• RESEARCH IN SCHOOL & UNIVERSITY
    Rushil Reddy wins a second place at Pennsylvania Science Fair.
    Learn More
    OLYMPIAD
    In 2025, 10 INMO awardees are from Cheenta
    RESEARCH
    Cheenta student researchers are in Harvard & Stanford
    LEADERSHIP
    Building leadership projects with businesses from rural India.
  • LEADERSHIP PROGRAMS
    Souradip created Russian Math Circles in rural India.
    Explore
    OLYMPIAD
    In 2025, 10 INMO awardees are from Cheenta
    RESEARCH
    Cheenta student researchers are in Harvard & Stanford
    LEADERSHIP
    Building leadership projects with businesses from rural India.
  • OLYMPIAD PROGRAMS
    Arjun Gupta won a gold in IMO.
    Learn More
    OLYMPIAD
    In 2025, ten INMO awardees are from Cheenta
    RESEARCH
    Cheenta student researchers are in Harvard & Stanford
    LEADERSHIP
    Building leadership projects with businesses in rural India.

Mentoring & Advanced Programs

Since 2010, Cheenta has helped hundreds of students reach Ivy League calibre universities like Harvard, MIT, Stanford, UPenn, Oxford, Cambridge, ISI, and CMI. 

Our advanced programs on olympiads, research and leadership coupled with long-term mentoring for university applications provide unique opportunity for passionate students. 

Success Story since 2010

Understand Trial Process

Cheenta Trial Process includes live class, diagnosis test and mentor meeting. It also includes a week of software access for self-driven component of our program.
The goal of the trial process is two fold. Firstly we wish to provide the student a preview of the programs and processes at Cheenta. Secondly, since admission to Cheenta programs are competitive in nature, the trial process works as a screening mechanism.
Start with Trial

Videos on Beautiful Math

There is a shorter solution to this problem. We are going to ignore it, and count something else instead — and the detour teaches more than the shortcut did.The problem. In a chess tournament with n players, every player plays every other player exactly once. Someone wins, someone loses, there are no draws — so each player plays n − 1 games. If player i finishes with w(i) wins and l(i) losses, show that w(1)² + w(2)² + ... + w(n)² = l(1)² + l(2)² + ... + l(n)².The second solution looks at triples of players. Three players play three games among themselves, and those three wins split either as 1 + 1 + 1 or as 2 + 1 + 0. Call the 2 + 1 + 0 case a dominant triple. Count the dominant triples two ways — once by the winner, once by the loser — and the identity falls out.Along the way: double counting, partitioning into mutually exclusive and exhaustive cases, and a bijection you can see rather than compute.This is the second of two videos on the same problem. If you have not seen the first solution, watch that one first — the two together are the point.Who this is for: students in grades 8-12 and undergraduates preparing for AMC, AIME, IOQM, RMO, CMI and ISI entrances, or anyone who enjoys a clean counting argument.CHAPTERS 0:00 Why bother with a second solution? 0:33 The problem, one more time 1:44 The goal: Σw² = Σl² 2:00 A new object: triples of players 2:35 Three games, two ways to split the wins 3:30 The dominant triple 3:44 In how many triples is P₁ dominant? 4:58 A worked example with five players 6:14 Summing Wᵢ choose 2 over every player 7:31 Mutually exclusive and exhaustive 7:55 Doing the same count with losses 8:56 The bijection: winners ↔ losers 9:56 The algebra: expand, cancel, done 11:19 Why the longer solution was worth itTRY IT YOURSELF Pause at 6:14, before the sum is written down. Can you say, in one sentence, why no triple gets counted twice? That sentence is the whole proof.ABOUT CHEENTA Cheenta Academy runs small-group programs in mathematics, physics, computer science and research for school and college students. Math Olympiad, Physics Olympiad, Informatics Olympiad, research projects and leadership projects — details and enrolment at the link below.https://www.cheenta.com#matholympiad #combinatorics #doublecounting #IOQM #AMC #cheenta
Dominant Triples and the Chess Tournament Problem | Olympiad Combinatorics
In a chess tournament where every player faces every other player exactly once, the sum of squared wins equals the sum of squared losses — always, regardless of results. This video proves it two ways, using the invariant principle and bijection counting, and shows you why solving a problem once is never really the end of the story.What you'll learn: ✦ How to identify invariants in a combinatorics problem — quantities that stay fixed no matter how the tournament plays out ✦ Why the bijection between matches and wins is the hidden engine behind the proof, and how to make that reasoning airtight ✦ A clean algebraic factorisation that reduces the entire result to two lines once the invariants are in place ✦ Why a second, more instructive method exists — and what it reveals about double counting as a general strategy (covered in Part 2)Chapters: 00:00 — Problem setup: the chess tournament 02:30 — Invariant 1: wins + losses = n − 1 for each player 04:15 — Invariant 2: total wins = total losses = C(n,2) 06:00 — Algebraic factorisation and the proof 09:00 — Bijection principle — the hidden idea 10:30 — Challenge problem and Part 2 previewCheenta Academy teaches olympiad mathematics the way it is actually practised — through problems that open into techniques, and techniques that generalise into ideas. Every result here is a starting point, not a finish line.→ Explore our Olympiad programmes: cheenta.com#Combinatorics #InvariantPrinciple #MathOlympiad #IOQM #RMO #DoubleCounting #Cheenta #OlympiadMath #Bijection #AMC12 #ChessMath #CombinatoricsProof
Chess Tournament Problem — Invariant Principle for Olympiad Math
Derivatives don't just give you slopes — they give you the machinery to measure length on curved spaces like spheres and tori. This video builds arc length from first principles using tangent vectors and a fully worked example.✦ What you'll learn: → How manifolds (spheres, tori, Klein bottles, Möbius strips) are built from flat patches via charts → How to define a path on a manifold and pull it back to the plane using a chart map → Why the derivative of that pulled-back path is really a velocity/tangent vector → How summing scaled tangent vectors approximates arc length — and becomes an integral in the limitTimestamps: 00:00 — Introduction: Derivatives Beyond the Plane 00:45 — Manifolds: Spheres, Tori, Klein Bottles & Möbius Strips 02:00 — Charts: Mapping Manifolds to the Plane 03:15 — Defining a Path Between Two Points 04:30 — Composing the Chart Map with the Path 06:00 — Tangent Vectors as Velocity 07:30 — Worked Example: f∘γ(t) = (t², 2t) 09:30 — Approximating Arc Length with Derivatives 11:00 — From Riemann Sums to the Integral 12:00 — Closing Thoughts & Cheenta CoursesCheenta Academy trains olympiad and research-track students to see mathematics the way working mathematicians do — starting from intuition and building up to rigor. Our ISI-CMI Entrance and Research in School programs go beyond exam syllabi into the ideas that actually shape how mathematicians think.#Cheenta #ISICMIEntrance #DifferentialGeometry #Calculus #MathOlympiad #TangentVectors #Manifolds #ResearchMathematics #ArcLength #HigherMathematics
What is a Derivative? Concept in Mathematics and Calculus - Dr. Ashani Dasgupta
Subscribe

