Difference between revisions of "Number theory"

Revision as of 05:23, 20 February 2016

Number theory (or arithmetic, in the older sense) is a branch of pure mathematics devoted primarily to the study of the 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 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 By the early twentieth century, it had been superseded by "number theory".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
• Local analysis
• Mathematical logic
• Mathematics
• Peano arithmetic
• Prime number
• Rational number

External links

• Number theory @ Wikipedia