The Eighth International Conference on Science
and Mathematics Education in Developing
Countries

Dr Khin
Maung Win

Part 2

Stein’s ideas were
very general and the method was modified by Chen(1975) for Poisson
approximation.It has been applied in many areas including computational
biology, computer science,reliability theory and many more.The method remains
a very active research area.

The second paper on the second day 5

^{th}December was read by Dr Aung Thu ,retired rector of University of Yangon,entitled History of Mathematics and Exploitatyio of that for the Development of Future.The paper focuses on some mathematicians in different eras and their endeavours.According to historical records the ancient Egyptians made an effective use of mathematics in the building of pyramids.Although the Romans conquered Egypt and Greece in war,they did nothing to contribute towards the development of science and mathematics.The first foundations of pure mathematics were established by the ancient Greeks.To name a few well-known mathematicians _ Plato,Thales,Pythagoras, Euclid,Archimedes.Plato who realized the importance of Geometry as a way of thinking put a sign on the door step of his academy saying – Let no man ignorant of geometry enter here.
In 212 BC the Romans
conquered Europe and Archimedes was killed in the battle of Syracuse.After the
fall of the Roman Empire came the Dark Ages
in which all that had to do with knowledge and Culture disappeared .It lasted 1700 years until about 1400 the cultural
rebirth( Renaissance ) came.

During
the time Europe was lost in the Dark Ages,great advancements in Science
and Mathematics were made on the Eastern side of the
world,especially in Japan,India,China .In China algebraic equations were studied using words instead of
algebraic symbols.The 3x3 magic square in which the numbers 1,2,3,4 ,5,6,7,8,9 were arranged in 3rows,3 columns,so that the
row sum ,column sum and diagonal sum are
the same (15).But the numbers are not written in the way they are written
to-day.

To-day`s Magic Square

4 9 2 4+9+2 = 15

3 5 7 9+5+1= 15

8 1 6

In
Ancient Chinese Square circles
are joined by straight lines.The number of white circles give odd numbers,the
number of black circles give even numbers.

In about 5

^{th}century Tsu Chung Chih and Tsu Keng Chih,father and son gave the the value of pi as between 3.1415926 and 3.1415927,a value which was obtained in Europe after 1200 years.
In the middle ages,the mathematicians of India
obtained the value of pi correct to four decimal places.They also
obtained the solution of algebraic equations up to degree three.They also made
advancements in astronomy and calculated the orbits of planets and their
speeds.The mathematician Omar Khayyam was also known as the matnematician who
became famous for a single long poem which was called Rubiayat.The greatest
invention of India was the invention of Zero in about 600 A.D.

After the Reniassance one of the
greatest mathematicians was Fermat of France.One day he posed the
following question :

For all positive integer n
is

a
prime number ?

After
more than a hundred years later Euler
gave the answer.My mathematics teacher
recounted to us the dramatic story of how the Swiss mathematicsian Euler gave the answer in the following way
: Euler announced that he
would deliver an important result to the mathematics community on a certain day. On that particular day everyone was
waiting in the Assembly Hall –professors,lecturers,students etc
, with great expectations.
Students brought the note books to write whatever the professor was going to
deliver.

Euler entered the Hall with just a
piece of paper in his hand.He wrote on
the blackboard -

2x2 = 4,
4x2 = 8 , 8x2 = 16 ,
………

He continued 256x2 = 512 , 512x2 = 124
………

The
audience looked at on another.What are these ? They asked.After he had
multiplied 2 , 32
times.he wrote on one corner of the
board

He put the equation
inside a rectangle.He wiped the blackboard leaving the equation.Then he wrote the numbers 6700417
and 641 and multiplied them.Then
he wrote the answer as

6700417 x 641
= 4294967297

Then he showed the two equations by an arrow
.

Then Euler sat down without saying a
word. The audience looked at the two
equations,one after another.Then they
realized what Euler meant.They applauded. They say it was the most
illuminating exposition ever.

Dr
khin Maung Win

Retired
Professor of Mathematics

Rangoon
University

Burma
(Myanmar)

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