Math 45: Linear Algebra

Catalog Description

The use and application of matrices in the solution of systems of linear equations, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, diagonalization, and orthogonality. Linear algebra is a core course in many engineering, physics, mathematics, and computer science programs.

Special notes or advisories: Computer exploration is an integral component of this course. Students will also create and present oral and written analyses of a topic that requires use of the concepts and techniques learned in this course.

Prerequisites

Math 50A (or equivalent) with a grade of "C" or better.

Describe representative skills without which the student would be highly unlikely to succeed: Students must have well-developed mathematical reading and writing skills to be successful in this course. Some of the course material may involve concepts from differential calculus.


Student Expectations

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 also be a final project with a written report and classroom presentation.


Textbooks

The textbook used for the course will depend upon the instructor teaching the course. The textbook used in the Fall semester, 2012, will be Linear Algebra, by, David Lay. The official text site is here. We will not be using MyMathLab.


Calculators and Computer Software

The class will 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 room PS116 in the Physical Sciences building.

If you'd like to use Matlab on your personal computer, then you should consider purchasing the Student Edition of Matlab, available on line at the following URL:

Matlab and Simulink Student Version

You will also learn the basics of TeX, the mathematical typesetting language, for writing up proofs, your project paper, and your project presentation. TeX is also installed on the computers in PS116.

If you'd like to set up TeX on your personal computer, then you can download Miktex for PC's, or Mactex for Macintosh computers. Linux systems usually are already configured for using TeX.


Student Projects

In place of a final examination, students are expected to write a term paper for the course, and present their findings in a 15-minute slide presentation on the day appointed for the final examination. It is expected that Matlab is used for computation and programming, and the paper and slides are to be written in Latex. Instructions for incorporating Latex in student papers and slides is available at the following URL:

Writing Scientific Papers in LaTeX

Samples of former student papers and presentations are available at the following URL:

Student Projects in Linear Algebra

To get some idea of pace and project due dates, consult the Student Term Project Timeline used during the Fall semester, 2010. Ask your current instructor for his project timelines and expectations.


Sample Quizzes

To get some sense of the type of quizzes that will be administered in linear algebra, take a look at the page:

Sample Quizzes in Linear Algebra

Be sure to study the solutions provided in each quiz.

Important Links

Current Math 45 Home Pages

Past Math 45 Home Pages