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I think it would be nice to have a tag that marked that a question was 'about' (i.e. its central topic is) a specific mathematical object, in contrast to being about practical things like exams and homework, or curriculum questions, or philosophy, etc (which of course are all appropriate topics). Questions that would fit from the current front page:

Good motivation for the introduction of Lebesgue integral?

How to present ℤ/nℤ to highschool level audience

Eisenstein’s criterion

What different ways do people use to show students that ℝ is uncountable?

I'm not sure what it could be called: perhaps 'mathematical-object'...

Would other people like this?

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    $\begingroup$ In my opinion this tag would be too broad as a great many questions would be about content in the long run (or I misunderstand the purpose). We have tags for mathematical subjects, these could/should be used. (If they start to become too broad they can be refined.) $\endgroup$ – quid Mar 31 '14 at 18:40
  • $\begingroup$ Are you sure? E.g. 'pedagogy' seems to encompass every relevant question... $\endgroup$ – Marius Kempe Mar 31 '14 at 18:41
  • $\begingroup$ Also, not every, say, 'algebra' question would be one of these: you can ask questions like 'What should an algebra course contain?', 'Should we teach abstract or concrete algebra?', 'What are some good exam questions for a group theory course?', etc $\endgroup$ – Marius Kempe Mar 31 '14 at 18:42
  • $\begingroup$ I removed 'mathematical-content'; that indeed is too broad. The point is where one mathematical object/result is under discussion. $\endgroup$ – Marius Kempe Mar 31 '14 at 18:43
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    $\begingroup$ First: I already voiced my concern regarding pedagogy being too unspecific and/or overused some time ago. (I will come back to this in due course.) I also said the tag algebra should not exist as tag (already did something related to this, and intend to follow through with it). But more to the point: what you propose is a "meta tag" these should be avoided. Why would somebody be interested in each and every question that is concerned with some mathematical object/result. From rationals for secondary education over number fiels to tempered distributions? $\endgroup$ – quid Mar 31 '14 at 18:49
  • $\begingroup$ Good, I did not see those concerns of yours. I would be interested, for one (why else would I be asking the question?). I'm very interested in the 'conceptual flavour' of specific mathematical objects (more prosaically: how do people understand and conceive of them?). $\endgroup$ – Marius Kempe Mar 31 '14 at 18:53
  • $\begingroup$ Maybe if this was used in a narrow way; the initial mathematical-content set of some alarms and made me very hesitant. Also there is definitions as a tag. How would the tag you propse be different? $\endgroup$ – quid Mar 31 '14 at 19:05
  • $\begingroup$ Well, consider the Lebesgue integral or Z/nZ questions: if all we needed to present was a definition, the questions would be redundant, and indeed, most of this website would be redundant. $\endgroup$ – Marius Kempe Mar 31 '14 at 19:18
  • $\begingroup$ I think I wanted to deal with this too quickly and did not explain myself well. I will come back to this with a proper answer later (need to find some food first). Sorry for the back and forth. $\endgroup$ – quid Mar 31 '14 at 19:20
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    $\begingroup$ I think the pedagogy tag adds nothing to a question. Essentially every questin could be tagged with pedagogy. $\endgroup$ – Brian Rushton Apr 1 '14 at 1:50
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The tag mathematical-content seems too broad to me; but it seems we found agreement on this in comments.

For a tag mathematical-object: the tags seems like a bit of a 'meta tag' to me in that it rather describes the type (than the subject) of the question. However, a reasonable argument can be made that it actually does describe the subject.

Still, I do not fully understand the intended scope. Put differently, what is (and is not!) a mathematical object?

If we want a tag with this name it ought to be clear what this means (for the scope of the tag).

Going through the example questions, I would say to me only Z/nZ is clearly a (family) of mathematical object, as some set with some structure.

Already for the Lebesgue integral this is a lot less clear. Right, one could think of it (them?) as functionals on spaces of functions and so on, but still I feel that a certain flavor of integral is not among the things I think of when somebody says mathematical object. Rather this question is for

For showing that R is uncountable it is even less clear why this is to be tagged mathematical-object.. Sure it is about the mathematical object R but then just one aspect of it, and many a question would be about some aspect of some mathematical object. Rather this question is about in my opinion. Different ways to prove one and the same thing are to be compared.

Finally I am really at a loss for Eisenstein criterion. This is a result or an algorithm if one wants. Now, in theory, yes this can also be considered as a mathematical object, but frankly if every result and every algorithm is a mathematical object then we are back to mathematical content. Or, is the object here the polynomials that are concerned. But then again 'everywhere' some object will be concerned.

In brief, given the examples I am sorry but I do not understand what should be tagged mathematical-object.

