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By default to most non-mathematicians, algebra refers to the algebra of the real and complex numbers, including linear, polynomial, rational, logarithmic, and exponential expressions, functions, equations and inequalities, and systems of equations. This is the standard fare of pre-calculus mathematics in secondary education and in non-mathematical undergraduate education.

However, several of the early questions using the algebra tag were specifically about abstract algebra and it made sense to define a distinct tag for it.

Before proceeding to make a distinction by editing the tags, I thought it would be wiser to ask the community: Should the unmodified algebra tag be used by default to mean common real and complex algebra?

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  • $\begingroup$ If the agreement is positive, should someone who has the privilege add the new tags and convert old tags into the new ones? $\endgroup$ – Markus Klein Mar 18 '14 at 21:44
  • $\begingroup$ I would be willing, but early voting is going against this. $\endgroup$ – Confutus Mar 18 '14 at 22:03
  • $\begingroup$ In every case, I would wait for that for 1-2 days. But I think, it's not a bad thing to do that before public beta starts. $\endgroup$ – Markus Klein Mar 18 '14 at 22:11
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The tag should not exist at all (same for other subject names that tend to be widely used).

Given the description in OP, there might be a tag named "algebra-pre-calculus" or "pre-calculus-algebra" or something of this form. In this way we can have several "algebra" tags, with "graduate" "undergraduate" and so on.

To assign one particular meaning to the tag just called "algebra" will lead to many inapproiate taggings, and will render the tag "algebra" useless very soon.

See also https://matheducators.meta.stackexchange.com/q/63/

It is better to have tags that are not self-explanatory (we can explain them in the tag-wiki), rather than to have supposedly self-explanatory ones (or overly broad ones). I for one would never have thought an "algebra" tag would refer to what is mentioned in OP.

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  • $\begingroup$ This particular sense could be defined in the tag wiki. Secondary school algebra and even many courses entitled "College algebra" are largely limited to these topics. Mathematicians have a much wider and more inclusive understanding of algebra means, but most mathematics educators, especially at the lower levels, are not mathematicians. $\endgroup$ – Confutus Mar 18 '14 at 19:46
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    $\begingroup$ Your suggestion might work if (new) users would read tag-wikis and documentation. This is a gigantic "if"; I know some tags were the tag wiki says just: "Deprecated. Please use another tag." It still gets usage! And even then I do not see why this particular sense of "algebra" should get the tag. Why not say the math that can be found in, say, the Journal of Algebra? This is rhetorical I do not propose that; what I propose is in the answer. [I'd not say it is more inclusive; I doubt 'inequalities' and some other things mentiond, would get mentioned much if you ask algebraist to def "algebra".] $\endgroup$ – quid Mar 18 '14 at 22:14
  • $\begingroup$ New users are likely to look for the first familiar term. I proposed the definition because I thought it to be the default understanding of the unmodified term "algebra" for most potential visitors, not merely those familiar with, say, the Journal of Algebra or algebraists. $\endgroup$ – Confutus Mar 18 '14 at 22:46
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    $\begingroup$ Exactly! So if we have an "algebra" tag, most will take that one, because what else than what they understand could be meant, some will get lucky others not. If we don't they will search for "algebra" and then find various flavors of algebra tags, the more specific name or when in doubt description of which will tell them which one to use. (The tag box matches strings, if you type in "algebra" you would get the tags suggested; if we do algebra-pre-calculus it would also be in alphabetic order impossible to miss.) $\endgroup$ – quid Mar 18 '14 at 22:55
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    $\begingroup$ And while I was very clear regarding it let me stress again: I did not propose to use the algebra tag differently, I proposed not to use it at all. $\endgroup$ – quid Mar 18 '14 at 22:58
  • $\begingroup$ I cannot imagine that those aware of the existence of, say, linear algebra, or boolean algebra, or abstract algebra and not finding those topics under the "algebra " tag wouldn't go looking for a more specific tag. Especially if they know enough about the subject to be teaching it. $\endgroup$ – Confutus Mar 18 '14 at 23:30
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    $\begingroup$ I do not blame you. Wouldn't I be retagging question on a site full of mathematicians since years, I guess I too would be a lot more optimistic. Please, could you perhaps answer what is lost if the tag you have in mind is called algebra-precalculus (and we blacklist algebra)? Also, why do you think math.SE does no follow your scheme; but instead has, algebra-precalculus and any number of tags containing algebra yet not algebra? $\endgroup$ – quid Mar 18 '14 at 23:57
  • $\begingroup$ Many (even most) students of common algebra do not go on to study calculus. The variants I can think of seem to be a little more cumbersome with a possible loss of clarity and not much gain. There seem to be various differences in the intended audience of this site and math SE. $\endgroup$ – Confutus Mar 19 '14 at 0:23
  • $\begingroup$ Sorry I do not understand either of the two points you want to make. Perhaps it is a good idea we make a break, and wait for other opinions. $\endgroup$ – quid Mar 19 '14 at 0:27
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The unmodified term "Algebra" in US Secondary and undergraduate education overwhelmingly refers to the algebra of the real numbers, including linear and polynomial expressions, functions, and systems of linear equations.

In higher level courses, this is commonly extended to complex, rational, logarithmic, and exponential complex numbers, including linear, polynomial, rational, logarithmic, exponential, and trigonometric functions and equations, and some inequalities.

Although algebra has a much broader meaning to mathematicians, other algebras usually have specific distinguishing names, such as Boolean algebra, linear algebra, or even abstract algebra.

It may be confusing to those with limited experience with such other algebras to decide which tag is appropriate, and other terms, such as real algebra, or undergraduate algebra, or precalculus algebra seem to be cumbersome or carry other meanings.

If "algebra" is considered too broad a subject, it would be useful to find or recommend a better term for the most commonly encountered meaning.

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    $\begingroup$ Maybe someone could open a new question on meta to answer if/how it should be changed. As @quid pointed out in the comments, I would recommend to add something to algebra if you mean algebra in secondary education. If people wanted to ask questions and type "algebra" in the tags, they will see maybe algebra-in-secondary-education (It's too long, but it fits best for all names I have in mind), abstract-algebra, linear-algebra, etc. und then it is clear what to choose. $\endgroup$ – Markus Klein Mar 19 '14 at 7:57
  • $\begingroup$ Once again, algebra does not have a broader meaning 'to mathematicians.' Some of the notions you mentioned in generalized form are part of algebra; but other things you mention are not classified under "algebra" at all in the way I undertand it. Inequalities, logarithms, trigonometric functions, this is not algebra to many matheticians it is analysis. $\endgroup$ – quid Mar 19 '14 at 10:50
  • $\begingroup$ Trigonometry is arguably a distinct subject, although it is commonly taught along with algebra, as are the basics of logarithms and exponential functions. Inequalities are sometimes taught along with equations. The boundaries between mathematical subjects are not always distinct. $\endgroup$ – Confutus Mar 19 '14 at 16:17

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