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Only tangentially related, every once in a while I look for a book, video, or even course that concisely explains the “language” of mathematical notation. As so

Only tangentially related, every once in a while I look for a book, video, or even course that concisely explains the “language” of mathematical notation. As someone who is largely self-taught when it comes to the more advanced math it’s frustrating that so many resources assume a basic level of notational knowledge/understanding so they just skip right over it and you’re left piecing it together using context clues and LaTex crib sheets.

kmill 5y ago
For better or for worse, piecing things together using context clues never seems to really end :-) One useful heuristic is the "unambiguous parse rule." You think about different ways something might be read (even if you have no idea what it's trying to say yet) and try to work out which one would lead to the least ambiguity. This is helpful also when trying to figure out how to write using newly learned notation yourself. A good technique is to just not get frustrated. All math starts impenetrable. Read ahead, try to get a glimpse of an idea of what's going on. Go back, find other sources about the same thing, find sources about similar things. If the original source was worth anything, eventually it'll reveal itself. Sometimes you realize you weren't the target audience and you were supposed to have been exposed to more introductory material and you wish they had cited one, but anyway, you found it. Another thing is that sometimes you just need to ask an expert, someone who's steeped in the culture. math.stackexchange.com is open to notation questions, but the guidance you can get in-person can be much more nuanced. I actually like running into new notation (supposing I'm not on a deadline trying to figure something out...), be it math or a programming language. You're trying to solve the puzzle of the purpose of the notation, what function does it serve, why someone ever thought this was a good idea. I've exposed myself to a lot of bits of obscure programming languages over the years, which makes it easier to guess what things might mean. Maybe one more thing: math notation tends to be invented for specific purposes, and maybe most of it doesn't carry over from subject to subject. Arithmetic, function application, summations, integrals, and set notation are fairly universal though.

kmill 5y ago

For better or for worse, piecing things together using context clues never seems to really end :-) One useful heuristic is the "unambiguous parse rule." You think about different ways something might be read (even if you have no idea what it's trying to say yet) and try to work out which one would lead to the least ambiguity. This is helpful also when trying to figure out how to write using newly learned notation yourself. A good technique is to just not get frustrated. All math starts impenetrable. Read ahead, try to get a glimpse of an idea of what's going on. Go back, find other sources about the same thing, find sources about similar things. If the original source was worth anything, eventually it'll reveal itself. Sometimes you realize you weren't the target audience and you were supposed to have been exposed to more introductory material and you wish they had cited one, but anyway, you found it. Another thing is that sometimes you just need to ask an expert, someone who's steeped in the culture. math.stackexchange.com is open to notation questions, but the guidance you can get in-person can be much more nuanced. I actually like running into new notation (supposing I'm not on a deadline trying to figure something out...), be it math or a programming language. You're trying to solve the puzzle of the purpose of the notation, what function does it serve, why someone ever thought this was a good idea. I've exposed myself to a lot of bits of obscure programming languages over the years, which makes it easier to guess what things might mean. Maybe one more thing: math notation tends to be invented for specific purposes, and maybe most of it doesn't carry over from subject to subject. Arithmetic, function application, summations, integrals, and set notation are fairly universal though.