Can someone recommend a good resource for a game developer who wants to understand mathematical notation so he can dissect game development papers faster? Currently it takes me multiple days to understand a single formula.
It feels a bit like how I found it impossible to memorise all the countries of the world as an adolescent, but then when I discovered Seterra as an adult I was able to memorise them all in less than a week. I need an equivalent perspective shift, but for math.
Beyond a relatively small set of standard symbols and functions, notation is dependent on the field or subfield you're studying, so a "guide to mathematical notation" is not really possible. However:
> it takes me multiple days to understand a single formula
This is not weird. Papers are not hard because notation is hard but because the ideas behind them are difficult to understand. It usually takes me several hours of uninterrupted work to read a paper; I'm not a researcher and have never been in academia, but everyone I know says the same thing, so I'm comfortable reassuring you that you're definitely not the odd one out.
A few pointers to go faster:
- Write down your observations (on the paper itself, if you can print it). Ask yourself questions and see if you got things right. Try to replicate their computation steps. Actively engage the topic.
- Keep a dictionary of symbols. What do the authors mean with this ridiculous scribble? Ah, that thing.
- Mathematical notation suffers from catastrophic overloading. For example, if A and B are numbers, then AB is multiplication in their set. If they are matrices, it's matrix multiplication. If A is a matrix and B is a vector, it's the image of B through A. If one is a vector and the other is a number it's multiplication by a scalar, and so on. Try to undo this process and figure out what the virtual method call resolves to :)
- Try to assign "types" to variables. Notation is "dynamically typed", in the sense that a variable could (syntactically) be anything. If you have trouble understanding a formula, try to understand what kind of object each variable represents. Is this squiggle a set or an element? If an element, from what set does it come from? What are the arguments of this function? What is its image? Is this "i" a real variable or a mute variable? To what quantifier is this variable bound?
- Sometimes notation is abused. E.g. we may write:
10n^2 + n = O(n^2)
This is, strictly speaking, nonsense: O(n^2) is a set, and we're saying it's equal to some undefined stuff. What even is "n"? Obviously, it "compiles" to:
f(n) = 10n^2 + n
f(n) \in O(n^2)
It's normal to abuse notation, but it may cause confusion if one is unfamiliar with the topic. Try to undo this process if you find it's preventing you from understanding a formula.
Sorry I don't have a recommendation but this seems hard, symbols in math can mean different things depending on the context (the field you are looking in) and at least while I was in undergrad they seemed to change between professors all the time while meaning the same thing.
Hopefully I am wrong and there is a way to learn with a game as with Seterra.
It feels a bit like how I found it impossible to memorise all the countries of the world as an adolescent, but then when I discovered Seterra as an adult I was able to memorise them all in less than a week. I need an equivalent perspective shift, but for math.