Algorithm concept: choose the best description of an algorithm in computing and problem solving.

Introduction / Context:
An algorithm is the backbone of computing—an explicit, finite sequence of steps that transforms input into output. Recognizing what an algorithm is (and is not) helps distinguish coding syntax from problem-solving methodology.

Given Data / Assumptions:

• An algorithm describes logic, not programming language syntax.
• It must be precise, finite, and effective.
• It is independent of any particular hardware or language.

Concept / Approach:
The defining attributes of an algorithm include definiteness (each step is unambiguous), finiteness (terminates), and effectiveness (each step is basic enough to be executed). These criteria separate algorithms from vague heuristics and from descriptive prose.

Step-by-Step Solution:
1) Evaluate option texts against algorithm attributes.2) Option b matches: a finite, ordered sequence of steps to solve a problem.3) Options a and c misclassify the concept as a language or a math branch.4) Therefore, choose option b as the most accurate description.

Verification / Alternative check:
Classic examples—Euclid’s algorithm for GCD, sorting algorithms—exemplify stepwise procedures independent of any programming language.

Why Other Options Are Wrong:
Option a: a language is a notation for expressing algorithms, not the algorithm itself. Option c: algorithms are used in mathematics but are not a branch of it. Option d cannot be true because a and c are incorrect. Option e contradicts the definitive nature of algorithms.

Common Pitfalls:
Equating pseudocode or code with the algorithm; the algorithm is the logic, while code is one expression of it.

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