TITLE: Entering math through the side door
QUESTION [25 upvotes]: I am not really good at math, I'd say I'm a lot worse than good when it comes to math but I am a programmer so I have to learn to get over that fact.
A lot of times if I want to implement some code I have to read math formulas and it might as well be written in Russian... I speak no Russian.
Let's take "perturbation theory" for example. The formula looks like this:

now I know most of those symbols so that's not too bad.
but there's some formulas with like Sigma [summation] $\sum $ notation and a whole lot of other symbols that mean things in the math, physics world that I have no idea what they mean.
Like this squiggly $f$ or $s$ looking thing in this image:
$$\int_{-\infty}^\infty \sqrt{\frac{\sqrt{x^n}+1}{\alpha+\beta^\gamma}} \, dx$$
squiggly $f$ or $s$
square root of $x$ to the $n$th power plus one divided by alpha plus theta to the (?) power times a type of $d$ times $x.$
I know this might seem like a joke but i am very sincere with this question.
Is there a book or repository where these signs are laid out with their meanings? I've googled but can't find anything except maybe these images with names but that often leaves me more confused than I started.
So is there a singular book or at least a place that I can go to reference these symbols to get their meanings?
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I don't think this is the same question as the one it's being marked as duplicate. I read that question and that's a very general question about how to get better at math.
That's not my question, I am asking more for a definition of terms. When you look at math papers there's often very cryptic symbols in the function. I am looking for a resource to say what those cryptic symbols mean and not generally how to do math.
I've tried to make this distinction clear. Let's use something simple for example. 
If you didn't know the rules of summation, how can you even start to decrypt what that formula means. What if you don't even know that that symbol is called sigma, where do you start?
I thought that there would be some resource for math that gave the names of those symbols and a way to use them. Back to the sigma example, if there was some resource that says that's called sigma and 
Then I can say oh okay, I got it I can figure it out from here.
So while the other question was more general about learning math, this is more directed at how do I decypher those symbols. Hopefully that makes the differences between the questions more obvious.

REPLY [3 votes]: The best way to learn math is to learn math.  The best way to learn math, as someone who knows programming, is still to learn math.
Forgive the pithy wording, but I think it captures something important: you shouldn't be learning mathematical symbols, you should be learning math.  For instance, you saw $\int$, the "squiggly f or s thing."  I could tell you that that is an integral sign, but that won't do you a lick of good unless you have the 2-3 semesters of calculus under your belt that you need to actually use the sign.  Until then, they're nothing but shapes on a page.
I went through this process learning Tai Chi recently (disclaimer: that should probably read "I am still learning Tai Chi").  I approached Tai Chi from a completely scientific perspective.  I know science.  If you can give me hard definitions for everything in your martial art, I can work with it.  I tried to apply science to Tai Chi.
Fat chance.
It worked... well.. okay, I don't even have a euphemism for it.  It failed so completely and utterly that there was almost no reason to even mention that the attempt occurred.  I needed to try a different approach.
So, instead, I chose to learn Tai Chi.  I didn't try to define Tai Chi in scientific terms; I didn't try to bound Tai Chi with probabilities.  I learned Tai Chi.  I learned what yin and yang meant not from some exotic analogy to a scientific model involving oscillating variables, but from what yin is and yang is, and how they work together.
Then, along the way, I found easier ways to do things.  I found that Faraday waves over here could do a reasonable job of approximating one type of motion, so I developed my own way of thinking about that motion which flowed fluidly from "mostly Faraday waves, with errors described using yin and yang" when I just need something rough to work with to "yin and yang" on their own when I needed to actually delve further into the real nature of the motion.  I never sought to find approximations first.  I always sought to do it right, and lean on the approximations when they helped make it easier to reach further into the art.
You should do the same with mathematics.  It sounds like you never took calculus.  Don't learn what an integral sign is: take calculus and learn integration.  You'll realize, along the way, that you actually have to learn differentiation before hand... its really easier to learn it in that direction.  If I gave you the symbols ($\int$ and $\frac{d}{dx}(f(x))$), you wouldn't even notice they are related... yet the back and forth between those two is as fundamental to calculus as variables are to algebra.
This will save you a lot of trouble.  Then, along the way, you may find a reason a programmer will want to study an Abelian group.  You'll find that you don't need calculus for that one, but if you don't have a foundation in abstract algebra (which is different from the algebra you lean in high school), the  meanings behind those symbols they use will vanish.  However, if you took the time to do just a little abstract algebra, and Abelian groups look useful, you may be able to dig into it, using your programming knowledge to hoist you past some of the difficult details along the way.
Then you really use your programmer side.  But always learn the fundamentals first, the way the discipline wants you to learn them.  Its always worth it.