Tuesday, March 21, 2017

March 21, 2017 Tuesday

Bedtime Story 


The Last to get Mathematical Notation was Logic


Euler introduced the notation f(x) for the function f applied to argument x.

Further, he formulated the notations of trigonometric functions that we use today, the Greek letter  for summations, the letter  (Euler’s number) for the base of natural logarithm and the letter  to donate the imaginary unit. 

By the time of Euler then, mathematics began to have a pretty modern look.

But there was one aspect that lagged behind and whose bust of activity came in the 1800s; that was mathematical logic.

Though logic was deep-rooted and ever-present, the idea of arming it mathematical notation did not strike us apes for quite a while. 

The people who made early contributions to this exotic arena of mathematics were George Boole (English) in 1850s (and the other 2 Georges that I had discussed in one of my bedtime stories) and later Gottlob Frege (German) in 1879.

Boole showed in no uncertain terms that propositional logic or propositional calculus can be expressed mathematically.

Though the terms sounds scary, you need not have any fear because all of us use propositional logic without being acutely aware of it.

Take this simple exam for instance.

Take a classroom full of noisy kindergarten children.

You know that children make lot of noise in the absence of the teacher.

So one fine day you happen to be near that classroom and you get to hear a lot of noise.

In this case, you would presume or conclude that that particular classroom from which too much noise is emanating must be without a teacher.

This is a great example of propositional logic wherein from two propositions you arrive at a conclusion.

To make it slightly more formal, let me put this way:

Premise 1. If the teacher is absent, the children make a lot of ruckus.

Premise 2. There is a lot of ruckus today.

Conclusion: the teacher is absent.

Propositional logic or calculus is a study of the truthfulness or falsity of a proposition based on other propositions and on their logical connectives.

What are these logical connectives?

We will take that up in the next bedtime story.

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.
                   
  
                

             












Advertisements

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

No comments:

Post a Comment