Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Ask HN: How did you learn math notation?

news.ycombinator.com

Post reply on HN
Print view View original

121–130 of 258 posts

Re: Ask HN: How did you learn math notation?

#121

Post by bajsejohannes »

nicoburns wrote: post #86
bajsejohannes wrote: post #75

Earlier quoted context omitted.

> I think a real problem in this area is the belief that there is "one true notation" and that everything is unambiguous and clearly defined. Just to back up this point: In probably every university-level math book I've read, they introduce and explain all the notation used. In the preface and/or as concepts are introduced. There are lists at wikipedia [1] and other places, but I'm not sure how valuable it is out of…

Ha, you've clearly used better books than me. I've read plenty where they glossed over the notation and expected you to guess.

It's not entirely unlikely that I am remembering just the good stuff :) But I was surprised how many books would define even the most common notation, like ⊂, ∀, and ∃.

I guess if you call your book "Introduction to..." you ought to do that. And it seems that all books were called that, regardless of how narrow and advanced the rest of the title was :)

Re: Ask HN: How did you learn math notation?

#123

Post by Someone »

NamTaf wrote: post #24
ColinWright wrote: post #14

Earlier quoted context omitted.

You say "There's a formula with a triangle ..." without telling me where. That's not real helpful, and you're making me do the work to find out what you're talking about. If you want assistance to get started, you need to be more explicit. However, I have done that work, so I've looked, and in the second column of page 210 there's a "formula with a triangle": t_c = 5 \middot 10^{-5} \sqrt( V / Dt ) ... where the "D"…

I feel you're coming at this without appreciating your body of prior knowledge. Intended or not, your statment "But that can't be it, because just two lines above it we have..." assumes a whole lot of knowledge. You and I both know that it reads as one term, but for someone unfamiliar with calculus but exposed to algebra they are drilled to understand separate graphemes as separate items, because the algebraic 'multi…

> with calculus but exposed to algebra they are drilled to understand separate graphemes as separate items

But most will already be familiar with the family of goniometric functions such as sin and cos, there’s log and possibly exp and sqrt. There’s min and max; advanced math has inf and sup.

Re: Ask HN: How did you learn math notation?

#125

Post by mistrial9 »

Hermitian909 wrote: post #85
ColinWright wrote: post #58

Earlier quoted context omitted.

> I dislike maths notation as I find it lacks rigour. I see this a lot from programmers, but in essence, you seem to be complaining that maths notation isn't what you want it to be, but is instead something else that mathematicians (and physicists and engineers) find useful.

As someone who's studied math and CS extensively, it's not that mathematicians don't need that rigor it's only certain sub-fields have a culture of this kind of notational rigor. You absolutely see little bubbles of research, 2-4 professors, get sealed off from the rest of the research community because their notational practices are so sloppy that no one wants to bother whereas others make it easy to understand thei…

I read some graph theory papers from mid-20th Century and yes, this is true

Re: Ask HN: How did you learn math notation?

#126

Post by milesvp »

ColinWright wrote: post #58
cabalamat wrote: post #50

Earlier quoted context omitted.

> I think a real problem in this area is the belief that there is "one true notation" and that everything is unambiguous and clearly defined. One main cause for this belief is that in a programming there is one true noation (or rather, a separate one for each language) that is unambiguous and clearly defined. I dislike maths notation as I find it lacks rigour.

> I dislike maths notation as I find it lacks rigour. I see this a lot from programmers, but in essence, you seem to be complaining that maths notation isn't what you want it to be, but is instead something else that mathematicians (and physicists and engineers) find useful.

You may not realize that in a given field, the same variable that represents the same basic thing may be negated depending on the part of the world the paper is published from. This can be fine, if it’s your subfield, you happen to know to be careful with said variable. I don’t personally dig into a lot of disperate maths in different papers very often, but this is the single biggest complaint my polyglot friend talks about. The second biggest is when he has to read and parse the math from a dozen unrelated papers in a field to find out what some random undefined variable means in the actual paper he cares about.

Re: Ask HN: How did you learn math notation?

#127

Post by Syzygies »

I'm a math professor, and my students find it revelatory to understand math as I talk and draw.

Math notation is not math, any more than music notation is music. Notably, the Beatles couldn't read sheet music, and it didn't hold them back.

The best comparison would be is reading someone else's computer code. At its best computer code is poetry, and the most gifted programmers learn quickly by reading code. Still, let's be honest: Reading other people's code is generally a wretched "Please! Just kill me now!" experience.

Once you realize math is the same, it's not about you, you can pick your way forward with realistic expectations.

Re: Ask HN: How did you learn math notation?

#129

Post by Jtsummers »

kergonath wrote: post #114
Jtsummers wrote: post #110

Earlier quoted context omitted.

https://mitpress.mit.edu/sites/default/files/titles/content/... It's formula 1.12 at the start of section 1.5 on this page converted into a Scheme representation, in section 1.5.2.

Thanks! I am not sure I like the Scheme-like notation, but the effort is interesting.

It's actually executable, which is part of why they wrote this particular book. The intent was to have a more uniform syntax for presenting the math and being able to (programmatically) use it.
Post reply on HN