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 ) ,

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)

Burma (Myanmar)

## No comments:

## Post a Comment