I'm really fond of math, and would have studied that, if I didn't find software development even more interesting. Even though I don't study math, I do sometimes come across stuff I want to learn and/or understand, but cannot seem to grasp, mostly because, e.g., the formulas are presented in a notation that I am not used to.

Take for this one for example: http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Derivative

Some of this makes sense, like the "$n$" on the left and the "$(P_{i+1}-P_{i})$" on the right. The summation, "$\sum_{i=0}^{n-1}$", kinda makes sense to me, and stuff in the middle, "$b_{i,n-1}-(t)$", doesn't make much sense to me. I have a feeling this wouldn't be too hard for me to grasp, if only I was able to understand the notation.

Is there a place where I can read up on this kind of notation, and/or generally learn about more than just the most basic math notation?

(Bonus question: If someone is able to understand the formula, an explanation of it is very welcome.)

  • $\begingroup$ The “$(t)$ on the right” is actually the argument of $b_{i,n-1}(t)$, which has already been defined above. The B is a curve, namely, a collection of points (a line) in the plane. As the parameter t goes form $0$ to $1$, each of its values draws a point. What are the coordinates of such a point ? Well, you need the coordinates of $n+1$ other constant points $\mathbf P_k$ to compute them. $\endgroup$ – Lucian Dec 1 '14 at 11:06
  • $\begingroup$ I already knew most of the details. I did however miss that $b_{i,n-1}(t)$ had been defined earlier. The notation still kinda boggles me, but it's starting to make a lot more sense now. Thanks! :) $\endgroup$ – phaz Dec 1 '14 at 15:17

This is definitely very often a somewhat difficult issue when learning mathematics (and often times it's even worse in applications of math to the sciences!). As a rather contrived example, we can look at

$$x = {-b\pm\sqrt{b^2-4ac}\over 2a} \tag{1}$$

and then at

$$T^{\mu\nu} = \partial^\mu\phi\partial^\nu\phi - \eta^{\mu\nu}\mathscr L\tag{2}$$

The first of these is an extremely well-known formula, and quite "attractive" - it makes use of nothing more complicated than a square root sign. On the other hand, the second equation (which I'll add is not necessarily larger as in having more symbols than $(1)$ in any way) is almost anyone's intimidation - purely because of the fact that it uses a lot of scary symbols and greek letters.

I would say that the main solution to this is to not jump around Wikipedia looking for symbols attempting to understand them and moving on. There are simply a lot of different symbols, and in general without some sort of structure they'll just seem ever more intimidating. I would instead recommend setting aside a few hours and trying to truly learn the concepts behind the notations. If you're able to do this all of the seemingly scary notations will always begin to show some sort of structure. For instance, the concept presented by $(2)$ is every bit as beautiful and interesting as that presented by $(1)$ - it only requires an understanding of the stucture behind the notation to understand fully.

tl;dr - if possible, learn the concepts before the notations.

"We need new notions, not new notations." - Carl Friedrich Gauss

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I find that Mathematical Notation: A Guide for Engineers and Scientists is very handy for explaining notations.

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  • $\begingroup$ At first glance, this looks very much like what I had in mind. I'm gonna have to take a look at that. Thanks! :-) $\endgroup$ – phaz Dec 1 '14 at 17:48

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