July 13, 2018 Friday
Bedtime Story
Symmetry and Group
Last night I had introduced you to the
concept of geometrical symmetry which may not have been something sensational
as it kind of has a semblance to our intuitive and general understanding of the
word.
I do not know about you but to me the
mathematical definition of symmetry was certainly an eye opener.
Let us once again read the definition of
symmetry pertaining to pure mathematics.
A mathematical object is said to be
symmetric with respect to specific mathematical operation if it retains some
property of it after undergoing that operation.
Remember, it is not always possible for
most average apes to have a visual imagination of mathematical concepts, specially
the algebraic ones or the ones involving analysis (in contrast to Euclidian geometry).
From this definition of mathematical
symmetry arose the concept of group in mathematics; the set of mathematical
operations that preserve a specific property of a mathematical object form a
group.
You would then expect the concept of
mathematical groups to have arisen from geometry or perhaps topology but that
was not the case; it was in fact from the study of polynomial equations from
which arose the group theory.
The pioneer of this study was the young
French mathematician Évariste Galois who died very young at the age of just 20
in a duel at that tender age in 1832.
He is one of most curious characters in the
history of modern European mathematics in spite of taking into account the eccentricities
which many mathematicians are well known for.
At the age of 14 he got very much fed up of
studies and started taking interest in mathematics.
This is perhaps the greatest oxymoron that
I have come across but it is a fact – to be bored of studies and developing an
obsessive interest in mathematics.
His mathematical genius could be assuaged
by the fact that at the age of 14 when he came across the work of French
mathematician Adrien-Marie Legendre titled ‘Elements of Geometry’ (1794 - a
standard book on this subject for nearly a century), Galois “read it like a
novel” and mastered it in the very first reading.
At the age of 15 he was already reading the
original papers of our great Lagrange such as “Reflections on the algebraic
solutions of equations” (1770) that is regarded as one of the seminal works in
the history of mathematics related to abstract algebra.
Just remember, reading an original paper
does not come easy.
If you are reading this bedtime story then
surely you cannot be an average street dweller and in a way could be
categorized as an intellectual – an ape who has time to pursue knowledge
sacrificing the basic needs of mass reproduction and propagation of selfish
genes.
So if that be the case, ask yourself how
many original papers of your field of interest you have read so far, if any.
We shall continue with the story of Évariste
Galois in the nights to come.
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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