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# Cheenta week of Nov. 19

Every week we have a festival of beautiful mathematics, brain-boggling problems, and ecstatic ideas. Find out what is coming up this week.

Hello mathematician!

I do not like homework.  They are boring ‘to do’ and infinitely more boring to ‘create and grade’. I would rather read Hilbert’s ‘Geometry and Imagination’ or Abanindranath’s ‘Khirer Putul’ at that time.

Academy Award winner Michael Moore, Finland’s educators (who have the number 1 education system for school students) and Rabindranath Tagore are some other people who do not like homework.

Here is a short documentary on why you should never do your homework (ehm..), climb a tree instead of going to school and play all the time.

Naturally, you might wonder that if not ‘assignments’ and ‘exams’ then what? What is it that you should do beyond school and tutorial hours to master your trade? After all, you really like mathematics (otherwise you would not be in Cheenta in the first place).

One thing that you could do is, ask your teacher for a beautiful book/resource that has inspired ner to do mathematics. Then run to local bookstore or library to find that book. Try it on your own. You may or may not like it. If you do, then try to rigorously work through that resource.

Here is one book that I find intriguing and am using in one of my courses: Geometry Revisited by Coxeter.

And while we are on it, why don’t you also look into Coxeter Groups. They are fantastic extensions of the idea of reflection.

There is another thing that I do all the time (and found very useful). Keep your brain busy with a couple of beautiful problems. Carry a small notebook and scribble in it new ideas and perspectives on these problems. Here are two problems that are keeping me busy right now.

1. The Gromov Boundary of one-ended hyperbolic groups are locally connected! (Bestvina is so cool!)
2. Is there a thing called parallel groups? How about amalgamating a bunch of groups about common beads and defining an action of those vertex groups on embeddings of [0,1] in a metric space that leads to non intersecting foliations?

This week, we have some brilliant adventures in mathematical science in store for the classes. Stirling Numbers are hard to compute. We look into some recursions that lead to them. Duality is everywhere. We explore its omnipresence in the context of linear functions and platonic solids. Infinite sequences are very useful to understand finite numbers. Madhavacharya of Kerala did some fantastic work on this. Swiss mathematician Euler also used it all the time. We will expand on our previous investigations of infinite sequences to understand one of the most beautiful constants of mathematics: the Euler Number. Graph and Number Theoretic Algorithms will be examined in our Computer Science Program (did you watch Alan Turing’s life story? Google it). Pierre De Fermat has intrigued mathematicians for centuries. This civil servant from France, created some of the most interesting musings in mathematics. We explore his little theorem (and while you are on it google Fermat’s Last Theorem). From Fermat’s Number Theory to Felix Klein’s weird bottle, we have a festival of mathematics in store for you.

Remember to have some serious fun!

Here is the weekly schedule.

Ashani Dasgupta

Passion for Mathematics

# Monday, November 19

#### 4;45 PM – 6:15 PM

I.S.T., Monday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Polynomial and Exponents

Description: After getting acquainted with cubic polynomials last week, we shall look at a different class of polynomials this week, namely those of the form x^n = 1. Of course, x_0 = 1 is a root, but what else?

#### A.R. Sricharan

Pursuing B.Sc. in Mathematics and Computer Science from Chennai Mathematical Institute.

Sricharan was a student of Cheenta. He joined the faculty team after qualifying for C.M.I. Entrance.

#### 7:15 PM – 9:15 PM

I.S.T., Monday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: IUPAC Name

Description: In chemical nomenclature, the IUPAC nomenclature of organic chemistry is a systematic method of naming organic chemical compounds as recommended by the International Union of Pure and Applied Chemistry.

#### Devilal

M.Sc. from I.I.T. Delhi (in Chemistry).

#### 8 PM – 9:30 PM

I.S.T., Monday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Problem Solving

#### Swarnabja Bhowmick

Pursuing B.Tech in Computer Science from Rajabazar Science College.

#### 9;30 PM – 11:00 PM

I.S.T., Monday

Problem List for the Week

Books

Other Stuff

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

Topic:  Limit & Sequences

Description: Sequences occur frequently in calculus. It is very powerful tool for problem solving.

#### Kaurag Mukherjee

B.Math from I.S.I Bangalore

Research Interest: Graph Theory

#### 9.45 PM – 11:15 PM

I.S.T., Monday

Problem List for the Week

Books

Other Stuff

## College Mathematics Program

Topic: Connectedness, compactness, uniform continuity on R^n.

Description: Lets look on Heine-Borel Theorem.

#### Subhajit Bhattacharya

Pursuing Ph.D. at TIFR. B.Math from I.S.I. B’lore..

Research Interest in Probability Theory. Cheenta Alumni turned Faculty

# Tuesday, November 20

#### 8;30 PM – 9:30 PM

I.S.T., Tuesday

Problem List for the Week

Books

Other Stuff

## CHEENTA Z

Topic: Duality

Description: We will continue with one of the most fundamental themes in Mathematics: Duality. We will examine dual graphs and Euler’s theorem concerning it. We will draw dual platonic solids and examine their relationship.

