Another reason why the (algebra) tag should be allowed.

This question is one example of why I think the (algebra) tag should not be treated as deprecated (blacklisted). This isn't really "abstract" algebra because it's all done within one particular field, $\mathbb C$, and that and some of its subfields were studied before abstract algebra evolved.

(Another reason is that the tag is sometimes used on questions that are not really prerequisites to calculus, and I think tags should be about subject matter rather than being defined in terms of conventional courses of study.)

I certainly agree with "tags should be about subject matter rather than being defined in terms of conventional courses of study". And the way I see , it is defined by enumeration of relevant topics in the tag-excerpt:1

Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

Typically, any question where an important part is manipulating with expressions containing variables would qualify.

So this tag is not defined based on a content of a course, it is defined in terms of topics which fall under this tag. It is therefore not surprising that occasionally even questions about something which is definitely not taught in precalculus course and which would be too advanced for students taking this course might get this tag. (Similarly as, for example, we may have questions about open problems or research-level question in . If a question is tagged it does not mean that it is something every student taking first linear algebra course should be able to solve it or that it should be solvable using only methods of linear algebra.)

To me it seems that many users felt that the tag was used in two rather separate meanings and there was a need to somewhat improve the usage. Therefore two new tags were created, where some kind of "disambiguation phrase" was added to the word algebra: and . (If there are suggestions for better names, we can still add synonyms. The important thing is that if a user starts typing "algebra" in the tag field, they see these two tags together with the tag-excerpts explaining the usage.)

The fact that the content of this tag more-or-less coincides with a course named precalculus (which is taught mainly in the USA, as far as I know) is basically a good thing. It might help some users which are not yet familiar with the tag system here to tag their questions correctly.

1Admittedly, the tag-wiki gave a bit different impression than the tag-excerpt, so I edited it. Further improvements are more than welcome. But tag-excerpt is the information which is displayed to the users when choosing tags, so the wording of tag-excerpt is probably what most users wondering about the choice of tags for their post view.