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I've recently volunteered as a tutor for "higher-level mathematics" as a Calculus student because I'm required by my school to achieve at least twenty volunteer hours for service learning.

When applying to the NPO as a volunteer, their only position available was for a "higher-level mathematics tutor". I've been a Calculus AB student and T/A for my Calculus AB teacher since the start of the year (we're on our third chapter) and I've only recently touched upon Calculus so I'm unsure whether my skills are on par with "higher-level mathematics".

Soon after I left their building, the connection between "higher-level education" and "higher-level mathematics" hit me. This NPO is from the elementary to the high school level so I became confused.

Could someone define "higher-level mathematics"?

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7  
Shouldn't you, er, ask them? –  Qiaochu Yuan Oct 15 '10 at 8:01
    
Well I just got home and I didn't realize what I've gotten myself into at the time. I was just curious what certain people mean by "higher-level mathematics". –  Gio Borje Oct 15 '10 at 8:11
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It means different things to different people. That's why you should ask. –  Qiaochu Yuan Oct 15 '10 at 8:12
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It's the stage in your education where you suddenly notice that all your math textbooks are no longer named "Advanced [...]" but rather "Introduction to [...]". ;-) –  Hans Lundmark Oct 15 '10 at 11:39
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Voting to close. "Higher-level mathematics" might mean different things in different contexts and even if there were to be a specific answer in the OP's context, it would be too localised. I don't even know what the NPO is. –  Jyotirmoy Bhattacharya Oct 15 '10 at 12:39
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closed as too localized by Jyotirmoy Bhattacharya, Chandru1, Rahul, Aryabhata, WWright Oct 15 '10 at 18:53

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I think this is a soft question (and have tagged it as such; you can roll it back if you disagree) but I'll try to answer. First, since the NPO only works up to high school, their definition of "higher-level" probably doesn't correspond to the typical one. Just think of it in terms of your school. If it has AP classes, Calc BC is probably the highest math class available, and it's possible a few people are taking basic college-level classes (say, multivariable calc or linear algebra), though they probably won't need tutors. As a blind guess, I'd say that you'd probably have to tutor kids in calculus, which could be a problem if you're still learning it. The best solution is to tell them where you are now and ask them or previous tutors what level is required.

(For me, what "higher-level mathematics" really is is the things a math major starts doing around the middle of his or her career -- not linear algebra, multivariable calculus, or basic group theory, but topology, commutative algebra, real/complex analysis, etc. would all be there. Presumably, mathematicians would find some of this elementary, but there is an objective change in the way the math is done around this time. You move from calculations and applications of theorems to proving the theorems yourself and learning to work rigorously, axiomatically, intuitively, etc.)

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Luckily, I haven't had any problems with Calculus yet and I've already gone beyond my Calculus teachers' scope: Lambda/FOL for my studies involving computational theory. Do you think I could pull off tutoring for Calculus students if I stay 1-2 chapters ahead of my own class? (Assuming that we have similar schedules). –  Gio Borje Oct 15 '10 at 8:09
    
@Gio: Yes, if you understand the material well, I see no problem with you being able to tutor students at your own level. Staying a little bit ahead can help you guide them towards future results (as textbooks tend to do). –  Brandon Carter Oct 15 '10 at 17:41
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