Director's Desk

Motivated students and passionate teachers are the building blocks of Cheenta. Since 2010, hundreds of our students have joined premier universities such as Harvard, MIT, Stanford, ISI, CMI to name a few. They have enriched our faculty and research teams.
Dr. Ashani Dasgupta
PhD in Mathematics, University of Wisconsin-Milwaukee. Published researcher at London Mathematical Society's journal. Math Olympiad Coach since 2010.

  • Students & Parents Say


    "Advanced concepts are introduced in a very structured and engaging manner... I feel the online platforms used by Cheenta are truly exceptional"

    Anirban Chatterjee

    Parent. India.

  • Students & Parents Say


    "has helped my son to perform well at competitions including USAJMO and others. He has grown more confident in his math abilities over the past year and half and is hoping to do well in the future. I am impressed with their quality and professionalism."

    Murali Kadaveru

    Parent. Virginia, USA.

  • Students & Parents Say


    "We are extremely pleased with the difference he has been making. Under his tutelage, Sam has secured several gold awards from the UK Mathematics Trust (UKMT) and Scottish Mathematical Council (SMC). Recently Sam received a book award from the UKMT"

    Jayanta Majumdar

    Parent. United Kingdom.
0
Qualified in INMO 2025
0+
Students from India, US, UK+
0
2025 Ox-Bridge Admits
0
Years of Experience
0+
2025 Honors in AMC 10, 12
hello world!
Oct
14
2026
Start - October 14, 2026 1:00 pm 
End - October 14, 2026 1:00 pm
What Doesn't Change

22 Lake Place Road, Kolkata, West Bengal

As data science and AI evolve rapidly, the core habits of mathematical thinking remain unchanged. This talk explores how skills such as precise problem definition, questioning assumptions, reasoning with uncertainty, and testing conclusions are central to real-world data science.
Using examples from healthcare analytics, the session will show why good analysis is not just about coding or models, but about asking the right questions of the data.
The key message: tools will change, but mathematical thinking will remain fundamental to making reliable decisions in an AI-driven world.

Sep
12
2026
Start - September 12, 2026 1:00 pm 
End - November 21, 2026 4:15 pm
University Mathematics Programs at Cheenta

22 Lake Place Road, Kolkata, West Bengal

Two roads between algebra and geometry, one Saturday. At one, a new course opens on commutative algebra: rings, ideals and modules, where prime ideals become points and the spectrum of a ring turns algebra into a space you can look at. At three, the geometric group theory course runs the other way, reading a group through the geometry it acts on, and presses on toward Cannon’s conjecture: must a hyperbolic group whose boundary is a 2-sphere act geometrically on hyperbolic 3-space?

Jan
3
2026
Start - January 3, 2026 12:00 pm 
End - January 3, 2026 12:30 pm
From Research to Business of Common Good

22 Lake Place Road, Kolkata, West Bengal

This Cheenta Mathematical Science Seminar brings together ideas from research, industry, and innovation to explore how advanced science and technology can be directed towards the common good. Through real-world examples and insights from impact-driven work, the session highlights the journey from deep scientific research to scalable solutions that address pressing social and environmental challenges.


View All Events

Olympiad Software on Beautiful Mathematics

Try problems. Ask doubts. Take mock tests. Track university application growth path.
Start with Trial 

Olympiad, Research, Leadership 
Mentored growth for Path to Ivy Leagues

© 2010 - 2025, Cheenta Academy. All rights reserved.
linkedin facebook pinterest youtube rss twitter instagram facebook-blank rss-blank linkedin-blank pinterest youtube twitter instagram