#### Ashani Dasgupta

Pursuing Ph.D. at University of Wisconsin, Milwaukee, Founding Faculty.

Research Interest in Geometry Group Theory.

# Wednesday, November 21

#### 4;45 PM – 6:15 PM

I.S.T., Wednesday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Polynomial and Exponents

Description: After getting acquainted with cubic polynomials last week, we shall look at a different class of polynomials this week, namely those of the form x^n = 1. Of course, x_0 = 1 is a root, but what else?.

#### A.R. Sricharan

Pursuing B.Sc. in Mathematics and Computer Science from Chennai Mathematical Institute.

Sricharan was a student of Cheenta. He joined the faculty team after qualifying for C.M.I. Entrance.

#### 8:30 PM – 10:30 PM

I.S.T., Wednesday

Problem List for the Week

Books

Other Stuff

## Bridge Session

Topics: Various problem on Combinatorics

#### Swarnabja Bhowmick

Pursuing B.Tech in Computer Science from Rajabazar Science College.

Cheenta Alumni turned Faculty.

# Thursday, November 22

#### 8;30 PM – 10:30 PM

I.S.T., Thursday

Problem List for the Week

Books

Other Stuff

## Bridge Session

Topic: Conic Section

#### Sourayan Banerjee

Pursuing Ph.D. from IISER Bhopal.

Research Interest in Algebraic K-Theory. Cheenta Alumni turned Faculty.

#### 9 PM – 10:30 PM

I.S.T., Thursday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Graph theoretic & number theoretic algorithms, competitive programming problems

Description: An algorithm is a specific method for solving a problem – generally a mathematical function or procedure.Today numbertheoretic algorithms are used widely, due in part to the invention of cryptographic schemes based on large prime numbers .

#### Dr. Prabir Dasgupta

Dr. Dasgupta is a Ph.D. in computer science and enggineering from I.I.T. Kharagpur. He was a senior scientific officer at BARC.

Dr. Dasgupta has multiple publications in reputed journals. His research interest is in cryptography, and automata theory

# Friday, November 23

#### 8;20 PM – 9:50 PM

I.S.T., Friday

Problem List for the Week

Books

Other Stuff

## Early Bird Math Olympiad (IND Group)

Topic:Fermat’s little theorem

Description: Fermat’s little theorem states that if p is a prime number, then for any integer a, the number aᵖ − a is an integer multiple of p. In the notation of modular arithmetic

#### Writabrata Bhattacharya

Pursuing B.Sc. Math from C.M.I. Chennai

He was a student of Cheenta. He joined the faculty team after qualifying for C.M.I. Entrance.

#### 8:15 PM – 9:45 PM

I.S.T., Friday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Application of Euler Number

Description: we will discuss how Euler’s theorem can be used to encrypt a message and how to transfer that message securely through public communication system.

#### Sauvik Mondal

Pursuing B.Math from I.S.I. Bangalore.

Research Interest in Geometric Group Theory. Cheenta Alumni turned Faculty

#### 9.45 PM – 11:15 PM

I.S.T., Friday

Problem List for the Week

Books

Other Stuff

## College Mathematics Program

Test on Linear Algebra

#### Subhajit Bhattacharya

Pursuing Ph.D. at TIFR. B.Math from I.S.I. B’lore..

Research Interest in Probability Theory. Cheenta Alumni turned Faculty

# Saturday, November 24

#### 8;00 AM – 9:30 AM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: One Two Three….Infinity…….

Description: Borrowing from Gamow’s title, we will continue our journey in the infinity. We will examine the nature of Euler’s number, bounded infinite Sequences and plight of Pythagoras.

#### Ashani Dasgupta

Pursuing Ph.D. at University of Wisconsin, Milwaukee, Founding Faculty

Research Interest in Geometry Group Theory

#### 10;00 AM – 11:30 AM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

## Early Bird Math Olympiad (AU Group)

Topic: Combination

Description: Injection and Bijection Principle plays an important role. We will learn about it.

#### Arnab Dey Sarkar

Pursuing Ph.D. from Saint Louise University, 1 N Grand Blvd, United States in Mathematics.

Integrated BS-MS in Mathematics from IISER Bhopal.

Research Interest: Number Theory

#### 2:30 PM – 4:30 PM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Atomic structure revision and introduction to periodic table

Description: The periodic table, or periodic table of elements, is a tabular arrangement of the chemical elements, ordered by their atomic number, electron configuration, and recurring chemical properties, whose structure shows periodic trends.

#### Faculty

Pursuing integrated MS in Chmeistry from IISER Bhopal.

#### 6:00 PM – 8:00 PM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

## Mathematics Doubt Clearing Session

Make sure to post your doubts in www.cheenta.com/support

#### Faculty

Pursuing Ph.D. from IMPA Brazil

B.Sc. Math from C.M.I. Chennai

INMO Awardee

#### 8;00 PM – 9:30 PM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Stretch and Glue

Description: We will extend our investigation of equivalence relation by examining examples from Geometry and Number Theory. Klein Bottle and Real Projective Plane along with the Theory of Congruence by Gauss will form the go to examples.

