Linear algebra began as the study of linear systems of equations. Currently, linear systems remain of great importance, in part due to their relative simplicity. For true mastery in any field, from physics to computer science, an understanding of linear algebra is fundamental. One might even argue that linear algebra and its applications are even more important than those of calculus in today's world.
This course provides an introduction to linear algebra from a concrete point of view. We emphasize understanding through intuitive exposition and plenty of examples and applications. Whilst we will need to understand theory, we will focus on the concrete setting of Euclidean space and relegate more abstract ideas such as general vector spaces to a second course.
Co-taught with SHW tutor @Yu Heng L, who also developed the series idea, overview, and outline!
High school Algebra I and II are required. Pre-calculus, trigonometry, and calculus are not necessary.
1. Linear Systems (~5 sessions)
2. Matrices (~4 sessions)
3. Determinants (~2 sessions)
4. Eigenvalues and Eigenvectors (~4 sessions)