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.