How to become a number theorist?

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Discussion Overview

The discussion revolves around the path to becoming a number theorist, focusing on the necessary knowledge and courses required for specialization in number theory. Participants share their experiences and seek advice on prerequisites and relevant fields of study.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses a newfound interest in number theory after taking a course in naive (elementary) number theory, highlighting its connection to abstract algebra.
  • Another participant inquires about the prerequisites for becoming a number theorist, mentioning naive number theory, abstract algebra, complex analysis, and real analysis as potential areas of study.
  • A participant shares a link to resources that may be useful for learning about number theory.
  • There is mention of the perceived difficulty of analytic number theory compared to algebraic number theory, though this is noted as second-hand knowledge.
  • One participant raises a question about the definition of "naive" number theory, seeking clarification on its meaning.
  • A later reply clarifies that "naive" refers to elementary number theory, while also sharing a personal perspective on their experience with the subject.

Areas of Agreement / Disagreement

Participants express varying levels of interest and experience in number theory, with some agreeing on the importance of foundational courses, while others share differing opinions on the appeal of elementary number theory. The discussion does not reach a consensus on the best path or the relative difficulty of different branches of number theory.

Contextual Notes

Participants mention various prerequisites and fields related to number theory, but there is no comprehensive agreement on a definitive list of necessary courses or knowledge areas. The discussion reflects individual experiences and perceptions rather than a unified framework.

Who May Find This Useful

Individuals interested in pursuing number theory, particularly students considering graduate studies or those exploring different branches of mathematics.

Arian.D
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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.
 
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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?
 
practice, practice, practice!
 
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?
 
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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