# Cheenta week of Dec. 10 to 16

“You must not attempt this approach to parallels” – Bolyai (Sr.)

*Janos Bolyai squarely disobeyed his fathers advise.*

Hello mathematician!

I am working my way through a curious monologue: *Groups acting on Graphs* (by Dicks & Dunwoody). Dunwoody is one of the giants of Group Theory and low dimensional topology. His style of writing is reminiscent of Serre (another stalwart in this field). Dunwoody’s algebra is clean, notations and definitions are exhaustive and examples are abundant.

Dunwoody reminds me of classical texts in Euclidean geometry where one would painstakingly make ner way through axioms, definitions, and theorems in a sequential manner. This trend of *writing mathematics* was rekindled by Bourbaki in the last century.

There is another trend of ‘writing’ mathematics. **This can be loosely described as the ‘populist’ method.** Its roots can be traced back to French mathematician Alexis Claude Clairaut. His book on geometry (Elements de Geometrie, 1741) was a clear departure from medieval geometry texts. The rule of the day was to mention all axioms, definitions, and theorems in a deductive continuity.

Clairaut did not care about this ‘rigor’. He would quickly enter realms of ‘reality’ after loosely describing the initial ideas. For example, he would quickly move to the descriptions of Canal engineering, from the definition of parallel lines.

Some historiographers of mathematics are of the opinion that this departure from rigor actually led to the discovery of non-euclidean geometry. If this is true, then it would earmark one of the most astounding connections between reality and abstraction.

This style of writing was later adopted by other giants of mathematics. Two of the absolute masterpieces of this genre are:

- Three-dimensional geometry and topology by Thurston
- Geometry and Imagination by Hilbert

Both of these works quickly move from ‘initial ideas’ to ‘applications’ and ‘examples’. However, these applications and examples are more mathematical in nature (compared to canal engineering). Both authors are not worried about ‘taking care of all initial ideas’ before they embark upon the exciting mathematical expedition. They freely use ‘rigorously unexplained’ words and concepts.

This is in stark contrast to what Dunwoody does in his work.

Some authors have taken a ‘middle path’. Recently Dr. Chakraborty’s Real Analysis (in Bengali) is an example to the point. It has a more conversational and expositional temper though he is careful enough to maintain ‘completeness’. Hatcher’s Algebraic Topology does something similar. Excursion into Mathematics (Beck, Crowe, and Bleicher) is yet another example from pre-college mathematics.

Personally, I am unsure about my preference. Though the informal tone of Hilbert and Thurston is more inviting in the beginning, one quickly seeks more rigor to reaffirm one’s own theoretical understanding of the subject. One should probably work hard on a rigorously presented idea and keep an informal masterpiece as an interlude in ner journey.

This week we hope to see you in classes. We have some beautiful formal and informal adventures in mathematics waiting for you.

Cheenta Weekly Schedule – December 10 to 16, 2018

All the best!

Ashani Dasgupta

Passion for mathematics.

# Monday, December 10

#### Live Lecture Hour

#### 8 PM – 9:30 PM

I.S.T., Monday

Problem List for the Week

Books

Other Stuff

#### Program Description

## Computer Science Olympiad Program

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

#### Faculty

#### 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

.

#### Live Lecture Hour

#### 9;30 PM – 11:00 PM

*I.S.T., Monday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## 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.

#### Faculty

#### Kaurag Mukherjee

B.Math from I.S.I Bangalore

Research Interest: Graph Theory

# Tuesday, December 11

#### Live Lecture Hour

#### 8;30 PM – 9:30 PM

*I.S.T., Tuesday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## CHEENTA Z

Topic: Complex Number and Geometry

Description: We explore the field theoretic properties of complex numbers.

#### Faculty

#### Ashani Dasgupta

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

Research Interest in Geometry Group Theory.

# Wednesday, December 12

#### Live Lecture Hour

#### 8:30 PM – 10:30 PM

I.S.T., Wednesday

Problem List for the Week

Books

Other Stuff

#### Program Description

## Bridge Session

Topics: Various problem on Combinatorics

#### Faculty

#### Swarnabja Bhowmick

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

Cheenta Alumni turned Faculty.

# Thursday, December 13

#### Live Lecture Hour

#### 8;30 PM – 10:30 PM

*I.S.T., Thursday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## Bridge Session

Topic:Preliminary idea of Limit

#### Faculty

#### 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.

#### Live Lecture Hour

#### 9 PM – 10:30 PM

I.S.T., Thursday

Problem List for the Week

Books

Other Stuff

#### Program Description

## Computer Science Olympiad Program

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 *number*–*theoretic algorithms* are used widely, due in part to the invention of cryptographic schemes based on large prime *numbers* .

#### Faculty

#### 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 14

#### Live Lecture Hour

#### 8;20 PM – 9:50 PM

*I.S.T., Friday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## Early Bird Math Olympiad (IND Group)

Topic: Number Theoretic Function

Description: Number theoretic functions appear and are employed in studies on the properties of numbers. However, the theory of number theoretic functions is also of independent interest. The laws governing the variations of number theoretic functions cannot usually be described by simple formulas

#### Faculty

#### 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.

#### Live Lecture Hour

#### Program Description

## Intermediate Math Olympiad Program

Topic: Modular Arithmetic

Description: primitive roots and order of an element with respect to prime modulus.

