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

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

                                      Dr Khin Maung Win 

                                                              Part  III      

                         

     After Dr Aung Thu gave an exposition on some Mathematicians of different eras, Professor Dr Toh Pee Choon of  National Institute  of Education ,Singapore submitted the paper on The Teaching of Problem Solving in Undergraduate Mathematics .The goal is to help undergraduate s develop problem solving skills alongside the learning of the subject matter.

      Since the time given for the question time was so little,I had to suppress myself from asking the following question -  How much importance should we place on the speed of calculation ?    Although the chairman asked  - Are there any questions ?  It was clear that the questions were not welcome and he was in a hurry to call the next speaker.

 

(At Arts Assembly)

     Then came the third day-  6^th December.The programme started at  8  am.The first paper was read by Professor Fairweather  of American Mathematical Society  on Numerical Calcuus in Approximate Solution of Differential Equations.Numerical calculus involves solving calculus-related problems using numerical techniques.This paper is about the approximate solution solution of differential equations  in which approximate value of derivatives and integrals  play ann important role.The solution of differential equation ,as we know,involves finding   y   from an equation  containing      

          

      dy

      dx  .
When   y =  f (x )   ,            

                                            dy  =   lim     f(x+h)  -  f (x)

                                                  dx      h--->0            h

                                                                                                     

The value without the limit  may betaken as the approximate value of the  derivative which is used in the approximate solution of the  D.E. Then the professor went on to describe the methods of the approximate solution  and their effectiveness in practice.   

       Professor Fairweather s paper was very interesting . There was one question which I would have liked to pose;  It was -  In the teaching of this method ,would it have been a  good way to test its    effectiveness  by using the differential equations  whose solutions are already known ? However the time given for question time was so  little .   

       The next paper was read by  Ruth j. Skulkhu of the Department of Mathematics .Faculty of Science,Mahidol University.It was called  Construction  of a Royal Road to Mathematics for Undergraduates ; an urgently needed mission.She said , generally,students coming to all fields of undergraduate study are mathematically weaker than expected.The situation is worsened when they are immediately concronted with a bulk of abstract mathematical concepts and various intimidating methods  all of which  help culminate  in their terror and failure.The speaker relates her experiences of how , through bypassing rigid Bourbakian linearly structured curriculum  practiced worldwide ,she could help students find their royal roads in mathematics  which make mathematics classes more bearable,pleasurable , and even inspirational.

    During the question and   discussion time ,I put forward  some criteria for the royal road  to mathematics as I see it.It was as follows ;  

(1) Emphasis on illustrative examples on a theory ;

(2) Testing a new method with examples whose solutions are already known;

(3) Courses in mathematics with as little mathematics content as possible ;

(4)Emphasis on application areas in which the subject whici is applied is given more  emphasis than mathematics itself;

(5)Course on history of mathematics in which more emphasis is given to history than to mathematics.

These , in my opinion ,give the criteria on the royal  road to mathematics .

Professor said that she agreed with what I said and took the photograph of what I have written in the note book.She promised to improve the royal road.

The next paper was on Geometry and Computer Vision by Professor Michel Jambu of  Laboratoire Dieudonne , University of Nice,France.The professor stated  construction of a  3 D  object from  some  2 D  images  may be quite simple for any human being, but for a computer,it is much more involved.It needs to use projective geometry and to define some specific  algorithms.A short introduction to the topic was given starting with some basic notions of projective geometry,and finally some some ideas of tools to make the reconstruction

   The paper was  interesting but not enough time was given for question and discussion.If there was time,I would have liked to ask ;Have the professor had experience with 3 D computer games?I have heard that the  3 D  war games were very realistic. The inventor of  3 D games , John Carmack was blamed for the shootings that took place  in USA. Do you agree with that point of view?

     The next paper was read by Professor Polly W.Sy . My memory does recall the title of the paper , but I only know that the paperdeals with Fibinacci sequences and other number sequences.Fibonacci sequence  is a sequence of numbers of the form    1,1 ,2,3,5,8,13,21,34,55, 89. , …….. 

The next term of the sequence is obtained by addind the last two  terms .For example    ,  1+1=2 ,  1+2 = 3 ,  3 + 5 = 8 ,  8 + 13 = 21 , 13 + 21 = 34 , 21+34=55 ,    ………..

If we take the ratios beginning from the third term , we get

2/3 ,3/5 , 5/8 , 8/13 / 13/21 ,  21/34  , …………...

They are called the golden ratios,because it is believed that the are the most beautiful ratios. The rectangles obtained with these sides are called the golden rectangles. If I was given enough time I would have liked to ask the following question :     

We know that the screens of the size of our television sets are determined by by the lengths of the diagonals  as  20 in,30 in, 40 in and so on.If we look at the lengths and breaths,we find that the lengths are too long compared with the breaths.Would it not be a good idea to determine the lengths and breaths according to the golden ratios?

   The next paper was read by May Thiri Zin of third year  ICOE , Mandalay University.The paper was titled  The Mathematical Culture in Myanmar.In this paper,the crucial role of mathematics in ancient Myanmar tradition is described.The traditional type of mathematical enigmas  and their solutions  and some unit conversions of quantities in Myanmar culture are also discussed.Mathematical activity of Myanmar  traditional daily life is discussed.

  Examples of Myanmar traditional measurement of time , distance , weight, volume are also given.Relation with the units of measurement round the world are also given.

       During the question time , I posed a question which has been in my mind  for a long time and which I could not answer.I posed the question but did not expect to get an answer which I did not. The question was This :  In the measure of the volume of rice  we have heard of the term    ‘ pyi ‘  . We also accept that   one pyi  equals  eight tins of condensed milk . The problem is this

The term has has existed   in our Myanmar tradition for a long time,whereas  the condensed milk is a modern invention? How come that this modern invention is thus related to our traditional measure?I posed this question with the  hope  of giving food for thought to our Myanmar friends.  

(To be continued)

Dr Khin Maung Win

Retired Professor of Mathematics

University of Yangon 
Burma (Myanmar)