Why are there so many questions based on calculus in math.stackexchange?

I am a $10^{th}$ grade student. I joined math.stackexchange because of my teacher. He once showed us a question about finding solutions to a question about Pythagorean triples from math.stackexchange. He then told us about math.stackexchange and about the vast community that it has. He also suggested us to check out this website.

The next day I checked out this website and just could not help but wonder how many questions are based on calculus. For a $10^{th}$ grade student like me, it's hard to understand what some people are even writing.

Is there any particular reason to this? I know that calculus is an interesting and one of the most important sections of mathematics, still Olympiads like IMO don't ask questions on calculus.

I am not saying by any means that calculus isn't a good topic. I am just wondering why are there not many questions based on elementary topics like number theory.

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    $\begingroup$ Topics like calculus and linear algebra are the basics. Anybody who studies exact sciences must learn them, even if not at the highest level. So of course there are more questions about them than about topics in pure mathematics which are being studied by much less people. $\endgroup$ – Mark Aug 27 '19 at 11:59
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    $\begingroup$ According to the help page "Mathematics Stack Exchange is for people studying mathematics at any level and professionals in related fields." As for why certain levels of skill or groups of people use this site, that is going to be largely conjecture, but I find the site traffic is heavily influenced by patterns in the school year as well as the content commonly asked is frequently the type of content people study in school. $\endgroup$ – JMoravitz Aug 27 '19 at 12:09
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    $\begingroup$ [elementary-number-theory], [elementary-set-theory] etc. do exists as tags. number theory goes a lot deeper than I think you understand. Some use linear polynomials some more complex objects like rings, groups, fields, finite fields, euclidean domains, etc. $\endgroup$ – user645636 Aug 27 '19 at 12:22
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    $\begingroup$ I guess a "grad 10th" student is about 16 years old? So that you have not yet learned calculus? You could read up on the "tag" system here. You can set your profile so that you do not even see things with certain tags. Then you will only see what is left. $\endgroup$ – GEdgar Aug 27 '19 at 12:24
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    $\begingroup$ @JMoravitz while indeed there is no restriction on the level of a question (though there is one on the form), I am always astonished how the target audience is quoted to show this. Would somebody show that phrase to me I would interpret it as being for students enrolled in a (university) program in mathematics (the level referring to undergraduate/graduate) or at least students doing university course-work in mathematics. First for intrinsic reasons, though that might be in part a language issue. Yet, second, as otherwise the professionals in related fields would not make sense. $\endgroup$ – quid Aug 27 '19 at 15:45
  • $\begingroup$ $@GEdgar$ I am 14 years old currently. In India, we complete school early. $\endgroup$ – Jayant Jha Aug 28 '19 at 17:30
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    $\begingroup$ This site has a very wide range; anyone is going to find many of questions they don't understand. You shouldn't feel bad, or feel that basic number theory is being denigrated, based on that (although as said above you may want to "ignore" certain tags to more easily see the content you actually care about). $\endgroup$ – Noah Schweber Aug 29 '19 at 18:11
  • $\begingroup$ I'm curious as to where you get your impressions. For my money calculus is near the bottom of the pecking order of math covered in this site, and number-theory runs from sophomore level up to research level. May be you missed that we have a separate elementary-number-theory about divisibility, modular arithmetic and such? Opinions will probably differ whether calculus or ENT is deeper math. Locally we teach both to freshmen, speaking in favor of calling them to be at the same level. I suppose if we put both on solid footing, calculus takes more steps after Peano axioms :-) $\endgroup$ – Jyrki Lahtonen Aug 30 '19 at 17:07
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    $\begingroup$ And, IMO, requires much more insight and talent than calculus. All the college kids learn calculus soon enough. It is rather mechanical, and mostly about turning the crank. IMO on the other hand... Admittedly there is also the side that teaching calculus, for its many nice applications in physics and engineering among other things, has been seriously worked on. Serious effort has gone to turning it from a beautiful art to a mechanical process requiring little creativity. $\endgroup$ – Jyrki Lahtonen Aug 30 '19 at 17:14
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    $\begingroup$ @JyrkiLahtonen: fully agree with your last comment here. Let's hope the community here does some bit about turning it back into a beautiful art. $\endgroup$ – Paramanand Singh Aug 31 '19 at 14:55
  • $\begingroup$ There are more (many more) students in calculus than in any other math course in the United Sates. $\endgroup$ – Matthew Leingang Sep 5 '19 at 15:26
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    $\begingroup$ People from other areas who have questions about Math will often be calculus-related because that's the branch they need for their field. No physicist or doctor will ever ask you questions on number-theory. Still, there are plenty of questions on topics like Statistics and, don't panic, I have a degree in Mathematics and still fail to understand most questions here $\endgroup$ – David Sep 9 '19 at 15:18
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    $\begingroup$ @Jyrki Lahtonen: And, IMO, requires much more insight and talent than calculus --- As I explained in my answer to Why are the contents of contest maths so different from contents of degree-level maths?, "IMO problems are pitched at cognitive difficulty levels beyond that which is needed to obtain a Ph.D. in math $[\cdots]$ even if every [U.S.] IMO participant eventually gets a Ph.D. in a mathematical science field, then fewer than 1% of those earning a Ph.D. in a mathematical science field will have participated in the IMO." $\endgroup$ – Dave L. Renfro Mar 31 at 19:35

