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# Cheenta week of Dec. 03 to 09

Gauss did not like term ‘complex number. He preferred lateral number instead.

Hello mathematician!

I was playing with a square. What if I glue the opposite edges of the square?

If I glue one pair of edges, we get a cylinder. (Ah! Are you wondering about the rules of ‘gluing’?)

Next, if we glue the two ends of that cylinder we may get a torus or a Klein bottle (depends on how we glue them). This discussion came up in one of our sessions. We wondered about the essence of this ‘gluing’ process.

Once we decide on the rule of gluing, we declare the glued points to be equivalent and get cylinder, torus, Klein bottle at various stages of the process.

Notice that we have so many things happening at the same time:

• gluing leads to the notion of equivalence relations which in turn leads to partition functions in combinatorics (Stirling numbers for example)
• rule of gluing leads us to vector maps and the notion of functions. After all, we have Klein bottle or torus depending on ‘how we glue’.

At once we are prompted to connect geometry and combinatorics.

Solving problems is one thing. Connecting seemingly different ideas is an entirely different business (though they have dependencies). It is extremely important to pause and let our imagination do its magic every now and then.

In this context let me quote two of the greatest minds of our times, Thurston and Rabindranath.

Thurston in Clay Research Conference (2010), started off with a very curious statement:

“A lot of mathematics is really about how you understand things in your head… we are not just general purpose machines, we are people, we see things, we feel things, we think of things,…, there is something significant about how the representations in your head, changes … profoundly changes how you think.”

Thurston drew different pictures (of 3-manifolds) than what his peers did. That is because he imagined things differently. And he was brave enough to follow his own imagination. It takes courage to not to parrot what the ‘system’ is teaching you.

It takes courage to let your imagination guide you. This is especially true in this age of rat race.

Rabindranath writes in Jibansmriti,

“বাহিরের সংস্রব আমার পক্ষে যতই দুর্লভ থাক্‌, বাহিরের আনন্দ আমার পক্ষে হয়তো সেই কারণেই সহজ ছিল। উপকরণ প্রচুর থাকিলে মনটা কুঁড়ে হইয়া পড়ে; সে কেবলই বাহিরের উপরেই সম্পূর্ণ বরাত দিয়া বসিয়া থাকে, ভুলিয়া যায়, আনন্দের ভোজে বাহিরের চেয়ে অন্তরের অনুষ্ঠানটাই গুরুতর। শিশুকালে মানুষের সর্বপ্রথম শিক্ষাটাই এই। তখন তাহার সম্বল অল্প এবং তুচ্ছ, কিন্তু আনন্দলাভের পক্ষে ইহার চেয়ে বেশি তাহার কিছুই প্রয়োজন নাই। সংসারে যে হতভাগ্য শিশু খেলার জিনিস অপর্যাপ্ত পাইয়া থাকে তাহার খেলা মাটি হইয়া যায়।”

Rabindranath was sceptic about ‘external tools’. Even in his other works in literature and pedagogy, this theme is iterated over and over again: let your internal imagination bring in happiness. Do not worry too much about the tools.

Pause for a moment, Look outside the window. Even the sun does not rise at the same position in the eastern horizon.

Ashani Dasgupta

Passion for Mathematics

# Monday, December 03

#### 4;45 PM – 6:15 PM

I.S.T., Monday

Problem List for the Week

Books

Other Stuff

Test on Algebra

#### 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 PM – 9:30 PM

I.S.T., Monday

Problem List for the Week

Books

Other Stuff

#### Program Description

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

#### 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

.

#### 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:  Limits of Functions

Description: One of the fundamental concepts in mathematics, meaning that a variable depending on another variable arbitrary closely approaches some constant as the latter variable changes in a definite manner. In the definition of a limit, the concept of nearness of the objects under consideration plays a fundamental role: only after a definition of nearness does a limit acquire an exact meaning.

#### Kaurag Mukherjee

B.Math from I.S.I Bangalore

Research Interest: Graph Theory

# Tuesday, December 04

#### 8;30 PM – 9:30 PM

I.S.T., Tuesday

Problem List for the Week

Books

Other Stuff

## CHEENTA Z

Topic: Complex Number and Geometry

Description: We start with the geometry of complex numbers. Rotation and Dilation are algebraically encoded in the ‘multiplication’ formula. We also cover field theoretic properties.

#### Ashani Dasgupta

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

Research Interest in Geometry Group Theory.

# Wednesday, December 04

#### 4;45 PM – 6:15 PM

I.S.T., Wednesday

Problem List for the Week

Books

Other Stuff

#### 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, December 06

#### 8;30 PM – 10:30 PM

I.S.T., Thursday

Problem List for the Week

Books

Other Stuff

## Bridge Session

Topic: Complex Algebra

#### 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, December 07

#### 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: Willson’s Theorem

Description: Wilson’s theorem is both necessary and sufficient for primality

#### 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: Diophantine Equation and Quadratic Integer

Description: we will solve diophantine equation using methods of infinite descent,primitive roots and various other methods.

#### 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

Topics: Chain rule, Implicit functions, Higher order derivatives
Description: We will describe the famous Chain Rule and also emphasize Higher order Derivative.

#### 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, December 09

#### 8;00 AM – 9:30 AM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Shape and Measure

Description: We collect more data to analyze and explore arithmetic notions. This data is then used in geometric sense..

#### 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: Principles and Techniques in Combinatorics

Description: Problems of this form are quite common in practice; for instance, it may be desirable to find orderings of boys and girls, students of different grades, or cars of certain colors, without a need to distinguish between students of the same grade (or cars of the same color, or people of the same gender).

#### 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

#### 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: Partition problems concerning gluing. Curve complex of a surface..

#### 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: Diophantine Equation and Quadratic Integer

Description: we will solve diophantine equation using methods of infinite descent,primitive roots and various other methods

#### 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: Willson’s Theorem

Description: We will continue Willson’s Theorem and do some problem on it.

#### 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

Description: We wrap up the first section with multi sets, review of injection principle and general distribution problems.

#### 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, December 09

#### 8;00 AM – 9:30 AM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topic: Shape and Measures

Description: We will use basic tools of Euclidean geometry to compare pieces ( smaller and larger )to a standard one. We will apply geogebra to render those constructions. Finally we will use a short python code to aid our understanding of the arithmatic of this division.

#### 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: Permutation with Repetation

Descritiption :Problems of this form are quite common in practice; for instance, it may be desirable to find orderings of boys and girls, students of different grades, or cars of certain colors, without a need to distinguish between students of the same grade (or cars of the same color, or people of the same gender)

#### 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

#### 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: Partition problems concerning gluing. Curve complex of a surface.

#### Ashani Dasgupta

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

Research Interest in Geometry Group Theory

#### 9:00 PM – 10:30 PM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

#### Program Description

Topics: Various problem Solving Strategy

#### Swarnabja Bhowmick

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

Cheenta Alumni turned Faculty.

#### 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 wrap up the first section with multi sets, review of injection principle and general distribution problems.

#### 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 of a Function

Description: One of the fundamental concepts in mathematics, meaning that a variable depending on another variable arbitrary closely approaches some constant as the latter variable changes in a definite manner. In the definition of a limit, the concept of nearness of the objects under consideration plays a fundamental role: only after a definition of nearness does a limit acquire an exact meaning..

#### 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: Problem Solving Session on TIFR 2018

#### Sourayan Banerjee

Pursuing Ph.D. at IISER-B.

Research Interest in Algebraic K Theory.

Cheenta Alumni turned Faculty