will be sufficient. On the other hand, there is a computational aspect of this course that students are expected to master as well, mostly involving matrices. If you have never had experience with matrices or with proofs, you might consider taking first Math 314 or Math 327, so that at least you have had some practice with one or the other.

Prerequisites: You need some mathematical maturity. We list as a prerequisite multivariable calculus: Math 264, or permission from the instructor. However, if you have had prior experience with matrices (like Math 314, or Math 316), or with proofs (like Math 327) it will help.

Homework: The problems and exercises in the textbook are an integral part of the course. You should do as many as possible. I will occasionally provide exercises or problems that are not in the textbook. In those occasions, solutions to the problems will be posted in the webpage.
Homework will be collected and returned every Tuesday in section meetings, starting on Tuesday, January 26, 2010. There will be twelve assignments. Each homework will consist of about ten problems of varying difficulty (both computational and theoretical). Occasionally you will have the opportunity to turn in bonus problems. The Homeworks will be posted on the Web, so you will have to check the course webpage every week. Only four of the questions, chosen at random, will actually be graded, however it is strongly recommended that you attempt all the questions in the assignment, and that you take advantage of the office hours provided by the instructor and the teaching assistant to help you get through them. Working in groups is a great idea, but after discussing and solving problems, each one of you should write the solutions on your own. There are many resources on the web, many handbooks/book on linear algebra, you are more than welcome to explore these resources, however, should you find a solution to a problem in any of the above, you should reference properly your source. If the grader identifies identical solutions, the grade will be split among the students involved and a warning will be issued.

Exams: There will be one midterm before Spring break (March 11, 2010) (Midterm 1) and a final exam on Tuesday May 11, 2010 from 10:00-12:00m.

Grades: Grades will be based on homeworks/quizes, one midterm and a final exam. The grading policies will be discussed in class.

Important Dates: Fall 2010 deadlines, Fall 2010 finals schedule .

Americans with Disabilities Act: Qualified students with disabilities needing appropriate academic adjustments should contact me as soon as possible to ensure your needs are met in a timely manner. Handouts are available in alternative accessible formats upon request.

Last updated: January 18, 2010