July 27, 2018 Friday
Bedtime Story
It started with Useful Linear Equations
As I was saying last night that almost
anybody who cares to read my bedtime stories will be very much familiar with
both the linear and quadratic equations.
We have also been taught to tackle system
of linear equations in the form of simultaneous equations.
Take for instance the following two
equations:
2x + 3y = 6
4x + 9y = 15
I am positive this would not frighten most
of us and even with our average algebraical skills we should be able to obtain
the value of the two unknowns.
In the language of mathematics, the
solution to the variables is arrived by the technique that is known as elimination
of variables.
Computers can be taught or rather
programmed with the algorithm of the elimination of variables to solve a system
of several such equations with not just two but multiple variables.
Keep in mind that the coefficients of these
equations can belong to any field and not just natural numbers or rational
numbers.
Such algorithms have a great many practical
uses in the field of engineering, physics, chemistry, computer science and economics.
Pure mathematicians though do not really
care about the practicality of it though some of them may as there is no
consistency with us apes, not even mathematicians.
Since these kinds of algebraic equations
are useful and come in handy in markets, economy, and architecture and so on,
they are not abstract and have been used since many centuries.
Abstract algebra too arose from such
need-based mathematical imperatives.
One of such attempts that was being
seriously investigated by some mathematical minds was the solutions to the
general polynomial equations of higher degree.
As is self-evident, much of normal life,
economics and markets would be able to run along fine with the so called elementary
algebra but mathematicians are never satisfied with that.
They are extremists not in the common
derogatory sense of the word but always try to extrapolate the matter further
and further away towards its extreme.
So once the solutions to linear equations
were known, their site was set to equations of higher degree and with more
variables or unknowns.
It is here that we introduce the
Diophantine equations.
Thus the target of such similar studies was
the arithmetical investigations of quadratic and higher degree Diophantine
equations, meaning polynomial equation with two or more unknowns wherein only
the integer solutions are sought.
An example of Diophantine equation would
be:
an
+ bn = cn
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
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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