Honors | Honors Course in Linear Algebra
S303 | 3106 | Livingston


Calculus teaches us to understand complicated curves by approximating
them by straight lines (the tangent line). Formulas for tangent lines
are easier to compute with, and provide excellent approximations for
the values of a function. For instance, the slope of the tangent line
tells us how a function changes. Similarly, calculus understands
surfaces through the tangent planes. Lines and planes are low
dimensional examples of linear space. The fundamental principle of
calculus is that linear space is easier to understand and work with
than non-linear space.

Linear Algebra investigates linear space, and function representing
linear space. Although we will sometimes use calculus to motivate
linear algebra, it is not the subject of this course. If you have had
multivariable calculus it may help motivate this course. However, if
you haven't, this course will be valuable when you take multivariable
calculus.

This course deals with both the calculational and the theoretical
aspects of Linear Algebra. You will learn about doing mathematics, not
just using it. I recommend this course particularly for students who
will continue with graduate work in the sciences or mathematics, or
who love mathematics and wish to share this enthusiasm with me.

The text will be Linear Algebra, by Robert J. Valenza. Students can
expect 6-10 difficult assignments and 1-3 take home exams. The precise
structure of the course is flexible and will depend on the nature and
desires of the particular students registered.