A main source of questions are those of beginning university/college students, or those at this level, which can include some advanced high-school students. More abstractly, persons towards the beginning of their tertiary education, or very close to the end of their secondary education.

Now, a main subject of study in mathematics at this level is calculus/introduction to real analysis (limits, differentiation, integration) and notions of linear algebra (solving systems of equation, vector spaces, linear independence, determinant). These subjects are obligatory for many students, not only those studying mathematics. By contrast, courses on elementary number theory are not nearly as universal in curricula in mathematics, and even more important are mostly confined to mathematics and closely related fields while courses in calculus are taken much more broadly. For example, many engineering and science programs will contain such courses.

Now, in a way this only moved the question to why the source I mentioned above is a main source.

That there are not more questions from more advanced students is explained on the one hand by the sheer numbers, especially as we lose most of the non-mathematics students, and on the other hand by the existence of a second site for mathematics questions (MathOverflow) that absorbs a lot of questions related to current research in mathematics and questions of more advanced students (students in the process of writing a doctoral thesis, mostly).

The question why there are not more questions from less advanced students is somewhat less clear. I believe that for average students at a younger age, in particular those not specifically interested in mathematics, the idea of searching information and help on the internet just might not really arise or it might just not be viable and efficient, as there are other more accessible sources for assistance.

You mention the International Mathematics Olympiad. Indeed, students involved in this and related competitions could be, and are, a source of questions. But, there are also other venues for this, for example, see https://artofproblemsolving.com/ and like various others I do not know about.

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  • $\begingroup$ I'm on a question ban or I'd ask about improving a semiprime sieve based on the sieve of sundaram's arguments. $\endgroup$ – user645636 Aug 27 '19 at 16:39
  • $\begingroup$ Sorry about that. I assume you know that this is an automatic thing. You might try to restore and improve some of your existing Q's. $\endgroup$ – quid Aug 27 '19 at 17:55
  • $\begingroup$ I only have 1 question with downvotes, I just typically removed my own downvoted material. That lead to them not accepting questions from the account. anyways back on topic. $\endgroup$ – user645636 Aug 27 '19 at 18:07
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    $\begingroup$ Yes, but AFAIK deleted content is also taken into account. Thus it might help to undelete some Q and improve it. That's what I meant with "restore" If you want to discuss this in more detail, you could ask me in chat. In my room or the math mods offfice. $\endgroup$ – quid Aug 27 '19 at 18:20
  • $\begingroup$ @RoddyMacPhee Deleted material really hurts you in terms of such blocks/bans. Somebody posted a question about those here during my term, and the exact formula was spelled out by somebody in the know. I'm afraid I couldn't find that thread. This post in Meta.SE has some explanations/links. $\endgroup$ – Jyrki Lahtonen Aug 28 '19 at 5:53
  • $\begingroup$ I mostly delete downvoted material people clearly don't like. only time I know of that I've deleted a meta post is about a symbol in mathjax that really has no usefulness, after the post was edited by the asker themselves. and the one time I remember deleting a positive voted main thread, was because the OP wasn't going to accept any other reasoning other than their own. A classic case of Bayes rule tells you not to argue with such a user. $\endgroup$ – user645636 Aug 28 '19 at 12:28
  • $\begingroup$ @RoddyMacPhee The formula deciding whether you are allowed to post something new does not take into account the reasons for the deletions. IIRC it only counts the number of deleted/closed/negatively scored posts, and checks how high a fraction those make of all your posts. $\endgroup$ – Jyrki Lahtonen Aug 29 '19 at 5:39
  • $\begingroup$ @RoddyMacPhee The OP isn't the only or most important audience of a question. There's little reason to delete an answer with a positive score just because the OP won't accept it. The main reason I can think of to do that is that you don't want to receive notifications from comments on the answer. In my experience, that's not necessary. After an initial burst of comments from the OP, they usually won't continue commenting if you don't respond. $\endgroup$ – Derek Elkins left SE Sep 1 '19 at 0:21
  • $\begingroup$ look, I give up. It it weren't for passing time, I might not be on here. $\endgroup$ – user645636 Sep 1 '19 at 0:28

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