It is use to define/initialize some variable or function in the programming language. $"="$ is often use to compare stuff to check for instances "if"s like if(x=2) then... while "$:=$" is often used to initialize a parameter, see for example page 19 of your notes, the bubble sort:
The author sets $i$ and $ swap$ to $0$ and then checks some condition with the "if". If he had wanted to check eqality at step $2$, he would ahve used " if $X_i=X_{i+1}$. Then he, if that condition is met, he sets $swap$ to be $1$ by doing $swap:=1$.
=– Bill - The Butcher - Cutting Sep 15 '13 at 15:09=makes more sense and is more clear. – Bill - The Butcher - Cutting Sep 15 '13 at 15:11=and==are standard ways to differentiate between assignment and equality. JavaScript, Java and other popular languages use this syntax. Also math uses=to represent assignment. The professor is using outdated ( or simply less used ) CS language ( not his fault the notes are from 2003 ) syntax when he should be using modern CS language syntax or pure math. – Bill - The Butcher - Cutting Sep 15 '13 at 15:19