Olympiad Mathematics

Olympiad Mathematics

The four olympiad pillars taught as real proof-based problem solving, for students who have outgrown school maths.

12 months (48 weeks), joinable any month Students roughly aged 12 to 18 who are strong at school maths and want genuine olympiad problem solving 2 live classes/week + weekly problem sets and timed mocks Course-completion certificate from Modern Age Coders

Syllabus updated July 2026

Olympiad Mathematics: IOQM, INMO and AMC Preparation

Flexible course duration

Duration depends on the student's background and pace. Beginners (kids / teens): typically 6 to 9 months. Adults with prior knowledge: often shorter, with an accelerated path.

Standard pace6 to 9 months
AcceleratedAdd class frequency to finish faster

For personalised duration planning, call +91 91233 66161 and we'll map a schedule to your goals.

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₹1,499/month

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₹4,999/month

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Program Overview

Olympiad mathematics is a different subject from school mathematics wearing the same name. School maths asks you to apply a method you were just shown. Olympiad maths hands you a problem you have never seen, gives you no method, and asks you to construct an argument that is airtight. Students who top their class routinely struggle at first, and that is normal, because nothing in the school syllabus trains this.

This course teaches the four pillars that every olympiad is built on: number theory, algebra, combinatorics and geometry. Each is taught for genuine understanding and then drilled on real past problems, because olympiad ability is built by attempting hard problems and failing productively, not by watching solutions.

It is aimed at both the Indian and international ladders. In India the path runs through IOQM, the Indian Olympiad Qualifier in Mathematics, on to INMO and the training camp beyond it. Internationally students target the AMC 10 and AMC 12, then AIME. The formats differ, and we prepare for each specifically, but the underlying skill is the same: reading a problem properly, finding the idea, and writing an argument that survives scrutiny.

Proof is taught explicitly from the start. Most students arrive able to find an answer but unable to justify it, and at INMO level the justification is the entire mark. We fix that early, because a correct answer with a hand-waving argument scores close to nothing.

What Makes This Program Different

  • All four pillars taught properly: number theory, algebra, combinatorics and geometry, not just contest tricks
  • Proof writing taught explicitly from the start, because at INMO level the argument is the mark, not the answer
  • Prepared for both ladders: IOQM and INMO in India, AMC 10, AMC 12 and AIME internationally
  • Built on real past problems, since olympiad ability comes from productive failure on hard problems
  • Students are taught to sit with a problem instead of giving up after two minutes, which is the actual skill
  • Live, small batches where solutions are critiqued line by line for rigour, not just marked right or wrong

Your Learning Journey

Phase 1
Proof technique and number theory, the natural entry point into olympiad thinking
Phase 2
Algebra and combinatorics, including inequalities and counting arguments
Phase 3
Geometry, then full contest simulation for IOQM, INMO and the AMC or AIME

Career Progression

1
Genuine readiness for IOQM and INMO in India, or the AMC and AIME internationally
2
Proof-writing ability that makes university mathematics far less of a shock
3
A distinctive strength in competitive university applications
4
Problem-solving stamina that transfers to physics, computer science and research
5
The confidence that comes from having solved problems you once could not start

Detailed Course Curriculum

Explore the complete week-by-week breakdown of what you'll learn in this comprehensive program.

Topics Covered
  • The difference between checking cases and proving a statement
  • Direct proof, and writing it so every step is justified
  • Proof by contradiction
  • Proof by contrapositive, and when it is easier
  • Reading a written solution critically and finding the gap
Projects You Build
  • Write five full proofs and have every line challenged in class
Practice & Assignments

Prove supplied statements and rewrite them after critique

Topics Covered
  • Mathematical induction, including strong induction
  • Common induction errors that void the proof
  • Invariants and monovariants, and the problems that hide them
  • Extremal arguments: taking the largest or smallest case
  • Recognising which technique a problem is inviting
Projects You Build
  • Solve a set of invariant problems and articulate the invariant explicitly in each
Practice & Assignments

20 induction and invariant problems

Assessment

A proof-writing assessment marked on rigour, not just the final answer

Topics Covered
  • Divisibility, GCD and the Euclidean algorithm
  • Primes, factorisation and the fundamental theorem of arithmetic
  • Modular arithmetic and congruences
  • Fermat's little theorem and Euler's theorem
  • Diophantine equations at olympiad level
Projects You Build
  • Solve a graded ladder of number theory problems from IOQM level upward
Practice & Assignments

