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I am a master's student currently deciding between two different Ph. D. programs in mathematics. The two programs have very different teaching opportunities as a grad student. One of the two programs I'm applying to allows (and encourages) students to teach a first-year calculus course, and the other one does not. However, I would be able to teach a college algebra or precalculus course at the other school. Would it reflect badly on me as a job applicant if I have no experience teaching calculus?

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    What are the other differences between the two programs? – cartonn Mar 31 '13 at 0:33
  • @cartonn: Thank you for asking. There are lots of other differences between the two programs. One of the programs is the one where I am currently doing my master's, so it is more "familiar". I already have professors here who have agreed to advise my Ph.D. if I remain. The other program is comparable in how well-regarded it is in my general area (analysis), but the specific research going on there is closer to my current mathematical interests. There are other differences too. I guess the main thing is I think I'd be happy at either place, but I want to make the best possible decision. – Anonymous_User Mar 31 '13 at 1:10
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    If you might end up working at a university with relatively nonselective admissions, then experience teaching algebra might be an advantage. They need people to teach remedial math. (Your question has "university" in the title, but this would apply even more at a community college. At the community college where I teach, many applicants have a masters in math education and aren't even competent to teach calculus. Your PhD shows you know calculus, but it doesn't show you can deal with remedial courses.) – Ben Crowell Feb 16 '14 at 0:39
  • You should also look at how the schools are regarded in mathematics as a whole, not just analysis. Hiring committees will be composed of a variety of mathematicians, and at teaching colleges your fate may be decided by one mathematician and several other STEM faculty who won't know the difference between a good Analysis school and a good Algebra school. For teaching colleges the general reputation of the University is important. Same goes for if you decide to end up in industry. But of course go where you think you will do the best research (if that is what you want to do in the future). – WetlabStudent Feb 16 '14 at 16:35
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I would be truly shocked if any hiring committee cared at all about whether you taught calculus versus pre-calculus. Doing well at either would show that you can adequately handle teaching service classes.

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    I'd second this. The math is easy, the extra-mathematical issues are the potential challenge. Indeed, I'd dare say that "service courses" are not really about mathematics itself at all, they are about teaching and testing certain habits and skills of the students in the more-objective-than-some-things venue of "calculus" or "pre-calculus" or "college algebra". Attention to detail, following instructions, being on time, being organized. Slightly disappointing that it's not about mathematics, but it's a good thing to help kids attend to these skills. – paul garrett Mar 30 '13 at 23:48
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Part of the answer depends on your prospective area of expertise. Usually math professors teach the undergraduate courses that are closer to their research area. So, if you work in analysis, you will likely be assigned a calculus course; if you study algebraic geometry, you will probably get an introductory abstract algebra course; if you do research in Riemannian geometry, linear algebra.

That said, I would not worry much about which course you teach at this point. This distinction should not be your primary concern in deciding between two PhD programs. Any teaching experience will do for now, and you will have many opportunities to compensate in future. Moreover, most hiring committees will focus more on your research activity than on your teaching in any case.

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    Maybe this varies between countries, but in the U.S. the question of who teaches relatively low-level math courses (such as calculus or linear algebra) is entirely independent of research expertise. – Anonymous Mathematician Mar 30 '13 at 20:38
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    "Most hiring committees will focus more on your research activity than on your teaching": This assumes you are looking for a job at a research-focused department. These are the highest profile employers, but employ a relative minority of mathematicians; many more departments will be most interested in your teaching ability. But I agree that calculus versus pre-calculus is a minor distinction. – Nate Eldredge Mar 30 '13 at 22:22
  • @AnonymousMathematician, NateEldredge: you are right, I should have specified that this answer is based on experience in Europe. From what I read in many places, the US is a different thing. – Federico Poloni Mar 31 '13 at 9:54
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    In my experience, hiring committees focus on both research and teaching. If you have sufficiently good research, you can be certainly be hired at research-focused departments without being a great teacher (and not vice versa), but even at research-focused departments, teaching is one of the components in the hiring decisions. – Peter Shor Mar 31 '13 at 16:40
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    Maybe you've misunderstood what "calculus" means in the US. It is not a real analysis course and the people taking it are not usually math majors. – Noah Snyder Feb 15 '14 at 16:35

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