Abstract

In this thesis, I present a small experiment of teaching the singular value decomposition (SVD) of matrices using a computational approach. The goal of the experiment was to check if students who completed the first two undergraduate linear algebra courses are prepared for this topic and if they would be satisfied with the computational approach.
The experiment took place in the summer of 2011 and consisted in two sessions of lectures of four hours each, in a computer lab, on the premises of Concordia University. The same four students attended both sessions.
The approach consisted in first introducing students to the general ideas and then gradually zooming into the details of the theory and the computational techniques and algorithms. In the instructional sessions, lecturing by the teacher alternated with participants’ exploring the theoretical results and algorithms using prepared Maple worksheets.
Before the sessions started, participants were asked to respond to a questionnaire (Pre-test) that verified their knowledge of basic linear algebra concepts necessary for understanding the SVD theory. After the session, participants were asked to respond to another questionnaire (Post-test) addressing their understanding of SVD and their opinions about the teaching approach and the teaching of SVD in an undergraduate program. Participants’ responses to test questions were collected and analyzed.
One of the immediate conclusions is that without a good understanding of the fundamental concepts of linear algebra the topic of singular value decomposition of matrices could prove challenging for even the top achieving undergraduate students.
The participants showed interest in the teaching method, but mentioned that more time would be required to really benefit from learning about the numerical advantages and the vast applications of the singular value decomposition.