#### Ashani Dasgupta

Pursuing Ph.D. at University of Wisconsin, Milwaukee, Founding Faculty

Research Interest in Geometry Group Theory

#### 8:15 PM – 9:45 PM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Application of Euler’s Number

Description: we will discuss how Euler’s theorem can be used to encrypt a message and how to transfer that message securely through public communication system.

#### Sauvik Mondal

Pursuing B.Math from I.S.I. Bangalore.

Research Interest in Geometric Group Theory. Cheenta Alumni turned Faculty

#### 8;20 PM – 9:50 PM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

## Early Bird Math Olympiad (IN Group)

Topic: Test on Number Theory

#### Writabrata Bhattacharya

Pursuing B.Sc. Math from C.M.I. Chennai

He was a student of Cheenta. He joined the faculty team after qualifying for C.M.I. Entrance.

#### 9;30 PM – 11:00 PM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

## Early Bird Math Olympiad (US Group)

Topic: Combinatorics 1

Description: We will continue with Stirling’s Number of first number second kind, some applications from Catalan Numbers and problems from AMC, AIME

#### Ashani Dasgupta

Pursuing Ph.D. at University of Wisconsin, Milwaukee, Founding Faculty

Research Interest in Geometry Group Theory

#### 9.45 PM – 11:15 PM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

## College Mathematics Program

Topic: Ring Theory

Description: In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers.

#### Arnab De Sarkar

Pursuing Ph.D. from Saint Louise University, 1 N Grand Blvd, United States in Mathematics.

Integrated BS-MS in Mathematics from IISER Bhopal.

Research Interest: Number Theory

# Sunday, November 25

#### 8:00 AM – 9:30 AM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic:  Graph theoretic & number theoretic algorithms, competitive programming problems

Description: An algorithm is a specific method for solving a problem – generally a mathematical function or procedure.Today numbertheoretic algorithms are used widely, due in part to the invention of cryptographic schemes based on large prime numbers .

#### Dr. Prabir Dasgupta

Dr. Dasgupta is a Ph.D. in computer science and engineering from I.I.T. Kharagpur. He was a senior scientific officer at BARC.

Dr. Dasgupta has multiple publications in reputed journals. His research interest is in cryptography, and automata theory

#### 8;00 AM – 9:30 AM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: One Two Three….Infinity…….

Description: Borrowing from Gamow’s title, we will continue our journey in the infinity. We will examine the nature of Euler’s number, bounded infinite Sequences and plight of Pythagoras.

#### Ashani Dasgupta

Pursuing Ph.D. at University of Wisconsin, Milwaukee, Founding Faculty

Research Interest in Geometry Group Theory

#### 10;00 AM – 11:30 AM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

## Early Bird Math Olympiad (AU Group)

Topic: Combination

Description: Injection and Bijection Principle plays an important role. We will learn about it.

#### Arnab Dey Sarkar

Pursuing Ph.D. from Saint Louise University, 1 N Grand Blvd, United States in Mathematics.

Integrated BS-MS in Mathematics from IISER Bhopal.

Research Interest: Number Theory

#### 1;00 PM – 3:00 PM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Test on Electrostatics

#### Utkarsh Tripathi

Pursuing Integrated MS in Physics from IISER Bhopal

#### 7;00 PM – 9:00 PM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Heat Transfer

Description: The transfer of energy between objects that are in physical contact. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes.

#### Faculty

Pursuing Ph.D. from IMPA Brazil

B.Sc. Math from C.M.I. Chennai

INMO Awardee

#### 8;00 PM – 9:30 PM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Stretch and Glue

Description: We will extend our investigation of equivalence relation by examining examples from Geometry and Number Theory. Klein Bottle and Real Projective Plane along with the Theory of Congruence by Gauss will form the go to examples.

#### Ashani Dasgupta

Pursuing Ph.D. at University of Wisconsin, Milwaukee, Founding Faculty

Research Interest in Geometry Group Theory

#### 9;30 PM – 11:00 PM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

## Early Bird Math Olympiad (US Group)

Topic: Combinatorics 1

Description: We will continue with Stirling’s Number of first number second kind, some applications from Catalan Numbers and problems from AMC, AIME.

#### Ashani Dasgupta

Pursuing Ph.D. at University of Wisconsin, Milwaukee, Founding Faculty

Research Interest in Geometry Group Theory

#### 9;30 PM – 11:00 PM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

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

Topic:   Limit & Sequences

Description: Sequences occur frequently in calculus. It is very powerful tool for problem solving.

#### Kaurag Mukherjee

B.Math from I.S.I Bangalore

Research Interest: Graph Theory

#### 9;45 PM – 11:15 PM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

## College Mathematics Programe

Topic: Multivariable differentiability

Topic: Our next station shall be Patial Differentiation.

#### Subhajit Bhattacharya

Pursuing Ph.D. at TIFR. B.Math from I.S.I. B’lore..

Research Interest in Probability Theory.

Cheenta Alumni turned Faculty