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Cheenta Math Olympiad North America Work Group

Pause for a moment. Here is a food for thought:

What if you wanted to draw a square whose area equals the circumference of a unit circle? The side length of such a square has an incredible expression.

$$\displaystyle{\int_{-\infty}^{+\infty} e^{\frac{-x^2}{2}} } dx$$

What deep mathematics is hidden in this beautiful relation?

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# Open Boot Camp

9 + 1 =

## Spiral Similarity of cyclic quadrilaterals

Pedal triangles lead to spirally similar cyclic quadrilaterals in any triangle. A half turn and dilation by 1/8 create the new quadrilateral.

## I(N)MO Camp 2018-19

30 sessions, 45 hours, a team of 6 faculty members. Cheenta is presenting a camp for Indian National Math Olympiad (leading to International Math Olympiad). We begin on 14th December 2018 and it will run up to 19th January 2019.

## Shapes and Measure 1 – let us divide!

An experiment to teach percentage arithmetic, Euclidean geometry, rational and irrationals and computational software tools in an interdisciplinary manner. We extensively used GeoGebra and plan to use Python later in this sequence of discussions. The exposition is conversational (in the spirit of Tarasov’s Pre-Calculus). As a method of pedagogy, dialectics is subtly employed to enhance student’s grasp of the subject.

## AM GM Inequality, Euler Number – Stories in Real Analysis

A.M.- G.M. Inequality can be used to prove the existence of Euler Number. A fascinating journey from classical inequalities to invention of one of the most important numbers in mathematics!

## 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.

Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year.

Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.

# Curriculum

Math Olympiad Program at Cheenta has three levels. Early Bird, Intermediate and Advanced.

#### Number Theory

Congruence, Theorems of Fermat, Euler, Wilson, Quadratic Reciprocity, Lagrange, Properties of prime numbers.

#### Combinatorics

Bijection Principle, Inclusion, Exclusion, Pigeon Hole Principle, Combinatorial Arguments, Graph Theory.

#### Geometry

Synthetic Geometry, Geometric Transformations (Translation, Rotation, Inversion), Projective Geometry .

#### Polynomials

Integer Polynomials, Fixed Points, Rational Roots, Eisenstein Criterion, Diophantine Equations.

#### Complex Numbers

Field axioms, basic inequalities, algebra of rotation and homothety, applications in geometry and number theory.

#### Inequality

A.M.-G.M., Cauchy Schwarz, Jensen, Rearrangement, Geometric Inequality, Power Means.

# Problem-driven coursework

Beautiful problems are the bread and butter of our courses. Our pedagogical method typically involves a problem to concept pathway. The classes usually begin with a motivating problem. That unfolds into a deep conceptual framework, leading to more problems.

# Testimonials

## Jayanta Majumdar, Glasgow, UK

"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."

## Shubhrangshu Das, Bangalore, India

"My son, 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 of the students by discussing even minute concepts. His style of teaching is also unique combining different concepts and giving mathematics a more holistic approach. He is also very motivating and helpful. We are lucky that our son is under such good guidance. Rare to get such a dedicated teacher."

"“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.”

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Admission to Cheenta Advanced Program is selective. The prospective candidate is inducted into a trial process (involving an interview and a short test).

#### Live Online Classes

This program has the live online option. The classes are usually interactive and are supplemented by a monthly assignment cum evaluation test.