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Ask HN: How did you learn math notation?

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

#71

Post by CogitoCogito »

kaetemi wrote: post #62

Math notation feels like a write-only language somehow. I can read and understand undocumented code with relative ease. Reading math notation without any documentation seems pretty much impossible, otoh.

You get better at it the more you do. A tip is also to actually change a mathematical exposition into a form you better understand (e.g. by writing it in a different notation and/or expanding it out in words to make the existing notation less dense). Basically convert the presentation into the way you would personally like to see it.

If you do this enough, the process becomes easier and the original notation becomes easier to understand. But it takes a lot of time and patience (as I'm sure it took for you understand undocumented code did as well).

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

#72

Post by drdec »

randomNumber7 wrote: post #60
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.

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...

As someone trained in mathematics, I can tell you that using single character variables allows one to focus better on the concepts abstractly which is one of the goals of mathematics. That is to say, it is a practice well-suited to mathematics.

It doesn't carry over to programming where explicit variables are better suited. In mathematics one is dealing with relatively few concepts compared to a typical program so assigning a single letter (applied consistently) to each is not a problem. This is not so in programming, except for a few cases like using i and j for loop variables (back when programs had explicit loops).

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

#73

Post by ColinWright »

f38zf5vdt wrote: post #59
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'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 some things, but there's a lot of math that's still done by sketching why something is true and letting the reader work through it. Math notation isn't about executing algorithms, it's about communicating what the result is, and why it works.

"Doing Math" is not "Writing Programs", so math notation is different.

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

#74

Post by pjc50 »

throwaway31338 wrote: post #56
Jensson wrote: post #51

Earlier quoted context omitted.

> there is one true noation (or rather, a separate one for each language) that is unambiguous and clearly defined. This is such a disingenuous take. How many of the source code files you write are 100% self contained and well defined? I'd bet not a single one of them are. You reference libraries, you depend on specific compiler/runtime/OS versions, you reference other files etc. If you take a look at any of these sci…

One can look at the source code to a program, the libraries it uses, the compiler for the language, and the ISA spec for the machine language the compiler generates. You can know that there are no hidden unspecified quantities because programs can't work without being specified. When you get down to the microcode of the CPU that implements the ISA you might have an issue if it's ill-specified. You might be talking ab…

> because programs can't work without being specified.

Someone hasn't read the C spec, with all its specified as undefined behavior.

Programs working on real systems is very different from those systems being formally specified. I suspect that if you only had access to the pile of documentation and no real computer system - if you were an alien trying to reconstruct it, for example - you'd hit serious problems.

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

#75

Post by bajsejohannes »

ColinWright wrote: post #2

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. Yes, conventions have emerged, people tend to use the same sort of notation in a given context, but in the main, the notation should be regarded as an aide memoire , something to guide you. You say that you're struggling because of "the math notations and zero explanation of it i…

> 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 context.

[1] https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo...

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

#76

Post by colechristensen »

randomNumber7 wrote: post #60
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.

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...

Scientists and engineers write code with single variables all the time and don’t seem to have any large amount of trouble with it. Long variable names seriously limit the ability to put complexity in one place and make it understandable.

Take a look at this and tell me it would be easier to understand if all the symbols were words instead of single characters: https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html

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

#77

Post by throwaway31338 »

ColinWright wrote: post #69
throwaway31338 wrote: post #54

Earlier 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 really, really appreciate your reply and its tone. Thank you for that. You've given me some things to think about.

I often wish people were more like computers. It probably wouldn't make the world better but it would make it more comprehensible.

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

#78

Post by tgflynn »

It sounds like you're trying to read papers that assume a certain level of mathematical sophistication without having reached that level. Typical engineering papers will assume at least what's taught in 2 years of college level mathematics, mainly calculus and linear algebra, and no they aren't going to be explaining notation used at that level.

But it isn't just about the notation. You also need to understand the concepts the notation represents, and there aren't really any shortcuts to that.

These days there are online courses (many freely available) in just about every area of mathematics from pre-high school to intro graduate level.

It's possible for a sufficiently motivated person to learn all of that mathematics on their own from online resources and books, but it isn't going to be an easy task or one that you can complete in a few weeks/months.

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

#79

Post by readme »

ColinWright wrote: post #2

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. Yes, conventions have emerged, people tend to use the same sort of notation in a given context, but in the main, the notation should be regarded as an aide memoire , something to guide you. You say that you're struggling because of "the math notations and zero explanation of it i…

came here to say this

some people literally make the notation up as they go along

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

#80

Post by readme »

the notation you need to know should be defined somewhere in the book or paper you're reading

if it's not, try intuition

if that fails, email your mathematician friend and ask

don't have a mathematician friend? there's your next goal, go make one.

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