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How to become a number theorist?

  1. Jul 26, 2012 #1
    I'm sorry if I'm asking my question in the wrong section, but recently I have become interested in number theory after taking a course in naive(elementary) number theory. The ideas are simple and beautiful and they help me very much in abstract algebra as well. Many concepts that look vague in abstract algebra are now becoming clear for me, I mean I understood the proofs before taking number theory, but now I'm realizing why those theorems were necessary and how the discoverers had been able to find those theorems. I know that number theory is mainly divided into two branches. Analytic number theory and algebraic number theory. I also know, that at least in my place, number theory could be chosen as an independent field of study for graduates. I want to know that if someone wants to become a number theorist, what things does he/she need to know? Naive number theory, abstract algebra (to study algebraic number theory), complex analysis & real analysis (to study analytic number theory), and what else? I mean the prerequisites.
    And if there's someone here who's chosen number theory as their field of research, could they tell me what courses they have taken in graduate school or in PhD?

    Any help would be highly appreciated.
  2. jcsd
  3. Jul 26, 2012 #2


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    Last edited by a moderator: May 6, 2017
  4. Jul 26, 2012 #3
    I'd be interested in learning more about this, too. I've taken two courses in elementary number theory and really enjoyed them.

    I've heard that analytic number theory is a tougher field to get into than algebraic number theory, but that's second-hand knowledge and so I don't know if it's true. I think there is also a subfield in computational number theory, yes?
  5. Jul 26, 2012 #4


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    practice, practice, practice!
  6. Jul 27, 2012 #5
    Just out of curiousity, since I've taken a number theory course and I'm not sure where it's situated: what is "naive" number theory?
  7. Jul 28, 2012 #6
    He says by "naive" he means elementary. Incidentally, I took an elementary number theory class and didn't particularly like it. Which is only interesting because now I intend to become a number theorist.
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