40 number theory problems across the difficulty range

Assessment

Timed number theory paper under contest conditions

Topics Covered
  • Polynomial roots, factorisation and Vieta's formulas
  • Symmetric functions and their uses
  • Functional equations and the standard substitution strategies
  • Recognising the structure hidden in an ugly expression
  • Writing algebraic arguments cleanly
Projects You Build
  • Work a set of Vieta and functional equation problems from past papers
Practice & Assignments

30 algebra problems building in difficulty

Topics Covered
  • AM-GM and its many disguises
  • Cauchy-Schwarz
  • Rearrangement and Chebyshev
  • Normalisation and substitution tactics
  • Knowing when to stop searching for a slicker method
Projects You Build
  • Prove a graded set of inequalities, each with a fully justified argument
Practice & Assignments

30 inequality problems

Assessment

Timed algebra paper under contest conditions

Topics Covered
  • Counting properly: permutations, combinations and overcounting
  • The pigeonhole principle and its surprisingly deep uses
  • Inclusion and exclusion
  • Bijections and counting the same set two ways
  • Introductory graph theory and games
Projects You Build
  • Solve a counting problem two different ways and reconcile the results
Practice & Assignments

35 combinatorics problems

Assessment

Timed combinatorics paper

Topics Covered
  • Angle chasing done systematically rather than hopefully
  • Cyclic quadrilaterals and the power of a point
  • Similar triangles and ratio arguments
  • The classical centres and their properties
  • Drawing an accurate diagram, which solves more problems than any theorem
Projects You Build
  • Solve a ladder of synthetic geometry problems with full written proofs
Practice & Assignments

35 geometry problems from contest papers

Topics Covered
  • Coordinate geometry as a fallback when synthetic stalls
  • Trigonometric methods in geometry
  • Homothety and transformations
  • Choosing between synthetic, coordinate and trigonometric attacks
  • Recognising when a problem is resisting the method rather than you
Projects You Build
  • Attack the same hard problem three ways and compare which was cleanest
Practice & Assignments

25 problems requiring a deliberate choice of method

Assessment

Timed geometry paper

Topics Covered
  • Problems that do not announce their topic
  • Deciding quickly which pillar a problem belongs to
  • Working when the first idea fails, and the second
  • Managing frustration, which is a genuine competition skill
  • Building a personal record of techniques that worked
Projects You Build
  • Weekly mixed problem sets with no topic labels
Practice & Assignments

Mixed sets under time

Topics Covered
  • The IOQM format and how to pace it
  • AMC 10 and AMC 12 pacing, and the scoring implications of guessing
  • Answer-extraction techniques for short-answer formats
  • Knowing when to abandon a question and return
  • Accuracy under time, where most marks are actually lost
Projects You Build
  • Full timed IOQM and AMC papers every week
Practice & Assignments

Weekly full papers with question-by-question review

Topics Covered
  • The step up to full written proofs at INMO level
  • AIME format and its particular demands
  • Writing a complete solution under time pressure
  • Partial credit: how to secure marks on a problem you cannot finish
  • Contest-day routine, sleep and nerves
Projects You Build
  • Full INMO-style and AIME-style papers, marked on rigour
Practice & Assignments

Continuous full-paper cycle with detailed feedback

Assessment

Final full mock contest, marked as an examiner would, with an honest readiness assessment

Projects You'll Build

Build a professional portfolio with 50+ projects real-world projects.

Technologies & Skills You'll Master

Comprehensive coverage of the entire modern web development stack.

Career Outcomes & Opportunities

Transform your career with industry-ready skills and job placement support.

Prerequisites

Title
What Your Child Needs to Start
Items
Strong school mathematics and genuine enjoyment of hard problems,Roughly age 12 to 18, though we place by ability rather than age,No prior olympiad experience is required; proof technique is taught from scratch,Willingness to spend real time on problems between classes, since that is where the ability is built

Who Is This Course For?

Title
Who This Course Is For
Items
Students preparing for IOQM and INMO in India,Students targeting AMC 10, AMC 12 and AIME internationally,Strong school mathematicians who find their class work far too easy,Students who want mathematics rather than exam technique,Students aiming at competitive university applications where olympiad results carry weight

Career Paths After Completion

Readiness for IOQM, INMO, AMC and AIME
Proof-writing ability that makes university mathematics far less of a shock
A distinctive strength in competitive university applications
A foundation for research mathematics, physics or theoretical computer science
Problem-solving stamina that transfers to every quantitative field

Course Guarantees

Title
Our Commitment to You
Items
All four olympiad pillars taught properly, including the geometry most courses skimp on,Proof writing taught and marked for rigour from the first month,Real past problems throughout, not manufactured exercises,Solutions critiqued line by line, because a correct answer with a weak argument scores badly,A free demo class first, so you can judge the teaching before you pay anything

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