 
Summary: LINEAR ALGEBRA (MATH 317H)
CASIM ABBAS
Lecture 1
1. Mathematical models, mathematical objects
Because this is most probably your first 'real' mathematics lecture (Calculus does
not count) I will spend the three lectures explaining a few general issues relating not
just to Linear Algebra but to Mathematics in general. Much of this introduction is
from Timothy Gowers' book 'Mathematics A very short introduction' by Oxford
University Press. The main purpose is to explain what we will be doing during this
course and why on a very informal level. The first question we will think about is:
What is a mathematical model ?
We will look at some examples.
A. Throwing a stone at an angle
We will answer the following question: At which angle should we throw a stone
so that it travels as far as possible ? If we throw it at a steep angle the stone will
travel very high but not very far. On the other hand, if we throw it at a flat angle it
will travel far, but it will hit the ground faster. It seems the answer is a compromise
between these two extremes. Maybe the answer is 45
? You learned in a Physics
lecture or in Calculus how to deal with this question. We use the following notation
