February 05, 2017 Sunday
Bedtime Story
From George Peacock to George Boole
The beginning of it was led by 3 men, all of them being either
English or British.
1. George Peacock (1791-1858): He is known as the founder of
symbolic school of mathematics placing the algebra strictly on a logical footing.
Let us see what Peacock had to say about the foundation of the
general algebra that he established.
Peacock divided algebra into two forms, an arithmetical algebra
and symbolic algebra.
Let me explain this with a simple illustration.
2 + 5 = 7 is a form of arithmetical algebra since we are actually
using digits or integers.
But on the other hand if I write a + b = c, this would be symbolic
algebra.
These letters validity for all natural numbers, whole numbers and
fractions takes away lot of restrictions and makes it very universal.
In Peacock’s words:
“Symbolic algebra adopts the rule of the arithmetic algebra but
removes altogether their restrictions; thus symbolic subtraction differs from
the same operation in arithmetical algebra in being possible for all relations
of value of symbols or expressions employed.
All the results of arithmetical algebra which are deduced by the
application if its rules, and which are general in form though particular in
value, are results likewise of symbolic algebra where they are general in value
as well as in form.
Thus the product of am and an which is am+n
when m and n are whole numbers and therefore general in form though
particular in value, will be their product likewise when m and n are general in
value as in form.”
I shall not go too much in detail as I think with this you would
have got a sense of what George Peacock had achieved.
2. George Boole (1815-1864): From the dates you can see that both
the Georges were contemporary compatriots.
We had encountered George Boole sometime in the past but that was
from a different perspective.
Tonight the emphasis is on his contributions to mathematical
logic.
It is somewhat of a relief to know that such a renounced
mathematician like George Boole was not a child prodigy; his mathematical talents
were realized only during and after his university education.
It is hard to say what inspired him to even see a connection
between algebra and logic.
Perhaps it was some kind of desire to put the Aristotelian logic
on a more firm putting by applying mathematics into it.
We will cover his idea of algebraic logic in the nights to come.
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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