Bong Lian 连文豪

Course Description

Linear algebra may be thought of as the study of linear equations, like the familiar equation x + y + z = 1. But the subject permeates other ends of the mathematical world including topology,geometry, analysis, not to mention algebra itself! As a tool, it’s power can also be felt throughoutmathematical sciences at large, reaching the deepest corners of physics, biology, economics, andcountless other elds. All fancy stuff.

We, however, will go all the way back to the very beginning instead, and ask very basic questions. We solve equations using numbers. But what are numbers? Why linear equations? Solving them tellsus what? How do we solve them? How do we describe solutions – their shapes and sizes? What doesit mean to say that “the equation x + y + z = 1 describes a plane in 3-space?” Given a point P anda plane H in 3-space, how do we nd the point in H closest to P? Given n points on a plane, canwe nd a straight line that is the ‘closest’ to all those points? Some of these questions obviouslyconnect linear equations with geometrical objects we can visualize. We will dig deeper into thisalgebra-geometry connection to see how understanding objects in geometry tells us about linearalgebra problems and vice versa.

As for pre-requisite or background for this course, Mathcampers are not expected to have hadany prior advanced training in mathematics, but good working knowledge of high school algebra–equations in one or two variables, real numbers – some familiarity with calculus and complex numbers, plus a bit curiosity would give them a great start!

Homework problems will be assigned in class almost daily during the lecture, and they will bechecked and returned to students on a regular basis. One or more research projects will be an-nounced during the rst week of Mathcamp. Mathcampers will be meeting and working with twoCoaches in this course, in addition to the Lecturer. The Coaches will be meeting with Mathcam-pers everyday, to work with them on their homework assignments and their research projects.Mathcampers are also very much encouraged to work with each other.