# Math 254: Introduction to Linear Algebra

Course number: 22864
Fall 2007
MWF, 12:00 -12:50.
GMCS 306 ( NOTE ROOM CHANGE! )
San Diego State University
Final Exam: Wed. Dec. 12, 10:30-12:30

Professor: Mike O'Sullivan
Email: m.osullivan@math.sdsu.edu
Office: GMCS #579, 594-6697
Office Hours: MWF 8:00-9:45, 11:15-11:45.
You may also stop by on Tu or Th afternoon. If I am in and available, we can talk.
Other times: by appointment.

## Text

Bretscher, Linear Algebra with Applications 3rd ed.
Review for the final.

## Detailed Information

 SCHEDULE ASSIGNMENTS

## Course Description

Linear algebra is one of the most widely used and fundamental areas of mathematics. Linear algebra is an important tool in virtually all physical sciences, in economics and other social sciences, and in engineering. It is an important companion to calculus, but the flavor of the subject is different, as you will see in this course.

We will study matrices, rectangular arrays of numbers, and see how they are used in a variety of ways. First, matrices are used to solve systems of linear equations. They are an efficient means for recording the steps that are used to solve the system. Second, matrices are used to define functions, which we call linear transformations. An n x m matrix defines a function from m -dimensional space to n -dimensional space. From this perspective, solving a system of equations is essentially finding the preimages for an element of the n -dimensional space. Third, matrices are used to define a change of coordinate system.

The core material is in Chapters 1-4, which we will cover thoroughly. Chapters 5-7 develop the geometry of linear tranformations and change of coordinates. That is where it gets very interesting!

## Prerequisites

The main prerequisite is high school algebra.

## Schedule

Here is a rough idea of the amount of time I expect to spend on each topic. A day by day schedule (see above) will be maintained to keep you informed of upcoming and past lectures.

 SECTIONS TOPICS TIME Ch 1-2 Solution of Equations and Transformations 3 weeks Ch. 3 Subspaces of R^n 2 weeks Ch. 4 Abstract linear algebra 2 weeks Ch. 5 Orthogonality and projection. 2 weeks Ch. 6 Determinants 2 weeks Ch. 7 Eigenvalues and Eigenvectors 3 weeks