Mathematics Olympiad Masterclass
Develop deep mathematical reasoning for BdMO, APMO, and IMO competitions
What You'll Learn
- Construct rigorous proofs using direct, contradiction, and induction techniques to Olympiad presentation standards
- Solve number theory problems involving modular arithmetic, Diophantine equations, and p-adic valuations
- Apply combinatorial arguments including pigeonhole, double counting, and generating functions to competition problems
- Prove geometric results using synthetic methods, trigonometric identities, and coordinate techniques
- Manipulate algebraic inequalities using AM-GM, Cauchy-Schwarz, Jensen, and SOS methods
+1 more outcome
Your Instructor
Mathematics — APMO Honorable Mention
Honorable Mention at the Asian Pacific Mathematics Olympiad 2019, winner of the Bangladesh National Math Olympiad from 2014 to 2017, and a TST camper in 2018 and 2019.
Learn more about Md.Full Curriculum
- Introduction to mathematical problem solving and proof strategies
- Fundamentals of arithmetic: primes, factors, and number properties
- Divisibility rules, tests, and applications
- GCD, LCM, and the Euclidean algorithm
- Modular arithmetic: congruences, residues, and clock arithmetic
- Fermat's Little Theorem and modular inverses
- Applications to cryptography and competition problems
- Counting principles: addition, multiplication, permutations, and combinations
- The Pigeonhole principle and its creative applications
- Inclusion-exclusion and double counting
- Algebraic manipulation: factoring, expansion, and simplification
- Solving equations: linear, quadratic, and systems of equations
- Advanced equation solving: substitution, symmetry, and polynomial roots
- Inequalities: AM-GM, Cauchy-Schwarz, and proof techniques
- Triangle properties: congruence, similarity, and special triangles
- Angle chasing: inscribed angles, cyclic quadrilaterals, and parallel lines
- Triangle centres: centroid, incentre, circumcentre, and orthocentre
- Ceva's theorem and Menelaus' theorem
- Circle theorems: tangent lines, power of a point, and radical axes
- Area and length: Heron's formula, coordinate geometry, and trigonometric methods
- Symmetry: reflections, rotations, and transformations in problem solving
- Mathematical induction: weak, strong, and structural induction
- Induction in inequalities and divisibility proofs
- Problem selection and time management in BdMO/IMO-style exams
- Proof writing: clarity, rigour, and presentation
- Full-length mock examinations and solution review
Interactive Lessons
Step-by-step interactive lessons with animated geometry, proof visualizations, and quizzes.
Intro to Problem Solving
FoundationsProblem-solving methodology, contradiction proofs, and mathematical thinking strategies.
Fundamentals of Arithmetic
FoundationsNumber sets, Fundamental Theorem of Arithmetic, and prime factorization.
Divisibility
Number TheoryDivisibility rules, division algorithm, prime numbers, and Euclid's proof.
GCD & LCM
Number TheoryGreatest common divisor, least common multiple, and the Euclidean algorithm.
Modular Arithmetic
Number TheoryCongruence, Fermat's and Euler's theorems, Chinese Remainder Theorem.
Counting
CombinatoricsAddition and multiplication rules, permutations, combinations, and inclusion-exclusion.
Pigeonhole Principle
AdvancedThe pigeonhole principle and its powerful applications in olympiad problems.
Basic Algebraic Manipulation
AlgebraFactoring, completing the square, algebraic identities, and substitution.
Equation Solve
AlgebraSystematic techniques for solving linear and quadratic equations.
Equation Solve Part 2
AlgebraHigher-degree equations, functional equations, and advanced solving.
Inequality
AlgebraAM-GM, Cauchy-Schwarz, and inequality solving techniques.
Triangle Properties
GeometryParallel lines, equilateral, isosceles, congruent, and similar triangles.
Angle Chase
GeometryAngle chasing techniques in geometry and quadrilateral problems.
Triangle
GeometryTriangle centers, Stewart's theorem, angle bisector theorem, and cevians.
Circle
GeometryCircle properties, inscribed angles, tangent lines, and theorems.
Area & Length
GeometryArea formulas, Heron's formula, and coordinate geometry.
Symmetry
AdvancedLine symmetry, rotational symmetry, and symmetry arguments in problem solving.
Induction
AdvancedWeak and strong induction, common mistakes, and applications.
Sample Problem
A taste of the competition-level problems you'll tackle.
Problem 1 (Number Theory)
Determine all composite integers n > 1 that satisfy the following: if d_1, d_2, ..., d_k are all the positive divisors of n with 1 = d_1 < d_2 < ... < d_k = n, then d_i divides d_{i+1} + d_{i+2} for every 1 <= i <= k-2.
Frequently Asked Questions
School mathematics focuses on applying known formulas and procedures to standard problem types. Olympiad mathematics requires creative problem solving, proof construction, and deep conceptual understanding. There are no formulas to memorise for a problem you have never seen before; instead, you develop a toolkit of techniques and the mathematical maturity to combine them in novel ways. This course teaches you that way of thinking.
You should be comfortable with algebra (manipulating equations, factoring), basic geometry (triangle properties, circle theorems), and mathematical reasoning. Exposure to BdMO divisional-level problems is helpful but not required. We build up from fundamentals in each topic area.
Proof writing is central to mathematical Olympiads. A correct idea presented in a poorly written proof can lose significant marks. We dedicate substantial time to teaching clear, rigorous proof writing, and you will receive detailed feedback on your submitted proofs throughout the course.
Absolutely. Many students have uneven strengths across the four main areas (algebra, combinatorics, geometry, number theory). The modular structure allows you to strengthen weak areas while deepening your strong ones. We also offer targeted supplementary problem sets for students who want extra practice in specific topics.
Yes. The problem-solving techniques and mathematical maturity developed here are transferable across all proof-based mathematics competitions. While the course is designed around the BdMO-to-IMO pathway, students have successfully used the same preparation for APMO, the Putnam, and university-level competitions.
Ready to begin Mathematics?
Mathematics Olympiad Masterclass · 8 modules · Intermediate to Advanced