One of the ways to Understand Mathematics

         I have seen many people doing mathematics without thinking at all. They will do mathematics somehow like a computer which doesn’t know why it is doing.

      I don’t like to do pure Mathematics. What I mean by pure is somewhat not thinking about the Physical meaning. The concepts will look as a vague one.

There is difference between saying 

         one apple + two apples = three apples

from simply saying 1 + 2 = 3

      Human brain always used to understand anything by visualization.

      When you say “y is a function of x” there is no so much Understanding. But when you say “Velocity is the function displacement and time” there is a real understanding because it is understandable from everyday experience. 

          The reason is because the mathematics itself is created to explain physical things.

      When we do any mathematics, we should try to understand each and every line. It is nice to read mathematics in an elaborated manner and it will help you a lot to think. For example instead of studying “dy/dt” you can read it as

Rate of change of y with respect to x

   

   Instead of just saying, ∫ y dx (Integral y dx) you can read it as, summation of function y with respect to the independent variable x.     

   So each time you will remember the meaning of differentiation. And you will have a great clarity in the topic.

     

We should avoid using the formulas blindly.

    

     In any problem, we shouldn’t straightly use formulas but we should always try for the derivation.

     

     First it will take more time to completely derive all the things in a problem. But when you derive it for more than 5 or 10 times, then it will start to come fluently. 

     But after you got practiced, no matter what size the derivation is, it will come in a great flow and you can just do it in your mind. 

Depending on the size of the derivation, you need to practice it more times.

      So, we can learn everything in a perfect way.

Nothing needs to be remembered at all as a mug up thing. But everything can be remembered from the fundamental derivations.

    

    And it will also help you in thinking skills. Each time when you derive the formulas, you may not use the same method. But you will have the chance to derive the formula in a different ways. And you will get a different kind of thinking about the single concept.

   

     Maybe it will lead to great innovations!!    

When you try to analyze a mathematical thing to explain in words, you will get deeper understanding than just looking at the equation.

      Max Born got Nobel Prize only for his famous explanation on Quantum Mechanics.

      Explaining in words is a very good thing.

What My opinion is ,

       Studying mathematics using words is the one of the best way to understand any concept.

      So, you will always understand the physics behind that and may understand the real meaning of the concept.   

      That is why I used to discuss any concept in physics with mostly consisted of words other than just mathematical equations.