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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.

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#### 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.

## Average Determinant: TIFR GS 2017 Part A Problem 8.

This question has appeared in TIFR GS 2017 Entrance Examination and is based on Linear Algebra.

## A sequence of natural numbers and a recurrence relation

Understand the problemDefine a sequence by , andfor For every and prove that divides. Suppose divides for some natural numbers and . Prove that divides Indian National Mathematical Olympiad 2010 Number Theory Medium Problem Solving Strategies by Arthur Engel...

## Linear recurrences

Linear difference equationsA linear difference equation is a recurrence relation of the form $latex y_{t+n}=a_1y_{t+n-1}+a_2y_{t+n-2}+\cdots +a_ny_t+b$. If $latex b=0$, then it is called homogeneous. In this article, we shall also assume $latex t=0$ for...

## Functional Equation PRMO 2012 Problem 16

A beautiful functional equation problem from PRMO (Pre Regional Math Olympiad) 2012 (Problem 16). Use sequential hints and a video discussion to try the problem

## Spanning set of a matrix space: TIFR GS 2019, Part B Problem 6

It is a linear algebra question on matrices basically on spanning set of a matrix space. It was asked in TIFR 2019 GS admission paper.

## ABC of rank: TIFR GS 2019, Part B Problem 5

It is a linear algebra question on matrices. It was asked in TIFR 2019 GS admission paper. It is a true false question.

## 2013 AMC 10B – Problem 5 Maximizing the Difference:

This is based on simple ineqaulities on real numbers.

## Continuous map on countable space: TIFR GS 2019, Part B Problem 3

It is a topology question on real plane. It was asked in TIFR 2019 GS admission paper. It is true-false type question.

## Invertible Matrix implies identity?: TIFR GS 2019, Part B Problem 4

It is a linear algebra question on matrices. It was asked in TIFR 2019 GS admission paper.

## An inductive inequality

Understand the problemGiven and for all , show that Singapore Mathematical Olympiad 2010 Inequalities Easy Inequalities by BJ Venkatachala Start with hintsDo you really need a hint? Try it first!Use induction. Given the inequality for $latex n=k$, the inequality...