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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.

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#### 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.

## Solving a congruence

Understand the problemProve that the number of ordered triples in the set of residues of $latex p$ such that , where and is prime is . Brazilian Olympiad Revenge 2010 Number Theory Medium Elementary Number Theory by David Burton Start with hintsDo you really need...

## Inequality involving sides of a triangle

Understand the problemLet be the lengths of sides of a (possibly degenerate) triangle. Prove the inequalityLet be the lengths of sides of a triangle. Prove the inequalityCaucasus Mathematical Olympiad Inequalities Easy An Excursion in Mathematics Start with hintsDo...

## Spanning matrix space by niltopent matrices: TIFR 2018 Part A, Problem 15

This problem is a cute and simple application of spanning matrix space by niltopent matrices in the linear algebra section. It appeared in TIFR GS 2018.

## Calculating eigenvalues through geometry:TIFR 2018 Part A, Problem 14

This problem is a cute and simple application of calculating eigenvalues through geometry in the linear algebra section. It appeared in TIFR GS 2018.

## Direct product of groups: TIFR 2018 Part A, Problem 9

This problem is a cute and simple application of the direct product of groups in the abstract algebra section. It appeared in TIFR GS 2018.

## Real Symmetric matrix: TIFR 2018 Part A, Problem 6

This problem is a cute and simple application of the real symmeric matrices in the linear algebra section. It appeared in TIFR GS 2018.

## Chaos … at Cheenta!

Beautiful mathematics seminar on Chaos Theory by Cheenta.

## Integration of nonnegative function: TIFR 2018 Part A, Problem 4

This problem is a cute and simple application of the integration of nonnegative function in the analysis section. It appeared in TIFR GS 2018.

## Application of L’Hopital: TIFR GS 2018 Part A, Problem 2

This problem is a cute and simple application of the L’Hopital rule in the analysis section. It appeared in TIFR GS 2018.

## Vectors of prime length

This problem is a cute and simple application of the real symmeric matrices in the linear algebra section. It appeared in TIFR GS 2018.