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# OUTSTANDING MATHEMATICS FOR BRILLIANT STUDENTS

#### Pause.... think.

Suppose ABC is any triangle. D be any point on AB.

Can you find a point X on BC such that area of triangle XAD is equal to the area of triangle ACX?

Hint: Area and midpoint are intimately related.

# Three Outstanding Programs

for brilliant students

Advanced number theory, geometry, combinatorics, and algebra.

This problem driven, rigorous program is taught by olympians, researchers who are active mathematicians at leading universities around the world.

### I.S.I. & C.M.I. Entrance Program

B.Stat and B.Math Entrance Program at Indian Statistical Institute and B.Sc. Math Entrance at Chennai Mathematical Institute require special training in topics like number theory, geometry and combinatorics

This rigorous program for high school students is taught by students and alumni of I.S.I. & C.M.I.

### College Mathematics Program

Entrances of TIFR, I.S.I. M.Math and Subject GRE require advanced training in topology, analysis, abstract and linear algebra.

This advanced program is designed to take you ‘inside’ the beauty of mathematics.

## Group class + One-on-One

Brilliant mathematics … personalized

Step 1

#### Group Lectures

Brilliant Faculty members. Problem driven sessions.

Step 2

#### One-on-One

One mentor – one student.

Step 3

#### Problem Lists

Inspiring problems every week. Mentors  help students to solve.

We contacted Cheenta because our son, Sambuddha (a.k.a. Sam), seemed to have something of a gift in mathematical/logical thinking, and his school curriculum math was way too easy and boring for him. We were overjoyed when Mr Ashani Dasgupta administered an admission test and accepted Sam as a one-to-one student at Cheenta. Ever since it has been an excellent experience and we have nothing but praise for Mr Dasgupta. His enthusiasm for mathematics is infectious, and admirable is the amount of energy and thought he puts into each lesson. He covers a wide range of mathematical topics, and every lesson is packed with insights and methods. 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 and got invited to masterclass sessions also organised by the UKMT. Mr Dasgupta’s tutoring was crucial for these achievements. We think Cheenta is rendering an excellent service to humanity by identifying young mathematical minds and nurturing them towards becoming inspired mathematicians of the future.

Jayanta Majumdar

Father of Sambuddha Majumdar, Glasgow, Scotland

Our experience with Cheenta has been excellent. Even though my son started in Middle School, they understood his Math level and took personal interest in developing a long term plan considering his strengths and weakness areas. Through out the semester courses they have nourished him with challenging problems and necessary homework. His guidance 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. We are very thankful to Cheenta and hope to benefit from them in the coming years. I would strongly recommend them to any student who wants to learn Math by doing challenging problems, specially if they are looking for Math than what their school can offer.”

Father of Akshaj Kadaveru, Virginia, USA

## In the coming week..

#### Euler's totient function

Euler’s Totient function gives the reduced residue class for a number. It has beautiful properties including multiplicative (group homomorphism). We explore it in a seminar.

h

#### Geometry of varingon

Varingon quadrilaterals are actually parallelograms. They exhibit deep connection between area and midpoint. We explore it in our Math Olympiad Group.

U

#### Fun with group theory

Characteristic subgroups are super invariants of a group in some sense. Commutator subgroup is one example of characteristic subgroup. We explore its properties in a seminar.

## An Hour of Beautiful Proofs

Every week we dedicate an hour to Beautiful Mathematics - the Mathematics that shows us how Beautiful is our Intellect. This week, I decided to do three beautiful proofs in this one-hour session... Proof of Fermat's Little Theorem ( via Combinatorics )It uses...

## Polynomial Functional Equation – Random Olympiad Problem

This beautiful application of Functional Equation is related to the concepts of Polynomials. Sequential hints are given to work out the problem and to revisit the concepts accordingly.

## Number Theory – Croatia MO 2005 Problem 11.1

This beautiful application from Croatia MO 2005, Problem 11.1 is based on the concepts of Number Theory. Sequential hints are given to work the problem accordingly.

## Inequality – In Equality

This article aims to give you a brief overview of Inequality, which can be served as an introduction to this beautiful sub-topic of Algebra. This article doesn't aim to give a list of formulas and methodologies stuffed in single baggage, rather it is specifically...

## 4 questions from Sylow’s theorem: Qn 4

I have prepared some common questions ok application of Sylow’s theorem with higher difficulty level. It is most propably cover all possible combination.

## 4 questions from Sylow’s theorem: Qn 3

I have prepared some common questions ok application of Sylow’s theorem with higher difficulty level. It is most propably cover all possible combination.

## 4 questions from Sylow’s theorem: Qn 2

I have prepared some common questions ok application of Sylow’s theorem with higher difficulty level. It is most propably cover all possible combination.

## 4 questions from Sylow’s theorem: Qn 1

I have prepared some common questions ok application of Sylow’s theorem with higher difficulty level. It is most propably cover all possible combination.

## Arithmetical Dynamics: Part 0

Rational function $$R(z)= \frac {P(z)}{Q(z)}$$ ; where P and Q are polynimials . There are some theory about fixed points . Theorem: Let $$\rho$$ be the fixed point of the maps R and g be the Mobius map . Then $$gRg^{-1}$$ has the same number of fixed points at...

## Sum based on Probability – ISI MMA 2018 Question 24

This is an interesting and cute sum based on the concept of Arithematic and Geometric series .The problem is to find a solution of a probability sum.