Move from a pattern to a proof for every integer. Begin at the first unfamiliar idea; the prerequisite links help you find a shorter route. You can open any lesson.

Unsure where to start? Try the starting-point check.

  1. D01

    Why mathematical induction works

    Distinguish a conjecture from a proof covering all admissible integers.

    Inside: Patterns versus proof · Statements indexed by an integer

  2. D02

    Mathematical induction: the first principle

    Write a complete induction proof with a valid starting index.

    Inside: Base case and inductive step · Sums and divisibility · Inequalities and starting indices · Repairing false induction

  3. D03

    Strong induction

    Choose a sufficient induction hypothesis and justify every smaller case used.

    Inside: Why more than the previous case is needed · Factorisation and decomposition · Multiple base cases

These original lessons introduce the methods and give practice with solutions. A single short session is not a full assessment of Olympiad readiness. Build depth through the written challenges and your country’s official past papers.