Bong Lian

Research Projects

Research Projects


July 24 Homework

July 28 Homework

July 29 Homework

July 30 Homework

July 30 Homework

July 31 Homework

August 03 Homework

August 04 Homework

August 05 Homework

August 06 Homework

August 07 Homework

August 10 Homework

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 throughout mathematical sciences at large, reaching the deepest corners of physics, biology, economics, and countless other fields. All fancy stuff.

We, however, will go all the way back to the very beginning instead, and ask very basic questions. What are numbers? Why linear equations? Solving them tells us what? How do we solve them? How do we describe solutions { their shapes and sizes? What does it mean to say that "the equation x+y +z = 1 describes a plane in 3-space?" Given a point P and a plane H in 3-space, how do we find the point in H closest to P? Given n points on a plane, can we find a straight line that is the `closest' to all those points? Some of these questions obviously connect linear equations with geometrical objects we can visualize. We will dig deeper into this algebra-geometry connection to see how understanding objects in geometry tells us about linear algebra problems and vis versa.

As for pre-requisite or background for this course, Mathcampers are not expected to have had any 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 in this course!

Homework problems will be assigned in class almost daily during the lecture. One or more research projects will be announced dring the first week of Mathcap. Mathcampers will be meeting and working with two Coaches in this course, in addition to the Instructor. The Coaches will be meeting with Mathcampers on a daily basis, to work with them on their homework assignments and their research project. Mathcampers are also very much encouraged to work with each other.