DAMAGE CONTROL: PART 1

I have always felt that my less structured pursuance of Actuarial Studies (as for many other Actuaries in the country) will have its toll on me. Taking ACE or ACTEX manuals as the only required ingredient at passing Actuarial exams, the level of mathematical skill and mastery that should be fostered does not happen. However, I also know now that taking Mathematics as a subject in GCE A-Levels and nailing it with a “Too easy A” really meant nothing. I really should have questioned University of Cambridge GCE examination standards when I was commending my own intelligence.

While taking an online Coursera course entitled “Mathematical Methods for Quantitative Finance”, I have realized some embarrassing gaps in my mathematical knowledge:

 Evaluating Limits

The concept of limits is not an alien concept to me, but truth be told, I studied them hastily while preparing for university aptitude tests about 7 years ago and they were not part of the GCE Mathematics syllabus (unless you take Further Mathematics).

In an aptitude test preparation class, I recall a teacher demonstrating a relatively easy method at solving Limit Problems. He said, “Differentiate the numerator, differentiate the denominator, place in the value of x in both and pray to God it works.” At that time I admit in my naivety I took it for some secret black book method; a “MATH HACK”.

However, today I know this as the L’Hopital’s Rule and am thankful that all this time I haven’t been doing anything illegal:

Derivatives

Differentiation is such a simple and groundbreaking concept and Actuaries as well as all other professionals in related to any sort of Applied Mathematics appreciate it. I know it as sometimes “the rate of change” or “when determining minima or maxima”. Of course, I have always simply known differentiation as the process of doing this:

What I didn't know was that differentiation is “fundamentally” this:

And all of a sudden differentiation made so much sense. I tried a few differentiation problems and it holds, although later I felt like a fool when so many others of my colleagues already knew about this.

But just to make sure, I referred to a higher power above me; Maplesoft’s Maple confirms this:

Also when used in a more Black Scholes sorta situation:

The conclusion here is of course, that among all things discussed above, at least someone is an IDIOT, and that someone is very likely me. Nevertheless, I can safely bet that this shall be the case with other GCE A Level students taking Mathematics but not Further Mathematics.