Taylor Series, Newton's Method and Field and vector derivatives

For the past 3 weeks, I have been preparing for my university placement test, studying maths basically. I came across so much new ideas and techniques that aren't included in the IB, just showing me how beautiful maths is.

For example, the derivative of something can mean so much more than the rate of change of something, it can lead to a completely different idea, like the link between electricity and magnetism. Apparently, magnetism is simply the relativistic effects of electricity, I still haven't really grasped that.

And Taylor series, which through an infinite (really infinite) number of values can calculate the value of an irrational number like root(2) or sin(1). And how technically, any number can be written as a sum of a series, just that it would be an infinite series.

3 weeks with maths outside IB has further shown me how maths is not a dry and boring subject, it is a beautiful way of expressing ideas which have practical use.