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Homework, Duality, Euler Number and Cheenta 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, Rabindranath Tagore and Finland’s educators (who have the number 1 education system for school students) are some other people who do not like homework. I am pretty sure that Lalon Fakir did not like it either, though I do not evidence to back up this claim.

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).

find a beautiful book

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.

geometry revisited

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

one beautiful problem to keep your brain busy

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 is 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:

This Week

Ashani Dasgupta

Passion for Mathematics

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Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.