Thursday, February 16, 2017

February 16, 2017 Thursday

Bedtime Story 


Domain of a Function


f:X⟶Y can also be written as:

Y = f(x)

Examples are always good for understanding of a new concept.

A simple example would be a square function.

On the left column I have listed the first 5 natural numbers and on their right, the squares of each.

There is a left to right correspondence in terms of their squaring.

Natural number (n)                                  Square (n2)
1                                                                                                                                     1
2                                                                                                                                     4
3                                                                                                                                     9
4                                                                                                                                     16
5                                                                                                                                     25

So here, we can say f(5) = 25 which is essentially saying that 25 is a square function of 5.

A function can be defined either by a formula but more generally, by an algorithm.

Another aspect that is important considering the function is something known as domain.

Domain refers to what all numbers a particular function is applicable to or in other words what input numbers an argument can take for that function to work.

In our example of the square function, it would work for all positive integers, for negative integers, for zero (whose square is zero) and even for fractions (example square of ½ is 1/4).

So the domain of square function is all positive and negative integers and fractions.

There is another very interesting function in mathematics that goes by the name of logarithm.

I wish to point out that one must not confuse the terms algorithm and logarithm.

Both are very similar but totally different concepts in spite of the statement that one can construct an algorithm to calculate the logarithms.

You may wonder how this damn logarithm popped up in the minds of this upright ape.

Well…it started with multiplication and exponentiation.

I will take up logarithm in the nights to come and try to take away the fear and terror that you may be having with it.

That is very much possible if you look at it from the point of view of function much as we did with the squaring of the 5 natural numbers.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.in/
                              
Good night mon ami and my fellow cousin ape.
                   
  
                

             












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Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:


All his books can be downloaded for free through this link:


For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

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