MATHS 217:  LINEAR ALGEBRA (4)

Syllabus

1. Prerequisite:  MATHS 159 and either 162 or 165 or permission of the department chairperson.

Note:  Although MATHS 159 is the preferred prerequisite for all students taking this course, we understand that some non-mathematical science majors (currently Computer Science, Mathematical Economics, and Pre-Engineering) are required to take MATHS 217 and we will allow substitution of CS 120 from their programs for MATHS 159. 

2. Course Description:  Theory and application of systems of linear equations, vector equations, linear transformations, vector spaces, and inner product spaces.  Includes the use of computer software. 

3. Course Objectives:  Students will learn to solve basic computational problems involving systems of equations, matrices, vector spaces and linear transformations.  Students will master fundamental concepts and will learn to use precise language related to the theory of vector spaces and linear transformations.  Students will become acquainted with technology (e.g. calculators and/or computer software) that is helpful in solving computational problems in linear algebra.  

4. Course Rationale:  Linear algebra is a fundamental topic in mathematics that finds wide application in computer science, engineering, physics, and other fields.  It is fundamental in solving certain types of systems of equations (namely, linear equations). Further, since many systems can be approximated by linear systems, the techniques of linear algebra provide powerful tools in solving applied problems.  Finally, many geometric transformations (e.g. rotations and reflections of the plane) are linear transformations, and because of this, linear algebra has important connections to geometry. 

5. Course Content:  Linear equations and vector equations; Gaussian elimination.  Matrix algebra and linear transformations.  Determinants.  Vector spaces and subspaces: linear independence and spanning; dimension, coordinates, and change of basis.  Null space, column space, and rank of a matrix..  Eigenvalues and eigenvectors of a linear transformation.  Inner products, orthogonality, and projections.  Diagonalization of symmetric matrices.  Applications and advanced topics at the discretion of the instructor. 

6. Course Format:  lecture/discussion.

7. Methods of Evaluating Student Performance:  Typical components include (but need not be limited to) homework assignments and projects and in-class examinations.  The evaluation and weight of these components are at the discretion of the instructor.  Students may be evaluated on their understanding of the content material of the course, their ability to solve problems related to the course material, and their ability to communicate mathematically to others orally and/or in writing. 

8. Evaluation of the Course:  The instruction of the course is evaluated by departmental student evaluations and peer evaluation.  The course is reviewed and revised periodically by the Departmental Undergraduate Programs Committee.

Revised M. Karls, Spring 2007