Let's think of a function as something which has an "input" and an "output". In school we learn of various functions which take numbers to numbers, such as the function which has as input x and as output the square of x. But it is also useful to consider functions which have as input not only numbers but also pairs of numbers, or triplets of numbers, or quadruples of numbers, or quintiples etc. One has to begin somewhere, and we start by looking at such functions which have the property that they are "linear". (A word that will be defined only later.) This leads to the field of linear algebra, of which we will study a tiny little bit.

Our goal in this project is to learn all the mathematics necessary to write down the google page ranking algorithm. The problem is the following. Pages on the web have links to other pages. We want to use the links to a page as a measure of how important a page is. But we also want links from important websites, such as that of newspapers, to "count more". Now which site is important is of course a matter of opinion, not mathematics. But we can say a site is important if many important sites link to it. And those other sites are important if the sites linking to them are important, and the latter are important if ... This reminds one of the chicken-and-egg problem, but there is a way to "formalize" the idea so that we can write down an equation which can be solved.

Activities:
* Mathematics
* Problem solving
* Computer simulations

• Mr. Gusti van Zyl