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.
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&keyw...
This again no mention: 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=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/