Algorithms and pseudocode
Objective. Specify terminating mathematical algorithms.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Algorithms and pseudocode describe a precise, finite sequence of steps that solves a mathematical problem, written in structured informal notation using loops, conditionals and variable assignment. A well-specified algorithm must terminate, meaning some quantity (a loop counter or a shrinking interval) must provably reach a stopping condition after finitely many steps. For example, pseudocode to find the maximum of a list sets max ← list[0], then loops through remaining entries, updating max whenever a larger value is found, terminating once every entry has been checked. Clear pseudocode states inputs, outputs, and the exact update rule at each step.
Worked example
Write pseudocode-based reasoning, as part of studying algorithms, to find the sum of the first n positive integers, then give the result for n = 10.
- 1Pseudocode: set sum ← 0, loop i from 1 to n, sum ← sum + i
- 2This computes sum = 1 + 2 + ... + n
- 3Use the closed form n(n+1)/2 to check termination value
- 4Substitute n=10: sum = 10(11)/2 = 55
Answer: 55
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Start practisingCommon mistake. Writing a loop condition that can never become false, such as 'while x > 0: x ← x + 1'; the algorithm never terminates because x only grows, so always verify the loop variable moves towards the stopping condition.
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