MO-ADVANCED — Math Olympiad Advanced (INMO/IMO Training)
Top-tier Math Olympiad preparation calibrated to INMO, IMOTC, and IMO standards. Covers advanced techniques across number theory (FFT-style methods), polynomial methods (Schur, Newton's), projective and inversive geometry, extremal combinatorics, and the probabilistic method. Includes a final problem-workshop chapter on past RMO/INMO/IMO papers.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply advanced number-theory and algebraic techniques to INMO/IMO problems [Apply]
- Analyze polynomial and algebraic inequalities using SOS, Schur, and Newton identities [Analyze]
- Construct rigorous proofs in projective and inversive geometry [Create]
- Apply the probabilistic method and extremal arguments to combinatorial extremal problems [Apply]
- Evaluate selected RMO/INMO/IMO problems with full multi-step rigour [Evaluate]
- Connect olympiad techniques across number theory, algebra, geometry, and combinatorics [Analyze]
📚 Chapters
- Advanced Diophantine Methods and the Local-Global Principle
- Algebraic Number Theory Snapshot for Olympiads
- Olympiad-Level Estimation and Bounds
- Advanced Functional Equations — Polynomial and Multiplicative Forms
- Polynomial Methods — Schur, Newton, and Symmetry Tricks
- Algebraic Inequalities — SOS, uvw, and Schur Identities
- Projective and Inversive Geometry Toolkit
- Mixtilinear Circles, Isogonal Conjugates, and Symmedians
- Geometric Inequalities — Euler, Erdős–Mordell, and Beyond
- Extremal Combinatorics and the Probabilistic Method
- Linear Algebra and Algebraic Methods in Combinatorics
- RMO / INMO / IMO Selected Problem Workshop
TutorDA LMS
MO-SENIOR — Math Olympiad Senior (Class 11–12, IOQM/RMO)
Senior-level Math Olympiad preparation calibrated to IOQM and RMO standards. Covers advanced number theory (quadratic residues, primitive roots), functional equations, advanced inequalities, projective geometry, generating functions, and graph theory. Designed for Class 11–12 students targeting the RMO selection.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply LTE, primitive roots, and order arguments to advanced number-theory problems [Apply]
- Construct solutions to functional equations using Cauchy/Jensen-type methods [Create]
- Analyze inequalities using power-mean, Schur, and rearrangement techniques [Analyze]
- Apply triangle-centre theorems (Euler line, Ptolemy, power of a point) to olympiad geometry [Apply]
- Construct generating-function and recurrence-based counting solutions [Create]
- Evaluate IOQM- and RMO-style problems with multi-step reasoning [Evaluate]
📚 Chapters
- Diophantine Equations and Pell's Equation
- Quadratic Residues and the Legendre Symbol
- Order of an Element, Primitive Roots, and Lifting-the-Exponent
- Functional Equations — Cauchy, Jensen, and Beyond
- Advanced Inequalities — Power Mean, Rearrangement, Jensen
- Polynomials over ℝ and ℂ — Symmetric Functions and Roots
- Triangle Centres, Euler Line, and the Nine-Point Circle
- Power of a Point, Ptolemy's Theorem, and Radical Axes
- Inversion and the Basics of Projective Geometry
- Generating Functions and Linear Recurrences
- Graph Theory — Trees, Bipartite Graphs, and Colouring
- Combinatorial Game Theory and Strategy Problems
TutorDA LMS
MO-JUNIOR — Math Olympiad Junior (Class 8–10)
Junior-level Math Olympiad preparation for Class 8–10 students. Goes deeper into Number Theory (modular arithmetic, CRT), Algebra (Vieta, inequalities), Geometry (cevians, circles), and Combinatorics (Pigeonhole, expected value). Calibrated to PRMO entry and IOQM-Junior level.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply Euclidean algorithm and CRT to solve linear congruences [Apply]
- Analyze polynomial factorisation using Vieta's relations and symmetric functions [Analyze]
- Apply AM–GM and Cauchy–Schwarz to prove standard olympiad inequalities [Apply]
- Analyze triangle and circle configurations using cevian theorems and inscribed-angle [Analyze]
- Apply pigeonhole and invariant arguments to combinatorial proofs [Apply]
- Evaluate probability and expected-value problems via bijective counting [Evaluate]
📚 Chapters
- Divisibility Rules, Bézout's Identity, Euclidean Algorithm
- Modular Arithmetic and Chinese Remainder Theorem
- Number-Theoretic Functions (Euler φ, σ, μ)
- Polynomial Identities and Factorisation Techniques
- Quadratic Equations and Vieta's Formulas
- Introduction to Inequalities — AM–GM, Cauchy–Schwarz
- Triangle Properties — Cevians, Centroid, Incentre, Circumcentre
- Circles — Tangents, Chords, and Inscribed-Angle Theorem
- Coordinate Geometry — Lines, Distance, and Locus
- Permutations, Combinations, and the Binomial Theorem
- Pigeonhole Principle and Invariants
- Probability, Expected Value, and Counting Bijections
TutorDA LMS
MO-FOUND — Math Olympiad Foundation (Class 5–7)
Foundation-level Math Olympiad preparation for Class 5–7 students. Builds intuition in the four classical olympiad areas — Number Theory, Algebra, Geometry, Combinatorics — through pattern recognition, logical reasoning, and competition-style problems calibrated to SOF IMO and NMTC Sub-Junior levels.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply divisibility, factorisation, and GCD/LCM techniques to integer puzzles [Apply]
- Analyze numerical patterns and sequences to predict terms [Analyze]
- Solve linear word problems using algebraic translation [Apply]
- Compute perimeter, area, and volume of plane and 3D figures [Apply]
- Apply systematic counting principles to combinatorial puzzles [Apply]
- Evaluate logical-reasoning and probability questions at SOF IMO Sub-Junior level [Evaluate]
📚 Chapters
- Divisibility, Primes, GCD and LCM
- Modular Arithmetic Basics
- Number Patterns and Sequences
- Variables, Expressions, and Linear Equations
- Ratios, Proportions, and Percentages
- Word Problems and Logical Reasoning
- Angles, Triangles, and Quadrilaterals
- Perimeter, Area, and Volume
- Symmetry, Reflections, and Tessellations
- Counting Principles and Tree Diagrams
- Introduction to Permutations and Combinations
- Probability Basics and Counting Puzzles
TutorDA LMS