Select Page

## Cheenta and Singapore Method – creating Mathematicians of the future

Recently, French mathematician Cedric Villani’s team came up with ’21 measures for the teaching of Mathematics’. I read through the report, with great curiosity. I happily noted that Cheenta’s Thousand Flowers program has already implemented some of his recommendations.

## Pythagoras Extended! – RMO 2008 Problem 6

Pythagoras theorem can be extended! What happens if the triangle is obtuse-angled (instead of right-angled?) We explore the idea by using a problem from Math Olympiad.

## A rejoinder to the ‘Discovery’

Nehru writes, 'very little original work on mathematics was done in India after the twelfth century till we reach the modern age. 'Discovery of India' was written over five months when Nehru was imprisoned in the Ahmednagar Fort. It was first published in 1946....

## Cyclic Pentagon – RMO 2008 Problem 1

Problem Let ABC be an acute-angled triangle, let D, F be the mid-points of BC, AB respectively. Let the perpendicular from F to AC and the perpendicular at B to BC meet in N. Prove that ND is equal to circum-radius of ABC. The discussion uses the following Theorems:...

## Set of Nilpotent Matrices – TIFR 2017

State True or False: The set of nilpotent matrices of $$M_3 (\mathbb{R} )$$ spans $$M_3 (\mathbb{R} )$$ considered as an $$\mathbb {R}$$ - vector space ( a matrix A is said to be nilpotent if there exists $$n \in \mathbb{N}$$  such that $$A^n = 0$$ )....

## Sequence of isosceles triangles – I.S.I. Entrance 2018 Problem 6

Let, $$a \geq b \geq c > 0$$ be real numbers such that for all natural number n, there exist triangles of side lengths $$a^n,b^n,c^n$$  Prove that the triangles are isosceles. If a, b, c are sides of a triangle, triangular inequality assures that difference of two...

## Bases, Exponents and Role reversals (I.S.I. Entrance 2018 Problem 7 Discussion)

Let $$a, b, c$$ are natural numbers such that $$a^{2}+b^{2}=c^{2}$$ and $$c-b=1$$. Prove that (i) a is odd. (ii) b is divisible by 4 (iii) $$a^{b}+b^{a}$$ is divisible by c Notice that $$a^2 = c^2 - b^2 = (c+b)(c-b)$$ But c - b = 1. Hence $$a^2 = c + b$$. But c...

## Area and inradius – Pre RMO 2018 Problem 2 Discussion

In a quadrilateral ABCD. It is given that AB=AD=13 BC=CD=20,BD=24. If r is the radius of the circle inscribable in the quadrilateral, then what is the integer close to r? Drawing a good picture is sometimes very helpful. Here is a computer drawn picture (using...

## Limit is Euler!

Let $$\{a_n\}_{n\ge 1}$$ be a sequence of real numbers such that $$a_n = \frac{1 + 2 + ... + (2n-1)}{n!} , n \ge 1$$ . Then $$\sum_{n \ge 1 } a_n$$ converges to ____________ Notice that $$1 + 3 + 5 + ... + (2n-1) = n^2$$. A quick way to remember this is sum of...

## Prime factor of last page – Pre RMO 2018 Problem 1 Discussion

A book is published in three volumes, the pages being numbered from 1 onwards. The page numbers are continued from the first volume to the third. The number of pages in the second volume is 50 more than in the first volume, and the numberpages in the third...

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