LINEAR ALGEBRA (MATH 317H) CASIM ABBAS 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 Collections: Mathematics