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
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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