The roots of linear algebra lie in the quest to solve systems of linear equations (equations in many variables where the variables only appear to the first power, with no higher powers and no two variables multiplied together). Matrices are introduced as tools to help with the bookkeeping involved in solving these systems, but we will quickly see that matrices are interesting algebraic objects in their own right, and much of this course will be devoted to studying them. Matrices also represent certain types of functions (linear transformations) from one Euclidean space Rⁿ to another, and the properties of these functions (are they one-to-one, what is the range, what happens if you apply the function over and over) can often be determined from algebraic properties of the matrices. As this is an honours course, we will also study more abstract vector spaces than Euclidean space and linear transformations thereon, and we will prove results that apply more generally to these vector spaces.

Use of the Web

Every enrolled student will be given an account on the Mathematics department undergraduate computer lab located in the MSRC building.  The computer lab is open 24 hours a day.  As part of your account, you will have a quota of 100 pages of free printouts.  You may also access the course web page on any public terminal at UBC, or via your own internet connection.

All documents will be posted in PDF format and can be read with the free Acrobat reader.  This software is already installed on the computers in the Math lab.  You may also download the free Acrobat reader at no cost.

Evaluation

• Final exam (Tuesday, April 9, 2002 from 8:30-11:00 am, GEOG 200): 50 percent
• Midterm exam (in class Friday, February 15, 2002): 30 percent
• Weekly homework and quizzes: 20 percent

Homework will be assigned on Fridays and due the following Friday at the beginning of class.  Late homework will not be accepted. We will also have a short quiz in class every Friday.  To account for forgetfulness or unforseen circumstances, each student's lowest homework score and lowest quiz score will be dropped.  Missed homework or quizzes will not be excused beyond this point, except for documented medical reasons.

Students are allowed to consult one another concerning the homework problems, but your submitted solutions must be written by you in your own words.  If two students submit virtually identical answers to a question, both can be found guilty of plagiarism.