In mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 and computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

, an algorithm is an effective method
Effective method
In computability theory, an effective method is a procedure that reduces the solution of some class of problems to a series of rote steps which, if followed to the letter, and as far as may be necessary, is bound to:...

 expressed as a finite
Finite is the opposite of infinite. It may refer to:*Finite set, having a number of elements given by some natural number*Finite verb, being inflected for person and for tense...

 list of well-defined instructions for calculating a function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

. Algorithms are used for calculation
A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change.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...

, data processing
Data processing
Computer data processing is any process that a computer program does to enter data and summarise, analyse or otherwise convert data into usable information. The process may be automated and run on a computer. It involves recording, analysing, sorting, summarising, calculating, disseminating and...

, and automated reasoning
Automated reasoning
Automated reasoning is an area of computer science dedicated to understand different aspects of reasoning. The study in automated reasoning helps produce software which allows computers to reason completely, or nearly completely, automatically...

. In simple words an algorithm is a step-by-step procedure for calculations.

Starting from an initial state and initial input (perhaps empty), the instructions describe a computation
Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...

 that, when executed, will proceed through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state.