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BEAUTY IN MATHEMATICS THAT FALL YOU IN LOVE FOREVER

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All Previous Blogs -

19)  Linear Algebra - Purpose to Application 

18)  Probability Distribution

17) The Axioms - Probability 

16) What is the probability you are going open this blog ?

15) Topological Surgery Theory

14) Topological Space

13) Lebesgue Measure on ℝ

12) Measuring a set

11) non-Euclidean geometry

10) TOPOLOGY - KING OF MATHEMATICS

9) Solution of the problem section of THE MATHEMATICS STUDENT (VOLUME- 88)(MS-2019, 3-4, PROBLEM 6)

8) Do you ever think how your imagination can help you remember mathematical formula and concept with the help of mathematical analysis?

7) INFINITY - AN ILLUSION OR A REALITY ?

6) Russell's Paradox

5) GOLDBACH FUNCTION

4) A point is a most simple geometric figure

3) TRIGONOMETRY- BASE OF MATHEMATICS

2) MATH MAJIC

1) MATHEMATICAL MODELLING - THE EFFECT OF CORONAVIRUS

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Idea of Superposition

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Let's start with a question, "Can I be in a different position at the same time ?" Obviously - No. Ok, let's ask the question more specifically, "Can I be in a mood of happy and sad at the same time ?"  🤔🤔🤔 Well, we can say many times in life we are not actually happy or sad, if we try to measure on a scale starting 1 with sadness and 10 with happiness, we may be in between 1 and 10. Let at 1 sad,  2 - 4 is more likely sad, 5,6 neither happy nor sad,  7 - 9  is more likely happy and at 10 is happy. Have a look at the following table and graph - (Scores actually represent inner psychological feelings) So for the whole day, since the average of all scores is 7, we can say more likely happy is the experimented mood, but if we see the data locally it does not say so, it can say we are in some ups and down combination of happy and sad (like a wave spread in a whole day). Two clever observations I would like to mention here, 1. As I mentioned earlier, although ...
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The development of Linear Algebra

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                   Linear Algebra is the most useful and powerful tool in Mathematics. In the last blog " Linear Algebra - Purpose to Application " we saw how a higher-order system of linear equations has been solved by transforming the equation into the matrix.                  Although it's good to mention that it only works if in the AX=B [A is m*n, X is n*1, B is m*1, so it has m equations and n unknowns ]  our A matrix is invertible, if it is not invertible i.e, in the sense of matrix it is rank of A is less than n and rank of (A;B) = rank of A < n, so the system of linear equation AX=B has infinitely many solutions, we can find the solution by converting the A matrix into row-echelon form, simply you will get the solution from bottom.         Note:-  1. The rank of a matrix - It is defined as the largest order square matrix whose determin...
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Probability Distribution

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             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 the last two blogs " The Axioms - Probability " and " What is the probability you will open this blog ? " we see how probability arises over time.         But the question is if the event space contains more than some finite or infinite elements, How will we calculate the probability?       Here the role of Probability Distribution came into the story. So instead of calculating, we evaluate how the probability is distributed over the region.       First, take the simplest example, " Tossing a coin ", so by the axioms of probability we have here two event spaces called head and tail. The probability of getting the head is 1/2 and the same for the tail.  ...
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