Friday, January 8, 2016

The Eighth International Conference on Science and Mathematics Education in Developing Countries by Dr Khin Maung Win

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 5th 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  5th 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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