MATH MAANIAC

                The word  " Probability " often comes into our day-to-day life referring to, " What is the probability of some random event ? " simply saying what at most chance the event to occur.                 In my last blog " What is the probability you will open this blog ? " I told you, why for a long time,  I have been in a dilemma, about why probability is so useful , my counter-argument was, "Probability tells us about the most probable event to happen based on the available ones, it does not give us the guarantee that the event to be happened for sure, then why it's so overrated ?" and I give you a classical definition of probability.             Although the classical definition easily gives us the probability, it has some ambiguity . 😢😢            1)  It is applicable when the total number of events are finite.                    2) All the events in the event space should be equally likely (they should be symmetrical with eac

                        The word  " Probability " often comes into our day-to-day life referring to, " What is the probability of some random event ? " simply saying what at most chance the event to occur.             For a long time, I have been in a dilemma about why probability is so useful , my counter-argument was, "Probability tells us about the most probable event to happen based on the available ones, it does not give us the guarantee that the event to be happened for sure, then why it's so overrated ?"                      I remember one day I was standing at the junction of three roads, from one way a car was coming, so the question is what can happen next? I assume the driver does not have the same question as mine so she would not stop the car and think, it's a three-junction road what does the boy do next? 😀😀 So she continuously drives...           Now if we analyze the question of what happens next, two options are there since there

           In my previous blogs " TOPOLOGY - KING OF MATHEMATICS " & " Topological Space " we came across Topology's beauty and discussed its properties. Now we flash on "Topological Surgery Theory" - a technique used to do surgery (cut - operation - join) on manifolds.      To remind you in simple words manifold refers to any object , formally saying" A manifold of dimension n is a Topological space M which is locally homeomorphic to n-dimensional Euclidean space, Hausdroff and has a countable basis. In topology, surgery theory is a procedure to transform one manifold into another manifold in a controlled way.  There are different kinds of surgery on a manifold.  The formal way is to identify an embedded structure X on the manifold M that we want to cut, then the embedding φ : X → M To exclude it, do the cutting operation M \ (int(φ(X))) where int is the interior of a set. For gluing back (if, ∂X = ∂N) use the o