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Ask HN: How can I learn to read mathematical notation?

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Re: Ask HN: How can I learn to read mathematical notation?

#111

Post by jfarmer »

cowboysauce wrote: post #56

I think you've got this backwards. You don't need to understand the notation, you need to understand the math. If you don't understand the notation then you probably don't understand the math in the first place so learning notation won't help. Learning how a matrix is written is useless without understanding what a matrix is. You need to find out exactly what type of math is used in the paper and learn that. Learning…

I second this. The notation was driven by the concepts, problems, and approaches. If the notation feels bizarre it’s because you don’t see how it improves/clarifies the underlying concepts, problems, and approaches.

Learning the notation itself can be useful as a way to point you towards relevant concepts, e.g., “Where did this symbol come from and why did it become the convention? What concept/problem/approach motivated it?”

But if your goal is to memorize a bunch of symbols you’re gonna have a bad time.

Re: Ask HN: How can I learn to read mathematical notation?

#113

Post by crawfordcomeaux »

eldavido wrote: post #52
crawfordcomeaux wrote: post #44

Earlier quoted context omitted.

Just because you choose to believe you need to be fed your information doesn't mean others do. I've tutored people carrying the thoughts you're expressing ("I need someone to teach me this because I'm not smart enough to learn it on my own"). The quickest way to success with them was shattering that myth. I did it by talking to them about their feelings/beliefs and helping them figure out practices for changing their…

It's not about being "fed information". It's the reality that being around a motivated group of peers confers real advantage. I look at the history of art (e.g. Impressionists), YC, winning athletics programs, Silicon Valley, or just about any well-regarded academic department as evidence. These places don't do well just because they select the best, they also MAKE the best by creating an environment that fosters it.

"The best" is purely subjective.

I look at indigenous cultures who were able to resolve conflicts and share resources without hierarchical governments. They developed approaches to doing things western culture is only now relearning.

Also, your "best people" developed systems to addict us with little concern for their systemic impacts. If that's your version of best, I want better.

Re: Ask HN: How can I learn to read mathematical notation?

#115

Post by lucb1e »

eldavido wrote: post #86
stillbourne wrote: post #81

Earlier quoted context omitted.

Don't listen to this asshat. There are 2 great resources for self education on Math. https://www.encyclopediaofmath.org/index.php/Main_Page and http://people.math.sfu.ca/~cbm/aands/abramowitz_and_stegun.p... Have a nice day.

Happy Thanksgiving to you, too.

Not sure this has anything to do with American holidays or traditions or whatever Thanksgiving is. It's not a thing here and idk if it's a thing in the country GP comes from. I wouldn't have known it was this month if you hadn't mentioned it.

Re: Ask HN: How can I learn to read mathematical notation?

#116

Post by lucb1e »

cowboysauce wrote: post #56

I think you've got this backwards. You don't need to understand the notation, you need to understand the math. If you don't understand the notation then you probably don't understand the math in the first place so learning notation won't help. Learning how a matrix is written is useless without understanding what a matrix is. You need to find out exactly what type of math is used in the paper and learn that. Learning…

Partly, perhaps. For me, a large part is the notation. I know conditionals, I know loops (as in for loops), I know SQL... but if you show me logic, set theory, a sigma, or, uh, what's this sigma but for multiplication, I wouldn't have known what you meant a few years ago. It's not only understanding the math, it's also the notation.

I still don't know how to read things like curly braces or matrices or a dozen other things that I don't even know the name for, and figuring it out is usually more work than it's worth. As a result, I don't understand Wikipedia articles that are supposed to be introductory and understandable to the masses, but because the article's writers are being fancy, it's only understandable for a privileged few. Often the concepts, if I do bother to understand them or look them up elsewhere, are rather simple.

It also doesn't help that people use things incorrectly or ambiguously. Sometimes a line over some math will mean the average (or "mean", to use the ambiguous lingo) and sometimes it's an infinite repetition.

