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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.

## Research Track – Cocompact action and isotropy subgroups

Suppose a group $latex \Gamma$ is acting properly and cocompactly on a metric space X, by isometries. (Understand: proper, cocompact, isometric action) Claim There are only finitely many conjugacy classes of the isotropy subgroups in $latex \Gamma$ Sketch Since the...

## I.S.I 2016 SUBJECTIVE PROBLEM – 1

Understand the problemSuppose that in a sports tournament featuring n players, each pairplays one game and there is always a winner and a loser (no draws).Show that the players can be arranged in an order P1, P2, . . . , Pn suchthat player Pi has beaten Pi+1 for all i...

## ISI 2019 : Problem #7

Understand the problem Let be a polynomial with integer coefficients. Define and for .If there exists a natural number such that , then prove that either or .   I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2019. Subjective Problem...

## Working backward – C.M.I UG -2019

Understand the problem If there exists a calculator with 12 buttons, 10 being the buttons for the digits and A and B being two buttons being processes where if n is displayed on the calculator if A is pressed it increases the displayed number by 1 and if B is pressed...

## Solution in Real – C.M.I -U.G-2019

Understand the problem .Find all real numbers x for which   C.M.I (Chennai mathematical institute ) U.G-2019 Algebra 8 out of 10.Start with hintsDo you really need a hint? Try it first!It is of the the form of . Do you observe ? where a=$$2^x$$ b=$$3^x$$...

## I.S.I 2019 Subjective Problem -4

Understand the problem Let be a twice differentiable function such thatShow that there exist such that for all . I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2019. Subjective Problem no. 4 calculus 8.5 out of 10Problems In CALCULUS OF...

## Sum Of 1’S C.M.I UG-2019 Entrance

Understand the problem Find the sum 1+111+11111+1111111+.....1....111(2k+1) ones  C.M.I UG-2019 entrance examAlgebra 3.5 out of 10 challenges and trills of pre college mathematics   Start with hintsDo you really need a hint? Try it first!can you some how...

## C.M.I-2019 Geometry problem

Understand the problemlet O be a point inside a parallelogram ABCD such that $$\angle AOB+\angle COD =180$$ prove that $$\angle OBC =\angle ODC$$ C.M.I (Chennai mathematical institute UG-2019 entrance Geometry 5 out of 10challenges and thrills of pre college...

## Triangle in complex plane – ISI 2019 Obj P8

This problem from ISI Entrance 2019 is an interesting application of complex numbers in geometry. Try your hands on this!

## Four Points on a Circle, ISI Entrance 2017, Subjective Problem no 2

Understand the problem Consider a circle of radius 6 as given in the diagram below. Let $$B,C,D$$ and $$E$$ be points on the circle such that $$BD$$ and $$CE$$, when extended, intersect at $$A$$. If $$AD$$ and $$AE$$ have length 5 and 4 respectively, and $$DBC$$ is a...