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If you don't know what a Monoid is you are probably a pretty poor mathematician as it is core structure to do even undergraduate abstract algebra. Many compute

by jroesch 13y ago

If you don't know what a Monoid is you are probably a pretty poor mathematician as it is core structure to do even undergraduate abstract algebra. Many computer scientists already understand reasoning about abstract structures and use them in their work. For example commutative operators are incredibly powerful tool in distributed systems, as I am able to disregard ordering. In general it is useful to be able to say that if I meet an abstract specification (i.e a Monoid, Group, Ring, ect) because it allows me to perform operations with confidence that they are correct. If you doubt the usefulness of this just look to Twitter (can't get much more "real world" than that) and see how they have been leveraging abstract reasoning in projects like Summing Bird (and its sub-projects like Algebird, Bijection, ect).

Iftheshoefits 13y ago
I think what you meant to say was "you are probably not very well versed in a specific branch of mathematics." Because otherwise you're coming off as needlessly--and baselessly--arrogant asshole who also has mistakenly generalized his specific area of expertise far beyond what it actually is.
coldtea 13y ago
>If you don't know what a Monoid is you are probably a pretty poor mathematician as it is core structure to do even undergraduate abstract algebra. Well, I asked undergraduate math students on their final year, and they didn't know. Perhaps all PhDs in math do, but that's not much of an argument in reusing those terms in CS. Myself had several classes of algebra in different years in university (for the CS degree) and we didn't ever talk about Monoids and such.
- nzp 13y ago
  > Well, I asked undergraduate math students on their final year, and they didn't know. I have no reason to not believe you, but how is this possible, and what does it say about either those students or that university or even both? Do they also not know what a group is? A ring, a field? How can a mathematician (and a nearly graduated student in maths is certainly a mathematician) not know what basic algebraic structures are? I'm shocked, frankly. It's literally equivalent to saying they don't know what real numbers are, without exaggerating one bit.
  - coldtea 13y ago
    >* I have no reason to not believe you, but how is this possible, and what does it say about either those students or that university or even both? Do they also not know what a group is?* They should know what a group is, because even us, CS students, were taught group theory for a whole semester. As for the monoid thing, I guess they could have been taught at some point, along with being taught 20 other branches and fields of mathematics in different classes, and they were more likely to remember a) the basic stuff, b) the stuff they started to specialize on and concentrated upon writing their thesis. So, I guess if I had talked to someone who had taken a preference to type theory and such, they would have known. >How can a mathematician (and a nearly graduated student in maths is certainly a mathematician) not know what basic algebraic structures are? I'm shocked, frankly. It's literally equivalent to saying they don't know what real numbers are, without exaggerating one bit. Is it? I don't know. You can read whole books in Algebra and not mean the word "Monoid" once in them, including some university books. For example (not even one mention): http://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9780387406244 http://www.amazon.com/gp/search?index=books&linkCode=qs&keyw... This again no mention: http://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9781285402734 http://www.amazon.com/gp/search?index=books&linkCode=qs&keyw... This (a "graduate level" book) only mentions Monoid once, somewhere on the first pages, and adds that it won't be emphasised: http://books.google.com.sg/books?id=C4TByeUh9A4C&printsec=frontcover#v=onepage&q&f=false http://books.google.com.sg/books?id=C4TByeUh9A4C&printsec=fr... And I'm pretty sure in our Algebra books (for CS students, 2 classes in the 1st and 2nd year) there was no much mention of monoids (or, possibly, the professor skipped over those chapters, maybe had some brief explanation and went on to other things). Of course, what university gradutes of a field do not know can sometimes be even more daunting. For example, a surprising percentage of degree-ed Computer Scientists cannot even solve the fizz-buzz problem: http://blog.codinghorror.com/why-cant-programmers-program/ http://blog.codinghorror.com/why-cant-programmers-program/
    - nzp 13y ago
      Of course, to not remember exactly what a monoid is is completely fine for a mathematician who's field isn't abstract algebra and related stuff, but to be clueless as to what the concept is at all is somewhat disturbing. I would have no problem if they said something like "ah, yeah, it's a little simpler than a group, I can't remember the exact properties ATM". Hm, I just gave a quick glance to one group theory textbook (the only one I have in English), and to be honest in the first 20 or so pages there is no mention of the word "monoid" (as far as I can see, I really just quickly scanned through the first chapter) but it does mention semigroups (which are just an identity element away from monoids)... > And I'm pretty sure in our Algebra books (for CS students, 2 classes in the 1st and 2nd year) there was no much mention of monoids (or, possibly, the professor skipped over those chapters, maybe had some brief explanation and went on to other things). Yeah, and that's fine, but for maths students to not even remember that it was mentioned is kind of sad. It shows they don't really care that much about what they're doing. If it wasn't even mentioned by the professor, shows a disinterest on his/her part to actually teach concepts. It's always much better when teaching a concept to also at least mention related concepts or similar ones at different levels of abstraction, that gives a complete picture in which you can neatly place things. A group doesn't just appear out of nowhere (although it certainly can be defined on it's own), and it's not alone... > For example, a surprising percentage of degree-ed Computer Scientists cannot even solve the fizz-buzz problem: Sigh... I know. But you see, that's why I found this discussion about the unintuitiveness of the word "monad", here of all places, absurd. I wouldn't expect people who cannot solve fizz-buzz to have any clue about anything, and on some level I'm fine with that, this is not an elitist rant, but people in a place like this? After all, programming routinely involves dealing with concepts that are much more unintuitive that a monoid, IMHO.

