Number theory - Revision history

Karl Jones: /* See also */

2016-10-05T12:58:31Z

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Karl Jones: /* External links */

2016-04-24T19:04:03Z

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Karl Jones at 14:17, 2 September 2015

2015-09-02T14:17:14Z

Karl Jones: Created page with "'''Number theory''' (or ''arithmetic'', in the older sense) is a branch of pure mathematics devoted primarily to the study of the integers. == Description ==..."

2015-09-02T14:10:34Z

Created page with "'''Number theory''' (or ''arithmetic'', in the older sense) is a branch of pure mathematics devoted primarily to the study of the integers. == Description ==..."

New page

'''Number theory''' (or ''arithmetic'', in the older sense) is a branch of [[pure mathematics]] devoted primarily to the study of the [[Integer|integers]].

== Description ==

It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline.

Number theorists study:

* [[Prime numbers]]
* Properties of objects made out of integers (e.g., [[Rational number|rational numbers]])
* Generalizations about integers (e.g., [[Algebraic integer|algebraic integers]]).

Integers can be considered either in themselves or as solutions to equations ([[Diophantine geometry]]).

== Questions in number theory ==

Questions in number theory are often best understood through the study of [[analytical objects]] (e.g., the [[Riemann zeta function]]) that encode properties of the integers, primes or other number-theoretic objects in some fashion. See [[analytic number theory]].

== Rational numbers ==

One may also study real numbers in relation to rational numbers, e.g., as approximated by the latter (Diophantine approximation).

== History ==

The older term for number theory is arithmetic. By the early twentieth century, it had been superseded by "number theory".

The word "arithmetic" is used by the general public to mean "elementary calculations"; it has also acquired other meanings in [[mathematical logic]], as in [[Peano arithmetic]], and [[computer science]], as in [[floating point arithmetic]].

The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. In particular, arithmetical is preferred as an adjective to number-theoretic.

== See also ==

* [[Arithmetic]]
* [[Mathematics]]

== External links ==

* [https://en.wikipedia.org/wiki/Number_theory Number theory] @ Wikipedia

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 * [[Algebraic integer]]
 * [[Algebraic number theory]]
 * [[Arithmetic]]
 * [[Complex analysis]]

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 * [[Algebraic integer]]
 * [[Arithmetic]]
 * [[Complex analysis]]

← Older revision		Revision as of 19:04, 24 April 2016
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	* [https://en.wikipedia.org/wiki/Number_theory Number theory] @ Wikipedia		* [https://en.wikipedia.org/wiki/Number_theory Number theory] @ Wikipedia
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		+	[[Category:Mathematics]]
		+	[[Category:Numbers]]

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 * [[Algebraic integer]]
 * [[Arithmetic]]
 * [[Computer science]]
 * [[Local analysis]]

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 * [[Algebraic integer]]
 * [[Arithmetic]]
-* [[Computer science]],
+* [[Computer science]]
 * [[Mathematical logic]]
 * [[Mathematics]]

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 Number theorists study:
-* [[Prime numbers]]
+* [[Prime number|Prime numbers]]
 * Properties of objects made out of integers (e.g., [[Rational number|rational numbers]])
 * Generalizations about integers (e.g., [[Algebraic integer|algebraic integers]]).
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 == See also ==
 * [[Arithmetic]]
 * [[Mathematics]]
 == External links ==
 * [https://en.wikipedia.org/wiki/Number_theory Number theory] @ Wikipedia