# I.S.I. & C.M.I. Entrance 2019 - Answer Key

Sequential hints for Objective and Subjective Problems Try# I.S.I. & C.M.I. Entrance Faculty Panel at Cheenta

#### Writabrata Bhattacharya

Faculty at Cheenta

Writabrata Bhattacharya is pursuing B.Sc. Math from Chennai Mathematical Institute. He is a faculty at Cheenta. He is also a Cheenta alumnus.

#### Sankhadip Chakraborty

Faculty, Admin at Cheenta

Sankhadip Chakraborty is an INMO awardee. He has a B.Sc. in Mathematics from CMI and is pursuing Ph.D. at IMPA, Brazil.

#### Ishan Sengupta

Faculty at Cheenta

Ishan Sengupta is pursuing B.Stat from Indian Statistical Institute, Kolkata. He is a faculty at Cheenta.

#### A.R. Sricharan

Faculty, Cheenta

A.R. Sricharan is a B.Sc. in Mathematics from Chennai Mathematical Institute. He is pursuing M.Sc. from CMI and is a faculty at Cheenta. He is also a Cheenta Alumnus.

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

Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are: B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.

The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.

# Curriculum

I.S.I. & C.M.I. Entrance Program at Cheenta includes advanced topics like Number Theory, Combinatorics and Geometry, apart from regular high school topics.

#### 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.

#### Calculus

Sequences, Limit, Continuity, Differentiability, Applications, Integral Calculus, Graph Drawing.

#### Trigonometry

Properties of triangles, trigonometric ratios, compound, multiple angles, Height and Distance related problems

#### Coordinate Geometry

Straight Lines, Circle, Parabola, Ellipse, Hyperbola, Locas problems, Polar coordinat, Barycentric coordinates.

# 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

# Admission Process

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.

#### At Calcutta Center

This program is also available at our Calcutta center. The offline contact classes are supplemented with the online option as well.

# Useful Documents

Download the curriculum and booklist