Or the lingo: a friend of my girlfriend was baffled I didn't have X in school and didn't know what it was (I think it's derivations). She kind of explained it to me and I kind of understood, not recognising it. Later that evening I used it, unknowingly, in programming. When showing my girlfriend what I made she pointed it out to me.

Heck, I recently used logarithms fairly intuitively where they were never properly explained to me. I just knew the formula for entropy calculation (log(possibilities)/log(2)) by heart and managed to make something that converts a number from any base into any base (e.g. base 13 to base 19). I can do math, just nobody bothered to tell me about the fancy symbols. To me, the symbols mainly seek to obfuscate, look smart, and ensure job security.

Re: Ask HN: How can I learn to read mathematical notation?

#117

Post by OJFord »

Koshkin wrote: post #107
woodson wrote: post #105

John von Neumann once said, "Young man, in mathematics you don't understand things. You just get used to them." While probably not the originally intended meaning, you can take the quote as saying that, after reading a lot of papers in a given field, you will “get used to it” and recognize recurring patterns and what they mean. This is particularly important as more often than not, part of the math is left out (presu…

> it’s just there to show off That is true, unfortunately, in much of the mathematical literature. Way too often authors use the formalized language where the plain language would suffice. This kind of abuse is extremely widespread. It is one thing when a formula is used to represent, say, a complicated integral; it is another when a formula is used to express something just as easily said in a couple of words.

Natural language can be extremely ambiguous though, and while the ambiguity may be resolved easily from context, someone in OP's situation doesn't have that context. The precision mathematical notation can afford (more readily than, say, English) actually helps. But of course, only of one knows the meaning...

I'm in a somewhat similar position to OP, it's extremely rare that I'd find a whole paper accessible, the best way I know is just to get gradually more specific, from a broad undergraduate textbook on 'logic' or whatever other similarly broad area, and hone in on the more specific area of interest. Notation will be introduced, and by the time the last 5% is, 80% will be second nature, and the remaining 15% will be familiar and 'let's see.. I think it was used in this book..'

Re: Ask HN: How can I learn to read mathematical notation?

#118

Post by eldavido »

stillbourne wrote: post #109
eldavido wrote: post #86

Earlier quoted context omitted.

Happy Thanksgiving to you, too.

As a high school dropout that is self educated, I don't appreciate people dogging those who take the effort to forge their own path. You can learn complex topics outside a formal education system and your comment offered no specific assistance. So in the spirit of the holiday, thanks for nothing.

So here's the thing: apart from you and maybe a few friends, nobody really cares about your "forging your own path". It may give your life meaning, which is important. But in any sort of professional / market context, people just emphatically. Do. Not. Care.

Speaking from experience, I have often taken the hard path. I've always regretted it and often, if I'm being honest, it's out of a misguided sense of stubbornness.

That's why I recommend trying college, to the OP. Maybe he can learn advanced mathematics by himself, in isolation. But that isn't the maximum-likelihood path. And when you're doing something hard, I've learned it pays to do everything you can to stack the deck in your favor.

I think the main thing is to realize you only live one. I have friends who are more successful than me in every way. One earns literally 10x what I do, others work at more famous companies, still others receive absurd amounts of money from their parents for sitting on their ass. You can't choose your hand in life, but you can choose how you play it. So it's really up to you, whether you want to play the game on easy mode, or hard mode. Or whether you want to feel sorry for yourself or just make something of the hand you're dealt, though it may not be "fair".

Re: Ask HN: How can I learn to read mathematical notation?

#120

Post by iguy »

ashelmire wrote: post #46

I've taken reasonably advanced math courses (I was, for a time, a math major), and I have a great deal of difficulty with machine learning papers. They often reference domain-specific formulas that are prerequisites, sometimes without naming them, and rarely does a paper actually define every symbol used in a formula (in fact, I don't think I've ever seen a paper do this - it's usually none, and they only define a fe…

Machine learning papers are a particularly toxic brew of people in a rush, who like to show off, and who spend all day fiddling with code & little time reading or writing mathematics. Lots of formulas for quite simple things are at best ambiguous and at worst simply incorrect.
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