MATH MAANIAC

           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 ...

        In my previous blog   "TOPOLOGY - KING OF MATHEMATICS"  , talked about geometric shapes and saw how "Distance" is the basic tool for the study of "Metric Space" and also saw how removing the notion of distance lead us to the more general study of spaces called "Topological Spaces".        The goal of today's blog is to understand the Topological Space more formally and challenge our normal understanding to an another level.       As in metric space main key-tool is distance, here it is neighbourhood.        First, we can start with what we mean by neighbourhood, its simply mean surrounding. If you choose a point and a r >0 radius circle around that point then that also a neighbourhood mathematically denoted as B(x,r) where x is point and r is my radius, this neighbourhood called r-neighbourhood. We can see one thing that if we choose r-neighbourhood the study came to study same as m...

                NON-EUCLIDEAN GEOMETRY                  Every mathematics student to professor everyone heard the name of Euclid. He is famous for his contribution to the mathematics. One of his great contribution is Euclidean geometry. That we study whole our school life, that all based  on Euclid postulate and axioms that he write on his famous book "The Elements", that book has13 chapters based on his geometry.     And the great thing you know before 19th century mathematicians believe that Euclid geometry is god's word so no another geometry not exist, and but some mathematicians are believe some of Euclid postulate is can derive from other, so some are trying to prove but many tries and fail.      In 19th century  János Bolyai  and  Nikolai Ivanovich Lobachevsky  (separately) thought that instead of proving one of them imply from another we can mak...

                  TOPOLOGY - KING OF MATHEMATICS           From our childhood we are studying geometry, there we are studying different shapes and objects and their properties like area and many. Although in mathematics we are not bounded by dimension so we make any dimensional object and study it. By studying this in higher dimension we know more about real world and we more understand more pattern, this patterns are always in front of us but we have to find this.          Although we are saying in any dimension we are able work in any objects is it not that if we choose any arbitrary shape its sometimes difficult to study this formally.          Many days earlier I am familiar with another branch of mathematics there we don't have this boundary. Although by doing these process we have to make our geometry deform or properly say we not that much focus on geometry...

  INTRODUCTION -    It is say that "If you don't  know the basic of any subject , you doesn't know anything about this subject".  As example "If you wish to build a building but the base of the building is not strong, then how the building is strong ?" In mathematics the base is "Analysis", the most fundamental part of mathematics. Many of  my reader may be familiar with "Real Analysis", "Complex Analysis" and many analytical concept we study in mathematics. If you are not familiar with this don't worry and if you someone who first ever listen about "ANALYSIS",  I promised you from start to the end of this blog is a great journey for you and it's gives your imagination a challenge to think. I request everyone who read this blog to read this without any pre-assumption and enjoy the journey.                   ANALYSIS  - Now you might be wonder and curious to know about " What is...

  A POINT TO A SPACE                   From after our birth to at before of our death what we saw outside us really very usual things but a mathematician eye always capture the beauty on it that's like a floating river and you flow within it . I remember when travel to college via local trains I saw skylines, clouds, lands, electric polls and others. Thats obviously usual things I belive who travel everyday saw this, but what I found interesting in this is everything have a proper shape and as required shape can be big or small not only that at the end to connect with one to one beautifully . If you not familier with such things I give you an usual example like you saw a book it has six sides with maximum three different areas in six sides. But this similar concepts varies and make it more interesting when add up differet kind of shape together. As a mathematician or as a seeker every new thing that we saw in our usual routine thats cha...