Honors | Honors Course in Linear Algebra
S303 | 3062 | Orr, K.
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.