# How hard is number theory?

1. Jun 22, 2009

### imranq

I'm taking the class next semester, and I heard that number theory is usually a difficult subject. Is that true? If so, how should I approach it?

2. Jun 22, 2009

### VeeEight

Introductory number theory is relatively easy. When I took it we covered primes, quadratic reciprocity, algebraic numbers, and lots of examples and relatively easy theorems. Most of the proofs we did in the class were very straightforward (wilsons & fermat's little theorem, etc) and was not difficult at all. The 'next level' of number theory, Algebraic number theory, involves upper level algebra and can be difficult at first glance, but if you have done any studying in field theory or a related subject you will recognize some stuff.

Number theory may not seem like the most practical thing to learn but it gets used in group theory, discrete math, and other typical third year math courses.

3. Jun 22, 2009

### thrill3rnit3

It's not that hard. The proofs and derivations are very straightforward, and it has a lot of useful and interesting applications, such as cryptology.

I guess it's the same thing as other math classes: don't get way behind, keep up with the work.

4. Jun 23, 2009

### Hurkyl

Staff Emeritus
The biggest thing is that Number theory is different; it simply doesn't have the same flavor as more continuous subjects.

It is a harder subject, but that's offset by the fact an introductory course is going to be working mostly with the simplest things: modular arithmetic, divisibility, multiplicative functions, and the like.

5. Jun 24, 2009

### PieceOfPi

I assume you mean number theory as a first-year, standard number theory course.

If you haven't taken a math course that requires you to write proofs, then you might feel number theory is a little challenging, but not too demanding, and it is also a good place to start seeing/writing proofs. On the other hand, if you have an experience with writing mathematical proofs, then I think you have no problem with number theory.

As Hurkyl mentioned, it is different from courses like calculus or linear algebra, which might make the subject harder.