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.
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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:
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