|
|
| (4 intermediate revisions by 3 users not shown) |
| Line 1: |
Line 1: |
| == Algebraic Number Theory ==
| | #REDIRECT[[Number theory/Advanced]] |
| [[Algebraic number theory]] studies number theory from the perspective of [[abstract algebra]]. In particular, heavy use is made of [[ring theory]] and [[Galois theory]]. Algebraic methods are particularly well-suited to studying properties of individual prime numbers. From an algebraic perspective, number theory can perhaps best be described as the study of <math>\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})</math>. Famous problems in algebraic number theory include the [[Birch and Swinnerson-Dyer Conjecture]] and [[Fermat's Last Theorem]]. | |
| | |
| == Analytic Number Theory ==
| |
| [[Analytic number theory]] studies number theory from the perspective of [[calculus]], and in particular [[real analysis]] and [[complex analysis]]. The techniques of [[analysis]] and [[calculus]] are particularly well-suited to studying large-scale properties of prime numbers. The most famous problem in analytic number theory is the [[Riemann Hypothesis]].
| |
| | |
| == Elliptic Curves and Modular Forms ==
| |
| (I don't really feel like writing this right now. Any volunteers?)
| |
| | |
| == See also ==
| |
| * [[Number theory]]
| |
