If you haven't already,
I would start by learning the Greek alphabet
and the sounds that the letters make.
Conventions like Σ for sum and Δ for difference seem much less strange
when you realize that they're basically just S and D.
Ask HN: How did you learn math notation?
191–200 of 258 posts
Re: Ask HN: How did you learn math notation?
#192Earlier quoted context omitted.
I would say that delta is typically used to mean difference of any magnitude (i.e. Δt could mean 2 hours).
Yes, small changes usually use lowercase delta, e.g. δt. Not to be confused with the derivative symbol dt, nor with the partial derivative symbol ∂t ! Before I continued my maths learning after highschool (ie before UK A-levels) I learnt the Greek alphabet to make it easier to understand maths notations as I could 'voice' (internally) all the funny glyphs adopted from Greek. At uni I learnt how to properly write an a…
https://en.wikipedia.org/wiki/Riemann_sum usually uses ∆. See also the explanation of ∆ at https://en.wikipedia.org/wiki/Derivative#Explanations .
That's the sense in which I'm using ∆, which is common, at least in the US.
Re: Ask HN: How did you learn math notation?
#193Earlier 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.
Formulas would also be easier to read if they would not name all their variables and functions with one character. If programmers would write code like that (even fortran programmers use 3 characters), noone would be able to understand the code...
People sometimes do that when their code is reasonably abstract. For example, usual convention for generic type in Java is something like T.
https://docs.oracle.com/javase/tutorial/java/generics/types....
Re: Ask HN: How did you learn math notation?
#194Earlier quoted context omitted.
The triangle, or “delta”, is used to indicate a tiny change in the following variable. Let’s say you go on a journey, and the distance you’ve travelled so far is “x” and the time so far is “t”. Then your average velocity since the beginning is x / t . But, if you want to know your current velocity, that would be delta x divided by delta t . The delta is usually used in a “limiting” sense - you can get a more accurate…
I would say that delta is typically used to mean difference of any magnitude (i.e. Δt could mean 2 hours).
True. To continue my example, the average velocity in the last hour would be taken with a ∆t of 60 minutes.
Re: Ask HN: How did you learn math notation?
#195Earlier quoted context omitted.
I'm glad I'm not the only person like this. I've never liked tradition math notation and found it about as useful as traditional musical notation, that is, hard to read for the layman and for no other reason than "this is how people have been doing it for a long time". Maybe I'm the minority, but when I read a CS paper I mostly ignore the maths and then go to the source code or pseudocode to see how the algorithm was…
> ...for no other reason than "this is how people have been doing it for a long time". I disagree. Math notation has evolved to be as it is because it is useful for the purpose of doing math. If there were some way of doing it better, people would be evolving to be doing so. In some ways they are ... people are using computer algebra packages more for a lot of the grunt work, and are using proof assistants to verify…
> If there were some way of doing it better, people would be evolving to be doing so.
I don't see why wouldn't it be some kind of local maximum. Maybe there are better ways, but they are sufficiently far away from current notation, that they aren't even thought about.
Re: Ask HN: How did you learn math notation?
#196Earlier 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. No, that belief isn't the problem; that actual status quo itself is obviously the problem. There are numerous notations and authors don't explain what they are using, assuming everyone has recursively read all of their references depth-first before reading their paper.
Why does RTFM not apply to mathematics dependencies?
Because there usually isn’t anything resembling an actual manual.
Re: Ask HN: How did you learn math notation?
#197Earlier quoted context omitted.
Yes, small changes usually use lowercase delta, e.g. δt. Not to be confused with the derivative symbol dt, nor with the partial derivative symbol ∂t ! Before I continued my maths learning after highschool (ie before UK A-levels) I learnt the Greek alphabet to make it easier to understand maths notations as I could 'voice' (internally) all the funny glyphs adopted from Greek. At uni I learnt how to properly write an a…
https://en.wikipedia.org/wiki/Riemann_sum usually uses ∆. See also the explanation of ∆ at https://en.wikipedia.org/wiki/Derivative#Explanations . That's the sense in which I'm using ∆, which is common, at least in the US.
But this is a physics paper, that isn't how you use uppercase delta in physics. It is just a range. In physics however you do a ton of approximations all the time in ways mathematicians hate (you don't care about errors smaller than you can measure), so uppercase delta is often approximated with derivatives etc, but it isn't a derivative. Math in physics is way more practical and uses very different techniques than math in math, often because physicists invented the math first and mathematicians later went and formalized it.
Re: Ask HN: How did you learn math notation?
#198One of the best things I figured out that at least in the last 70 years or so ago it's pretty easy to find the "first" or foundational paper for a particular construct where they have to explain their notation for the first reader or they have the vibe of working with the new idea in the raw rather than 40 years later where it is matured. One example I use for this is hamming codes where some of the recent examples or explanations don't build it from first principles, but the original articles do explain it very clearly.
Re: Ask HN: How did you learn math notation?
#199Earlier quoted context omitted.
Why does RTFM not apply to mathematics dependencies?
Because there usually isn’t anything resembling an actual manual.
Sure there is, read these and you will understand most math papers people here struggle with: https://mathblog.com/mathematics-books/
Of course you still wont be able to understand most math papers written by pure mathematicians, but it should be fine for whatever you need in CS. I know all the topics on that page, it is just a very fleshed out math major.
Re: Ask HN: How did you learn math notation?
#200Earlier quoted context omitted.
Came here to say the same thing harshly and laced with profanity. I guess I can back off a bit from that now. I was filled with crushing disappointment when I learned mathematical notation is "shorthand" and there isn't a formal grammar. Same goes for learning writers take "shortcuts" with the expectation the reader will "fill in the gaps". Ostensibly this is so the writer can do "less writing" and the reader can do…
You seem to be complaining that math isn't programming, that it's something different, and you've discovered that you don't like how mathematicians do math. Math notation is the way it is because it's what mathematicians have found useful for the purpose of doing and communicating math. If you are upset and disappointed that that's how it is then there's not a lot we can do about it. If there was a better way of doin…
I mostly agree with you.
That all said, it would still be quite nice if it was somehow more accessable. A lot of papers containing material that's probably actually quite standardizable remain opaque to me, and the notation invariably falls by the wayside if there's a code or language description available.
Many times, math notatons have been thought to be minimal, or most clear possibly, only to fall by the wayside
Whereas this notation serves domain specialists well, it still leaves people like me somewhat confused
A cheat sheet - even to the practical norms - would go a long way