Olympiad Maths: IOQM & Beyond

By the end

What you'll build

• Solve IOQM-style integer-answer problems across number theory, counting, geometry and algebra
• Apply Euclid's algorithm, Fermat's and Euler's theorems to remainder and divisibility questions
• Count with permutations, combinations, stars-and-bars, pigeonhole and invariants
• Chase angles, cyclic quadrilaterals and power-of-a-point through olympiad figures you draw yourself
• Write complete proofs by induction, contradiction and pigeonhole that a grader would accept

Curriculum

What's inside

5 modules · 28 lessons

1. 01

   Number Theory

   7 lessons
   • Start Here: The Olympiad Path
   • Divisibility, GCD and Euclid's Algorithm
   • Drill: Divisibility and GCDfill blank
   • Modular Arithmetic, Fermat and Euler
   • Drill: Modular Arithmeticfill blank
   • + 2 more lessons
2. 02

   Combinatorics and Counting

   6 lessons
   • Counting Principles: Product, Sum and Complement
   • Evidence Check: Counting Basicsquiz
   • Permutations, Combinations and Binomial Identities
   • Drill: Counting Numericalsfill blank
   • Pigeonhole and Invariants
   • + 1 more lesson
3. 03

   Euclidean Geometry

   5 lessons
   • Angle Chasing and the Derivation Chain
   • Circles: Inscribed Angles, Cyclic Quadrilaterals and Power of a Point
   • Drill: Geometry Numericalsfill blank
   • Theorem Deck: The Olympiad Toolkitflashcard sr
   • Geometry Checkpointquiz
4. 04

   Inequalities and Algebra

   4 lessons
   • AM–GM and Cauchy–Schwarz
   • Polynomials and Vieta's Formulas
   • Drill: Algebra and Inequalitiesfill blank
   • Algebra Checkpointquiz
5. 05

   Proof Writing Bootcamp

   6 lessons
   • What Makes a Proof
   • Induction and Contradiction
   • Writing Lab: Your First Olympiad Proofwriting lab
   • IOQM-Pattern Timed Mockquiz
   • Capstone: The Puzzle Paper, and Where Next
   • + 1 more lesson

The shape of it

How this course works