What is an Algorithm?
A step-by-step set of instructions designed to solve a problem or complete a task, where each step is clear, unambiguous, and must be followed in order.
You encounter algorithms every single day — a recipe, a set of assembly instructions, or the steps your phone follows to unlock using your face. In mathematics, algorithms give us a reliable, repeatable method for solving problems.
The power of an algorithm lies in its consistency: follow the steps correctly, and you will always reach the correct answer. This is why computers rely entirely on algorithms — they cannot guess or use intuition, so every instruction must be perfectly clear.
Think of an algorithm like a GPS navigation system. No matter where you start, if you follow each instruction precisely — "turn left," "continue for 500 m," "take the third exit" — you will always arrive at the right destination. Skipping or reordering steps would leave you lost!
Algorithms as Flowcharts
One of the most powerful ways to represent an algorithm is as a flowchart — a visual diagram that shows each decision and action as a separate shape connected by arrows.
Flowcharts are especially useful because they make the logic of an algorithm visible at a glance. You can see exactly where the process branches depending on the answer to a question.
Standard flowchart symbols:
- Oval/Rounded rectangle — Start or End
- Rectangle — An action or process step (e.g., "Divide both sides by the coefficient")
- Diamond — A decision point with YES/NO branches
- Arrows — Show the direction of flow between steps
In mathematics, flowcharts are used to model algebraic procedures, checking processes, and problem-solving strategies. They make hidden thinking visible — which is exactly what a model should do.
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