Mathematical Thinking in Computer Science

UC San Diego develops mathematical reasoning through problems that invite exploration and explanation. Examples and counterexamples lead into recursion, induction and invariants, ending with a puzzle-based application. It suits learners who want to explain why an algorithmic idea works rather than rely only on a few successful tests.

What you will learn

• Construct arguments and investigate counterexamples.
• Apply recursion and mathematical induction.
• Use invariants to reason about a changing system.

Who this suits

Learners beginning mathematical reasoning for computer science; allow time to work through the problems independently.

Before you enroll

Allow time to solve exercises independently rather than only following explanations. Software versions and setup instructions can change; compare them with current documentation. Mathematical and programming foundations develop through repeated practice, and completing an introductory course does not demonstrate expertise in every computing field.

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Put it into practice

Choose a small puzzle, propose an invariant, and test whether every permitted move preserves it before drawing a conclusion.

Source and review

This overview is based on the provider's published information, checked on 12 October 2026. It is an editorial assessment, not a claim that we completed the resource. Time filters are approximate study ranges; projects and exercises can take longer.

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