Foundations of algorithms: Which option best describes an algorithm in computer science and programming practice?

Introduction / Context:
An algorithm is a central concept in computing, underpinning tasks from sorting and searching to routing and cryptography. Clarity about what the term means enables better design, testing, and communication of solutions across languages and platforms.

Given Data / Assumptions:

• The question asks for a definition, not an implementation or language.
• Options include language, mathematical branch, and the procedural definition.
• We assume the general CS definition used in textbooks and standards.

Concept / Approach:
An algorithm is a finite, well-defined, step-by-step procedure that transforms inputs to outputs to solve a specific class of problems. It is language-independent and can be expressed in pseudocode, flowcharts, or any programming language. While algorithm analysis uses mathematics, the algorithm itself is not a programming language nor a mathematical branch; it is a procedure or recipe.

Step-by-Step Solution:

Verification / Alternative check:
Introductory CS texts define algorithm as a finite procedure to solve a problem; this matches the chosen option exactly.

Why Other Options Are Wrong:
Computer language: a tool to express algorithms, not the algorithm itself. Branch of mathematics: related in analysis, but not the definition. “All of the above”: overbroad and incorrect because the first two are not definitions.

Common Pitfalls:
Confusing implementation (code) with design (algorithm). Believing algorithms must be mathematical formulas—many are heuristic or procedural.

Final Answer:
A step by step procedure for solving a problem