Lagrange’s Theorem is one of the two Big theorems(along with Cayley Theorem) with actual people name on it that you can find in any basic textbook of Group Theory, see how C. Pinter describes this theorem in his book AAA.

Koch Snowflakes is this beautiful shape that I fell in love with in my school years, I didn’t know much math then( I don’t know much now either!),but the catchphrase is this shape has “infinite parameter but with a finite area”

If this phrase doesn’t make you uncomfortable you are very stoic person (hats off!), I got to know this fact for the first time from a Bengali child novel called “আমি তপু” (I am Topu) by Muhammad Zafar Iqbal, and probabily the only novel in Bangladeshi literature ever to romanticized math(but no one really remembers it somehow!)

I’m not going tell the story here but this kid named Topu discovers Koch snowflakes by himself while sleeping in the kitchen alone while talking to a rat!

And honestly when I first read it I didn’t appreciate it much, but nevertheless it is one of the fantastic beasts that math has to offer!

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Every year I want to go back to a calculus book just to see how my ideas of limits, derivatives and integrals has changed this time, and I think its true for all kind of mathematics that if you revise them in different parts of life you will get different realizations and often epiphanies! throughout my life I have thought of calculus as hard math that Newton(Leibnitz) created to instantaneous change with time to best fitting slope on a curve to convergence of sequence, and I know its not end yet!

What derivative is? well, it’s function! but maybe slightly unusual one( very common if you’re into mathematics for a long time). This function takes an input(real number) and a function and returns an output(real number) which you can interpret as instantaneous speed of the function at that point. and by breaking down this processes we will learn some core concept of analysis!

Just like Topologists can’t distinguish between a coffee cup and a doughnut(because they are homeomorphic), Group theorists have a hard time distinguishing between groups that are Isomorphic!

we will see example of two (or more) Groups, beside coming from different origin they are same in respect of Group theory.

I am omitting the basic definition of Group because I think there quite a few very good introductory content already exists, so without further ado let’s start.

Those of you have heard about topology often hear that ” everything is made of rubbery stuff ” or “you can squish or stretch any shape but never tear or add “, well I used to wonder how all of this is math!

Today we will try to make sense of one the main topics topology, which is homeomorphism. It sounds like a peculiar thing but actually a very basic concept in all of mathematics. Homeomorphism is nothing more than a function( a pair of functions actually!),but it’s not just any kind of function, it’s continuous functions between topological spaces.in the rest of the article we will take step by step to understand