Math 45: Linear Algebra
At College of the Redwoods, Math 45 is the course number for our Linear Algebra course, offered each Fall semester. The information on this page is designed for use by a number of constituencies:
- instructors of Linear Algebra,
- students enrolled in Linear Algebra, and
- all others interested in gathering information about our Linear Algebra course.
Be sure to visit this page often, as there may be updates to the information provided.
Student Information and Help Resources
COURSE DESCRIPTION: Linear algebra consists of an interesting mixture of computational techniques and abstract theory. The theory arises out of the study of the use and applications of matrices in the solution of systems of linear equations, and leads through the topics of determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors. Linear algebra also has many applications in other areas of mathematics, in the physical and social sciences, and in business. Consequently, linear algebra is a core course in many engineering, physics, mathematics, and computer science programs.
In a mathematics curriculum, linear algebra is usually the first course in which students are expected to understand all of the theory, and to learn to read and write proofs. That is because the theory is relatively accessible, and the proofs are generally short and fairly straight-forward. This gives students their first glimpse at how mathematical theory and rigor is developed, and how this development is the real basis of the subject. Another good reason for using linear algebra as a first “proof” course is that it also includes many computational aspects (i.e., it is not just abstract theory), and the theory can be easily demonstrated with examples.
In this course, you will study both the abstract theory and the computations, and will also look at some applications. There will be an emphasis on writing proofs and results. There will also be a final project with a written report and classroom presentation.
PREREQUISITES: Math 25 and Math 30 with a grade of C or better, or equivalent.
TEXTBOOK: Linear Algebra and its Applications, by David C. Lay (3rd edition). The textbook comes bundled with a CD which includes a Study Guide and other resources. The Study Guide includes detailed solutions to many of the odd exercise, supplementary material in the form of study notes and tips, key ideas, warnings, etc., and also has help resources for calculators and computers.
USE OF CALCULATORS AND COMPUTERS: A good graphing calculator is required. The calculator must have the capability to use matrices and to solve linear systems of equations.
The class will also make use of Matlab as a computational and visual aid to understanding the course material. You will use Matlab in the classroom, and you may also use it in the computer lab in 116 Physical Science. You will also learn the basics of TeX, the mathematical typesetting language, for writing up proofs and your project report. TeX is also installed on the computers in PS 118 and PS 116.
No software purchases are required, and no prior computer knowledge is required for the course - you will receive instructions on how to use Matlab and TeX.