There is the feature of tag wikis. I propose (here and in general) if somebody proposes a tag they should in addition propose a text for a (short) tag wiki that explains how to use the tag correctly.

To sum it up: I do not understand the intent of the tag and would not know how to use it. Thus, at the moment I am against it. Please explain how exactly it should be used, keeping the issues I raised above in mind. Then I might likely change my mind.

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    $\begingroup$ I agree with you in I do not understand the intent of the tag. There is a two-way of tag use: First, I can read the specific tag on the question site and know maybe what is the intent of the question there before I click there. (For all mentioned questions, it is clear that they are about a specific content by the title). Second, I can check the tag itself, e.g., when I have to teach real analysis, I would check that tag and can see questions like the mentioned one or a question about "What can I ask about this course in an exam?". If we had a tag like mathematical-object, (cont.) $\endgroup$ – Markus Klein Mar 31 '14 at 21:09
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    $\begingroup$ (cont.) then one can see from the list of the tag what question is about a specific object. However, this information can there be extracted by the title or missing tags like exam and similar. The problem with a tag like mathematical-object is: If you click and that tag, you get a lot of things from algebra, calculus to group theory, functional analysis, optimal control, etc. (Everyone would click on the specific topic like real-analysis). $\endgroup$ – Markus Klein Mar 31 '14 at 21:09
  • $\begingroup$ I think you should be less harsh in asking for precise definitions; this is mathematics education, not mathematics. And I disagree that 'everywhere' some mathematical-object is concerned. I will look at the first 10 questions on the front page right now: one is about logical implication (which would qualify), but the other nine are about how deeply to explain something, how to grade, how much time to allocate to a subject, a math text reader, whether to hand out lecture notes, education in Africa, how many textbooks to use, whether to use calculators, how many opinions to voice in teaching. $\endgroup$ – Marius Kempe Mar 31 '14 at 21:10
  • $\begingroup$ So far from the tag fitting 'everywhere', it in fact only fits in the minority of cases, which is exactly the point of having a tag (and I personally am more interested in such questions about concrete mathematical things). $\endgroup$ – Marius Kempe Mar 31 '14 at 21:10
  • $\begingroup$ @MariusKempe but then we are back to mathematical-content (if we understand mathematical-content as only/mainly mathemtical content and this was the 'everywhere')? Regarding being harsh in asking for defintions: but how should people use the tag. I really do not know which questions to tag with it. With mathematical-content I think I would understand what to do, but I think it is too broad. (And will be more so in the future, I think, since the current situation is a bit of an artefacat, I think.) $\endgroup$ – quid Mar 31 '14 at 21:15
  • $\begingroup$ @MarkusKlein Your example what happens when you click is somewhat misleading: The mathematical subject is not the only way to classify questions here. For example, one real-analysis question may be on introducing the lebesgue integral, on the course design for a multidimensional analysis course for engineers or on a literature reference for the implicit function theorem. Similarly, when you click on the course-design tag, you will see courses from algebra, logic as well as analysis. Imho, different tags can help to classify on different levels. $\endgroup$ – Roland Mar 31 '14 at 21:19
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I propose to tag the question (at least) with a tag suitable to the specific question, e.g. the question about Lebesgue integral would be tagged , that about Eisenstein criterion would be tagged .

If one clicks on the , one can find questions about specific content (like the question above). (I wanted to say what else one can find there, but I have no clue what else one can expect?).

In my opinion, this is even better than your suggestion since the specific topics are already sorted with the tags (If I would search for specific mathematical content, I'm even more happy when I can find the topics I'm more familiar with!).

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    $\begingroup$ As I said in the comments, not every, say, 'algebra' question would be one of these: you can ask questions like 'What should an algebra course contain?', 'Should we teach abstract or concrete algebra?', 'What are some good exam questions for a group theory course?', etc $\endgroup$ – Marius Kempe Mar 31 '14 at 20:44
  • $\begingroup$ These tags related to the mathematical subject are important, but if I understand it correctly, we are looking for one category of questions where all of OPs examples fit in, regardless of the mathematical subject. Hence a downvote as your answer is slightly missing the point (to my understanding). $\endgroup$ – Roland Mar 31 '14 at 20:59
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I propose .

This is not exactly what Marius was asking for, but I do think it serves the purpose well:

These questions are all about single subjects within a given course, and their presentation can be done within one lecture (or less).

We have already established , so I feel that it's convenient and natural to introduce a finer level of planning.

There are aspects of planning a single lecture which are not like the questions in the OP, so my proposal is a bit broader than intended, but it might be a good idea to approach this from a slightly more abstract level.

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