At first glance, Linear Algebra may seem an unusual offering in the high school curriculum. In my view, this discipline can play a valuable role in a student’s math career. Free of large crowds, or an AP framework, we are able…
to take the time to examine this topic is a careful and systematic way.
Mathematics is the language we use to describe our observations in nature. Increasingly, linear algebra plays a fundamental role in current developments in science. Disciplines from economics and finance, straight through to biology and physics rely on linear algebra as a fundamental tool. Our explorations in this class will equally benefit students anticipating future study in these areas, as well as those interested in math as a discipline. While we will spend most time on examples and problems, we will also develop the underlying theory from time to time as well.
Science today is becoming increasingly quantitative. Scientists are being confronted more and more with large amounts of numerical data, measurements of one form or another gathered from their laboratories, field experiments (like space probes), and surveys. But merely collecting and recording data achieves nothing–the collected data must be analyzed and interpreted. Mathematics is the chief tool for this analysis and interpretation, and one of the most useful branches of mathematics for this purpose is matrix algebra.
The central element of this course–solving systems of linear equations–is pretty approachable. We are familiar with this concept reaching all the way back to middle school. Finding the intersection of two lines can be framed as a good introduction to linear algebra. We’ll take a look at this simple problem in the next post.