Arithmetic

Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, division, factorization, multiplication, power computation, root extraction, and subtraction. Arithmetic was part of the quadrivium taught in medieval universities. A mnemonic for the spelling of "arithmetic" is "a rat in the house may eat the ice cream."

The branch of mathematics known as number theory is sometimes known as higher arithmetic.

Modular arithmetic is the arithmetic of congruences.

Floating-point arithmetic is the arithmetic performed on real numbers by computers or other automated devices using a fixed number of bits.

The fundamental theorem of arithmetic, also called the unique factorization theorem, states that any positive integer can be represented in exactly one way as a product of primes.

The Löwenheim-Skolem theorem, which is a fundamental result in model theory, establishes the existence of "nonstandard" models of arithmetic.

REFERENCES:

Derbyshire, J. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. New York: Penguin, pp. 371-372, 2004.

Karpinski, L. C. The History of Arithmetic. Chicago, IL: Rand, McNally, & Co., 1925.

Maxfield, J. E. and Maxfield, M. W. Abstract Algebra and Solution by Radicals. Philadelphia, PA: Saunders, 1992.

Thompson, J. E. Arithmetic for the Practical Man. New York: Van Nostrand Reinhold, 1973.

Weisstein, E. W. "Books about Arithmetic." http://www.ericweisstein.com/encyclopedias/books/Arithmetic.html.