by jroesch 13y ago

Iftheshoefits 13y ago

I think what you meant to say was "you are probably not very well versed in a specific branch of mathematics." Because otherwise you're coming off as needlessly--and baselessly--arrogant asshole who also has mistakenly generalized his specific area of expertise far beyond what it actually is.

coldtea 13y ago

>If you don't know what a Monoid is you are probably a pretty poor mathematician as it is core structure to do even undergraduate abstract algebra. Well, I asked undergraduate math students on their final year, and they didn't know. Perhaps all PhDs in math do, but that's not much of an argument in reusing those terms in CS. Myself had several classes of algebra in different years in university (for the CS degree) and we didn't ever talk about Monoids and such.

nzp 13y ago
> Well, I asked undergraduate math students on their final year, and they didn't know. I have no reason to not believe you, but how is this possible, and what does it say about either those students or that university or even both? Do they also not know what a group is? A ring, a field? How can a mathematician (and a nearly graduated student in maths is certainly a mathematician) not know what basic algebraic structures are? I'm shocked, frankly. It's literally equivalent to saying they don't know what real numbers are, without exaggerating one bit.
- coldtea 13y ago
  >* I have no reason to not believe you, but how is this possible, and what does it say about either those students or that university or even both? Do they also not know what a group is?* They should know what a group is, because even us, CS students, were taught group theory for a whole semester. As for the monoid thing, I guess they could have been taught at some point, along with being taught 20 other branches and fields of mathematics in different classes, and they were more likely to remember a) the basic stuff, b) the stuff they started to specialize on and concentrated upon writing their thesis. So, I guess if I had talked to someone who had taken a preference to type theory and such, they would have known. >How can a mathematician (and a nearly graduated student in maths is certainly a mathematician) not know what basic algebraic structures are? I'm shocked, frankly. It's literally equivalent to saying they don't know what real numbers are, without exaggerating one bit. Is it? I don't know. You can read whole books in Algebra and not mean the word "Monoid" once in them, including some university books. For example (not even one mention): http://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9780387406244 http://www.amazon.com/gp/search?index=books&linkCode=qs&keyw... This again no mention: http://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9781285402734 http://www.amazon.com/gp/search?index=books&linkCode=qs&keyw... This (a "graduate level" book) only mentions Monoid once, somewhere on the first pages, and adds that it won't be emphasised: http://books.google.com.sg/books?id=C4TByeUh9A4C&printsec=frontcover#v=onepage&q&f=false http://books.google.com.sg/books?id=C4TByeUh9A4C&printsec=fr... And I'm pretty sure in our Algebra books (for CS students, 2 classes in the 1st and 2nd year) there was no much mention of monoids (or, possibly, the professor skipped over those chapters, maybe had some brief explanation and went on to other things). Of course, what university gradutes of a field do not know can sometimes be even more daunting. For example, a surprising percentage of degree-ed Computer Scientists cannot even solve the fizz-buzz problem: http://blog.codinghorror.com/why-cant-programmers-program/ http://blog.codinghorror.com/why-cant-programmers-program/
  - nzp 13y ago
    Of course, to not remember exactly what a monoid is is completely fine for a mathematician who's field isn't abstract algebra and related stuff, but to be clueless as to what the concept is at all is somewhat disturbing. I would have no problem if they said something like "ah, yeah, it's a little simpler than a group, I can't remember the exact properties ATM". Hm, I just gave a quick glance to one group theory textbook (the only one I have in English), and to be honest in the first 20 or so pages there is no mention of the word "monoid" (as far as I can see, I really just quickly scanned through the first chapter) but it does mention semigroups (which are just an identity element away from monoids)... > And I'm pretty sure in our Algebra books (for CS students, 2 classes in the 1st and 2nd year) there was no much mention of monoids (or, possibly, the professor skipped over those chapters, maybe had some brief explanation and went on to other things). Yeah, and that's fine, but for maths students to not even remember that it was mentioned is kind of sad. It shows they don't really care that much about what they're doing. If it wasn't even mentioned by the professor, shows a disinterest on his/her part to actually teach concepts. It's always much better when teaching a concept to also at least mention related concepts or similar ones at different levels of abstraction, that gives a complete picture in which you can neatly place things. A group doesn't just appear out of nowhere (although it certainly can be defined on it's own), and it's not alone... > For example, a surprising percentage of degree-ed Computer Scientists cannot even solve the fizz-buzz problem: Sigh... I know. But you see, that's why I found this discussion about the unintuitiveness of the word "monad", here of all places, absurd. I wouldn't expect people who cannot solve fizz-buzz to have any clue about anything, and on some level I'm fine with that, this is not an elitist rant, but people in a place like this? After all, programming routinely involves dealing with concepts that are much more unintuitive that a monoid, IMHO.