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# Cheenta. passion for mathematics.

Pause for a moment. Let us divide letters by letters!

What if you wanted to divide the base by an exponent? This situation comes up quite often in Elementary Number Theory. Consider the following equation:

$$\displaystyle{ k! + 48 = 48 \times (k+1)^m }$$

Can you show that k divides m? The answer is hidden somewhere in our library articles.

#### What is Cheenta?

Cheenta delivers outstanding programs in Mathematics for Olympiads, I.S.I. & C.M.I. Entrance and College.

Since 2010, we have worked with hundreds of students from India, United States, UK, Australia, Singapore and Middle East

All of our classes are delivered exclusively live and online. Our main center in Calcutta (India) office hosts a reading facility for advanced learners.

#### Who are Teaching?

We have ex-Olympians and outstanding researchers who teach out of love for the subject.

In India: Indian Statistical Institute, Chennai Mathematical Institute, IISER, TIFR, Calcutta University, IIT KGP

Outside India: the University of Wisconsin Milwaukee (USA), University of North Carolina (USA), St. Louis University (USA), IMPA (Brazil), E’Cole (France)

Admission to a Cheenta program is highly selective. The prospective student must first go through a trial class.

Our courses are significantly more intense than regular school or college programs. Apply only if you are thrilled by the beauty of mathematics.

Math Olympiad, I.S.I. Entrance and College Mathematics candidates form the core student body of Cheenta.

## Stories in Real Analysis – Inverse Maps

Inverse maps are very important in Real analysis. They form the backbone of the definition of continuity. We explore one of it’s properties.

## RMO 2018 Tamil Nadu Problem 3 – Nonlinear Diophantine Equation

RMO 2018 Tamil Nadu Problem 3 Sequential Hints and Solution. A number theory problem with a pinch from diophantine equation.

RMO 2018 Tamil Nadu Problem 2 Sequential Hints and Solution. A polynomial problem with seasoning from geometric progression.

## RMO 2018 Tamil Nadu Problem 1 – angle bisector

RMO 2018 Tamil Nadu Problem 1 Sequential Hints and Solution. A beautiful geometry problem that uses properties of cyclic quadrilaterals.

## RMO2018 Tamil Nadu Solutions and Problems

Regional Math Olympiad (Tamil Nadu Region, 2018) Problems, Sequential Hints and Discussion.

## Golden Ratio and Right Triangles – when geometry meets number theory

The golden ratio is arguably the third most interesting number in mathematics. We explore a beautiful problem connecting Number Theory and Geometry.

## Proper Metric Spaces can be modeled by Rays!

‘Proper’ is a heavily overloaded term, both in life and in mathematics. It may mean different stuff in different contexts. Thankfully mathematics is far less complicated that life and we can rigorously define properness.

## Parity and Symbolic Divisibility – an excursion in Number Theory

Parity and divisibility are two interesting tools of elementary number theory. Coupled with an estimation with AM-GM inequality, we have excursion into the queen of mathematical disciplines.

## Compact Set, Proper Spaces and Annulus

Compact set in proper topological (metric) spaces have ‘euclidean’ character. We consider an example that takes advantage of this.

## I.S.I Entrance Solution – locus of a moving point

This is an I.S.I. Entrance Solution Problem: P is a variable point on a circle C and Q is a fixed point on the outside of C. R is a point in PQ dividing it in the ratio p:q, where p> 0 and q > 0 are fixed. Then the locus of R is (A) a circle; (B) an ellipse; ...

An advanced program in Mathematics for brilliant school students. Taught by ex-Olympians and active researchers in Mathematics.

By the way, are you interested in the fourth dimension? Here is a beauty to behold! Tetracube created the beautiful image of the Omnitruncated tesseract.

# Training brilliant minds.

Since 2010.

Cheenta has worked with brilliant maths and science olympiad students from over 6 countries. Our courses are specifically geared toward students with an exceptional interest in Mathematical Sciences.

Outstanding mathematics program for deserving school students.

For children who are starting out in Mathematics and Science.

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

For B.Stat and B.Math entrance at Indian Statistical Institute, B.Sc. Math at C.M.I. & KVPY.

#### College Mathematics

For I.S.I. M.Math, Mathematics Subject GRE, TIFR; Groups Analysis, Topology and more

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

B.Stat, B.Math Entrance at I.S.I. and B.Sc. Math Entrance at C.M.I. require special training in Number Theory, Geometry, Combinatorics and Algebra (apart from regular High School topics).

Problems from standard topics such as Calculus, Trigonometry or Coordinate geometry can significantly tricky.

Number Theory, Combinatorics, Algebra, and Geometry at Olympiad standard are both necessary and useful components of this course.

#### Regular High School Topics

Advance problems from Calculus, Trigonometry, Coordinate Geometry and Algebra are bread and butter for handling more complicated ones.

# College Mathematics

An advanced program for College Students as well as adults interested in modern mathematics. This program is useful for I.S.I. M.Math Entrance, Subject GRE, IIT JAM and similar entrances.

We work on Groups, Rings, Fields, Linear Algebra, Analysis, Topology and other advanced topics. As usual problem solving remains the driving force of the program.

The hyperbolic 3 space may come up in this course. Behold this beautiful Hyperideal Honeycomb created by Royce3 (under creative commons).

#### Continuing Education

Many adults, who are pursuing jobs or industry, have taken this program. A curious mind, coupled with a determination to take up challenges is sufficient.

This program is for the true math fanatic, who yearn to understand the anatomy of ‘reason’ a little better. Advanced problem-solving session every week!

# What is Torsion?

Geometry is everywhere. Enjoy this bit.

# Testimonials…

“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).” Jayanta Majumdar

Glasgow, UK

“Shuborno has been studying under Ashani from last one year. During this period, we have seen our son grow both intellectually and emotionally. His concepts and approach towards solving a problem has become more mature now. Not that he can solve each and every problem but he loves to think on the tough concepts. For this, all credit goes to Ashani, who is never in a hurry to solve a problem quickly. Rather he tries to slowly build the foundation..” Shubrangshu Das

Bangalore, India

“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.” Murali Kadaveru

Virginia, USA