Difference between revisions of "Number theory"
Karl Jones (Talk | contribs) (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 ==...") |
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Number theorists study: | Number theorists study: | ||
| − | * [[Prime numbers]] | + | * [[Prime number|Prime numbers]] |
* Properties of objects made out of integers (e.g., [[Rational number|rational numbers]]) | * Properties of objects made out of integers (e.g., [[Rational number|rational numbers]]) | ||
* Generalizations about integers (e.g., [[Algebraic integer|algebraic integers]]). | * Generalizations about integers (e.g., [[Algebraic integer|algebraic integers]]). | ||
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== See also == | == See also == | ||
| + | * [[Algebraic integer]] | ||
* [[Arithmetic]] | * [[Arithmetic]] | ||
| + | * [[Computer science]], | ||
| + | * [[Mathematical logic]] | ||
* [[Mathematics]] | * [[Mathematics]] | ||
| + | * [[Peano arithmetic]] | ||
| + | * [[Prime number]] | ||
| + | * [[Rational number]] | ||
== External links == | == External links == | ||
* [https://en.wikipedia.org/wiki/Number_theory Number theory] @ Wikipedia | * [https://en.wikipedia.org/wiki/Number_theory Number theory] @ Wikipedia | ||
Revision as of 08:17, 2 September 2015
Number theory (or arithmetic, in the older sense) is a branch of pure mathematics devoted primarily to the study of the integers.
Contents
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 numbers)
- Generalizations about integers (e.g., 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 By the early twentieth century, it had been superseded by "number theory".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
- Algebraic integer
- Arithmetic
- Computer science,
- Mathematical logic
- Mathematics
- Peano arithmetic
- Prime number
- Rational number
External links
- Number theory @ Wikipedia
