1. A logical step-by-step procedure for solving a mathematical problem in a finite number of steps, often involving repetition of the same basic operation.
2. A logical sequence of steps for solving a problem, often written out as a flow chart, which can be translated into a computer program.
3. A set of rules for solving problems or doing calculations, especially rules that a computer uses.
4. A completely determined and finite procedure for solving a problem; especially, when used in relation to mathematics and computer science.
5. A set of ordered steps for solving a problem; such as, a mathematical formula or the instructions in a computer program.

The terms algorithm and logic are synonymous because both refer to a sequence of steps to solve a problem; however, an algorithm implies an expression that solves a complex problem rather than the overall input-process-output logic of typical business programs.

7. Etymology: from the 1690's, or the late 17th century, from French algorithme, an alteration (under mistaken connection with Greek arithmos, "number") from Old French algorisme, "the Arabic numeral system" (13th century), from Middle Latin algorismus, a mistaken transliteration of Arabic al-Khwarizmi, "native of Khwarazm", the surname of the mathematician whose works introduced sophisticated mathematics and algorithms to the West.

The earlier form in Middle English was algorism from about the early 13th century, from Old French.

A defined set of instructions or procedural steps that leads to a logical conclusion to a problem.

In computer science, algorithms are generally the programmed steps that manipulate data and produce the desired results.