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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.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
A candidate definition was proposed independently by several mathematicians in the 1930s. [5] The best-known variant was formalised by the mathematician Alan Turing , who defined a well-defined statement or calculation as any statement that could be expressed in terms of the initialisation parameters of a Turing machine . [ 6 ]
If the domain of definition equals X, one often says that the partial function is a total function. In several areas of mathematics the term "function" refers to partial functions rather than to ordinary functions. This is typically the case when functions may be specified in a way that makes difficult or even impossible to determine their domain.
In mathematics, the theory of linear systems is a fundamental part of linear algebra, a subject which is used in many parts of modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra , and play a prominent role in physics , engineering , chemistry , computer science , and economics .
The word "formal" indicates that the series need not converge. In mathematics, and especially in algebra, a formal series is an infinite sum that is considered independently from any notion of convergence and can be manipulated with algebraic operations on series (addition, subtraction, multiplication, division, partial sums, etc.).