This is getting absurd. I request that the moderators close this thread.

Yes!

The uses of "of" in mathematics are precisely the uses of "of" in everyday English, as far as I know, and if you are aware of a counterexample then you should have stated it at the beginning. On the other hand, if you want examples of uses of the word "of", then I suggest reading the collected works of Charles Dickens and Henry James, which should probably give you a more than ample supply of data. Then go and search on Language Log.

My apologies if this seems brusque, but I am one of those old-fashioned types who can't bring himself to agree with the maxim that "there is no such thing as a stupid question". Consequently, this will be my last comment on this thread.

Should it not be the mathematians, that preserve the language of mathematics, who provide such a guide to this most grammaticalised of all prepositions?

If you look at a typical mathematics paper, you will see equations, symbols, and diagrams galore. That is partly because Mathematicians have long since learned of the inherent ambiguity of natural language. So while we may "describe" proofs and ideas in natural language, strictly speaking you cannot dissect the "language of mathematics" grammatically as you would English, and in particular you cannot pick-out what is the preposition "of". To put it another way: what English we do use in "mathematical writing" we use it like anyone will use English, except for a smattering of nouns and adjectives that form the jargon of mathematics. The rest, the symbolic and diagrammatic language of mathematics does not admit the word "of".

As an aside: it is a sad state of affairs that the teaching of mathematics have been reduced to the teaching of a supposed language of mathematics, which no practicing mathematician ever speaks. See Lockhart's Lament for a pungent description of why I consider comments about "many uses of the proposition 'of'" actually detrimental to mathematics education.

For the last time, no. Nobody here accepts the premise that mathematicians use the word differently from anyone else, and nobody here knows of any articles which discuss the usage of this word in mathematics.

(Mathematicians also use the word "no" in the same way everyone else does. Please stop asking.)

I think it is clear that no-one here knows any such articles of the kind your are looking for. Also, no-one here particularly seems to agree with the sentiment of the book that you are quoting from. Thus, I respectfully suggest that you pursue your literature search elsewhere.

Your sincerely,

Matthew Emerton

Moreover, your question is very "localized" in the sense that the only person who seems guaranteed qualified to answer it is whoever wrote that part of the teacher's manual. It stands to reason that if you really want to know the answer, your best bet is to contact the author of the textbook, the author of the teacher's manual and/or the publishing company in question.

But I can't help but wonder: why is this passing remark written in some teacher's manual so important to you if you can't find anyone else to corroborate it? In general "teacher's manuals" are not a genre of literature renowned for their careful writing. (Note that they are often not written by the author(s) of the text, but who the actual author is may not be so clear either. It may have been written by a consortium of educators, publishers and students / assistants of the actual author of the text. This is not a recipe conducive to deep contemplation of the significance of individual sentences.) I promise you that in the few circumstances where I have consulted the "teacher's solution manual" for a text, I found so many mistakes so as to become suspicious whether some of them were inserted intentionally to see whether I was awake and paying attention.

Presumably you have looked at the 63 definitions in the OED, which means that you are in a position to answer Willie Wong's question (3). I don't see why you expect him to look in the OED when you are the one asking people here to help you with your research, and he has aksed you an entirely reasonable question about whether mathematicians' usage of the word "of" differs from standard English usage. (Incidentally, in my experience, there is no difference, at least that I've noticed.)

Yours sincerely,

Matthew Emerton

(2) If you did ask everyone, have you entertained the notion that nobody has an answer because, well, nobody knows the answer?

(2a) Does the question really make sense as you asked it? (2b) If so, have you considered doing your own primary research in the area? (2b') Those linguistic sites may give you some pointers on where to find databases of linguistic bibliographic data.

(3) Do mathematicians really use "of" differently than laypeople? Is there a usage not covered in the Oxford English Dictionary?

Just because your question is math-related, doesn't mean that you should post it there, however.
Every question on that site should be sure to have actual mathematical content.
Remember that!
Kudos
!

Your question (closed at http://mathoverflow.net/questions/49905/mathematical-uses-of-the-preposition-of) is an interesting one for pedagogy or linguistics forums. But I don't think it is a good one for MathOverflow: it doesn't have a single answer, and is very dependent on the individual voice of the speaker/answerer. I don't know the linguistics literature, but I suspect this question has not been taken up --- that said, you might write to Language Log with the question.

The question is even more inappropriate for meta.mathoverflow, which is mostly about issues of running MO (not a back door for questions that have been closed).

-Theo

P.S. I do like the idea of starting "linguistics.mathoverflow.net", seeing as we do have a lot of questions about voice and style in mathematical (and, more broadly, academic) writing.