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| − | == 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]]. | |
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| − | == Analytic Number Theory ==
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| − | [[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]].
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| − | == Elliptic Curves and Modular Forms ==
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| − | (I don't really feel like writing this right now. Any volunteers?)
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| − | == See also ==
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| − | * [[Number theory]]
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