#### Faculty

#### Sauvik Mondal

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

Research Interest in Geometric Group Theory. Cheenta Alumni turned Faculty

#### Live Lecture Hour

#### 9.45 PM – 11:15 PM

I.S.T., Friday

Problem List for the Week

Books

Other Stuff

#### Program Description

## College Mathematics Program

Topics: Implicit Functions

Description: We will continue the previous lecture.

#### Faculty

#### 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 15

#### Live Lecture Hour

#### 8;00 AM – 9:30 AM

*I.S.T., Saturday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## Thousand Flowers Program (Pre-Olympiad)

Topic: Shapes and Measures

Description: We continue with elementary constructions in geometry. Our goal is to understand percentage. This has led us to a fascinating journey in euclidean geometry.

#### Faculty

#### Ashani Dasgupta

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

Research Interest in Geometry Group Theory

#### Live Lecture Hour

#### Program Description

## Early Bird Math Olympiad (A Group)

Topic: Distribution Problem

Description: Description : We will continue the previous topic with some sorted example.

#### Faculty

#### 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

#### Live Lecture Hour

#### 6:00 PM – 8:00 PM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

#### Program Description

## Mathematics Doubt Clearing Session

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

#### Faculty

#### Sankhadip Chakraborty

Pursuing Ph.D. from IMPA Brazil

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

INMO Awardee

#### Live Lecture Hour

#### 8;00 PM – 9:30 PM

*I.S.T., Saturday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## Thousand Flowers Program (Pre-Olympiad)

Topic: Glimpses of Geometry

Description: We explore elementary construction problems in Geometry. Our goal is to understand the work of Morley Mascheroni.

#### Faculty

#### Ashani Dasgupta

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

Research Interest in Geometry Group Theory

#### Live Lecture Hour

#### Program Description

## Intermediate Math Olympiad Program

Topic: Modular Arithmetic

Description: primitive roots and order of an element with respect to prime modulus.

#### Faculty

#### Sauvik Mondal

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

Research Interest in Geometric Group Theory. Cheenta Alumni turned Faculty

#### Live Lecture Hour

#### 8;20 PM – 9:50 PM

*I.S.T., Saturday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## Early Bird Math Olympiad (IN Group)

Topic: Number Theoretic Function

Description: Number theoretic functions appear and are employed in studies on the properties of numbers. However, the theory of number theoretic functions is also of independent interest. The laws governing the variations of number theoretic functions cannot usually be described by simple formulas.

#### Faculty

#### 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.

#### Live Lecture Hour

#### Program Description

## Early Bird Math Olympiad (U Group)

Topic: Combinatorics

Description: Combinatorial identities and shortest path problem.

#### Faculty

#### Ashani Dasgupta

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

Research Interest in Geometry Group Theory

#### Live Lecture Hour

#### 9.45 PM – 11:15 PM

I.S.T., Saturday

Problem List for the Week

Books

Other Stuff

#### Program Description

## 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.

#### Faculty

#### 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 16

#### Live Lecture Hour

#### 8;00 AM – 9:30 AM

*I.S.T., Sunday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## Thousand Flowers Program (Pre-Olympiad)

Topic: Shapes and Measure

Description: We continue with elementary constructions in geometry. Our goal is to understand the percentage. This has led us to a fascinating journey in Euclidean geometry.

#### Faculty

#### Ashani Dasgupta

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

Research Interest in Geometry Group Theory

#### Live Lecture Hour

#### Program Description

## Early Bird Math Olympiad (A Group)

Topic: Distribution Problems

Descritiption : We will continue the previous topic with some sorted example.

#### Faculty

#### 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

#### Live Lecture Hour

#### 8;00 PM – 9:30 PM

*I.S.T., Sunday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## Thousand Flowers Program (Pre-Olympiad)

Topic: Glimpses of Geometry

Description: From Morley Mascheroni theorem to Kleinian geometry of action on space.

#### Faculty

#### Ashani Dasgupta

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

Research Interest in Geometry Group Theory

#### Live Lecture Hour

#### 9:00 PM – 10:30 PM

I.S.T., Sunday

Problem List for the Week

Books

Other Stuff

#### Program Description

## Computer Science Olympiad

Topics: Various problem Solving Strategy

#### Faculty

#### Swarnabja Bhowmick

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

Cheenta Alumni turned Faculty.

#### Live Lecture Hour

#### Program Description

## Early Bird Math Olympiad (U Group)

Topic: Combinatorics 1

Description: Combinatorial Identities and shortest path techniques.

#### Faculty

#### Ashani Dasgupta

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

Research Interest in Geometry Group Theory

#### Live Lecture Hour

#### 9;30 PM – 11:00 PM

*I.S.T., Sunday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## 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..

#### Faculty

#### Kaurag Mukherjee

B.Math from I.S.I Bangalore

Research Interest: Graph Theory

#### Live Lecture Hour

#### 9;45 PM – 11:15 PM

*I.S.T., Sunday*

Problem List for the Week

Books

Other Stuff

#### Program Description

## College Mathematics Programe

Topic: Problem Solving Session on TIFR 2018

#### Faculty

#### Sourayan Banerjee

Pursuing Ph.D. at IISER-B.

Research Interest in Algebraic K Theory.

Cheenta Alumni turned Faculty