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A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. [1] [2] Common examples of computation are mathematical equation solving and the execution of computer algorithms. Mechanical or electronic devices (or, historically, people) that perform computations are known as computers.
A large part of computational mathematics consists roughly of using mathematics for allowing and improving computer computation in areas of science and engineering where mathematics are useful. This involves in particular algorithm design, computational complexity, numerical methods and computer algebra.
Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on.
But even with the greatest common divisor divided out, arithmetic with rational numbers can become unwieldy very quickly: 1/99 − 1/100 = 1/9900, and if 1/101 is then added, the result is 10001/999900. The size of arbitrary-precision numbers is limited in practice by the total storage available, and computation time.
Plot of y = 3 √ x.The plot is symmetric with respect to origin, as it is an odd function.At x = 0 this graph has a vertical tangent. In mathematics, a cube root of a number x is a number y that has the given number as its third power; that is =.
A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or results.The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people.
Computer arithmetic is the scientific field that deals with representation of numbers on computers and corresponding implementations of the arithmetic operations. [1] [2] It includes: Fixed-point arithmetic; Floating-point arithmetic; Interval arithmetic; Arbitrary-precision arithmetic; Modular arithmetic. Multi-modular arithmetic
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.