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" MATHEMATICS AND COMPUTER EDUCATION IN DEVELOPING COUNTRIES "

Mr. Vice-Chancellor, Pro Vice-Chancellor (Academic), Registrar, Members of the Assessing Board, fellow academicians and other members in the august audience, The main focus of my presentation is on the following points: (i) Need for proper curricula in all three levels of education: Primary, Secondary and Tertiary. (ii) Need for competent teachers not only at tertiary level but also in primary and secondary levels. This is paramount for the development of analytical brain – a key to the development of human resources – which a nation shall feel proud of. Dependence on expatriate staff need to be curtailed; which is possible only when the national skilled manpower is properly developed. Mineral resources are finite. A country cannot survive indefinitely on the basis of raw minerals only. It may be noted that PNG’s current GDP’s major share (approximately 65%) comes from minerals only but in due course of time this percentage shall dwindle and the country’s survival shall depend on how it develops its human resource. (iii) Inadequate thrust in Mathematics and Computer Science education is bound to be reflected in lack-lustre industrial growth. The country can only continue to export merely the raw minerals and not the finished goods. (iv) The Government needs to allocate proper outlay towards basic science and engineering education in order to join the club of “Developed Nations” in a defined time frame. This is only possible through adequate allocation of resources towards Mathematics & Computer Science education at all levels of study. (v) Importance of Computer Science development of hardware and software. Both Mathematics and Applied Mathematics have contributed to the revolution of Information Technology. Computer Science has played a vital role in the development of: I.T. industry, Manufacturing industry, Satellites, E-Banking, E-Commerce, Revolution in the field of Communication, Global Positioning System (GPS), Geographic Information System, Remote Sensing etc. To achieve these goals certain remedies are suggested as follows. It may be interesting to briefly touch upon some historical aspects of the core subject: especially Mathematics.

“MATHEMATICS AND COMPUTER EDUCATION IN DEVELOPING COUNTRIES” by Prof. Dr. R.B. Misra Mr. Vice-Chancellor, Pro Vice-Chancellor (Academic), Registrar, Members of the Assessing Board, fellow academicians and other members in the august audience, The main focus of my presentation is on the following points: (i) Need for proper curricula in all three levels of education: Primary, Secondary and Tertiary. (ii) Need for competent teachers not only at tertiary level but also in primary and secondary levels. This is paramount for the development of analytical brain – a key to the development of human resources – which a nation shall feel proud of. Dependence on expatriate staff need to be curtailed; which is possible only when the national skilled manpower is properly developed. Mineral resources are finite. A country cannot survive indefinitely on the basis of raw minerals only. It may be noted that PNG’s current GDP’s major share (approximately 65%) comes from minerals only but in due course of time this percentage shall dwindle and the country’s survival shall depend on how it develops its human resource. (iii) Inadequate thrust in Mathematics and Computer Science education is bound to be reflected in lack-lustre industrial growth. The country can only continue to export merely the raw minerals and not the finished goods. (iv) The Government needs to allocate proper outlay towards basic science and engineering education in order to join the club of “Developed Nations” in a defined time frame. This is only possible through adequate allocation of resources towards Mathematics & Computer Science education at all levels of study. (v) Importance of Computer Science development of hardware and software. Both Mathematics and Applied Mathematics have contributed to the revolution of Information Technology. Computer Science has played a vital role in the development of: I.T. industry, Manufacturing industry, Satellites, E-Banking, E-Commerce, Revolution in the field of Communication, Global Positioning System (GPS), Geographic Information System, Remote Sensing etc. To achieve these goals certain remedies are suggested as follows. It may be interesting to briefly touch upon some historical aspects of the core subject: especially Mathematics. 1. In ancient times, it was fascinating to study Mathematics in context with philosophical doctrines. To quote a few celebrated philosophers there were Aristotle, Thales of Miletus, Pythagoras and recently Prof. Bertrand Russell, who won his Nobel Prize for his literary write-ups in Mathematics. Due to immense applications of Mathematics to diverse scientific disciplines there developed a happy union of Mathematics and Physics. Later on, an off-shoot of Mathematics came into existence in the name of Statistics. Many other branches of Mathematics emerged with different names such as Business Mathematics, Econometrics, Bio-Mathematics and Operations Research etc. 2. The European Schools of Mathematics classified different topics of Mathematics into two main groups: Pure Mathematics and Applied Mathematics. The subjects with more theoretical and rigorous approach such as Algebra, Trigonometry, Analysis, Calculus, Geometry, Topology etc. were included in Pure Mathematics while Statics, Dynamics (so-called Mechanics), Hydrostatics, Hydrodynamics, Fluid Mechanics, Magneto-Hydrodynamics, Differential Equations, Astrophysics, Theory of Relativity and Cosmology, Field Theories etc. were part of Applied Mathematics. The domain of Applied Mathematics used to have such a large expanse as to cross the frontiers of Physics and Engineering. Many old European Schools of Mathematics used to teach even Electricity and Magnetism within the domain of Applied Mathematics and that too by Mathematicians. With the emergence of Mathematics Schools in the American continent the boundaries of Mathematics were diversified. In the American terminology Mathematics meant Pure Mathematics only and all above-mentioned subjects of erstwhile Applied Mathematics were restricted to Physics and Engineering disciplines. American Schools redefined the domain of Applied Mathematics (better understood as “Applicable Mathematics”) and included the computing and numerical aspects of Mathematics in the name of Statistics, Operations Research, Computer Science etc. Thus, in contemporary times, Mathematics includes the subjects of Pure Mathematics only. 3. The human mind is so fertile that newer and newer vistas of every subject are created at every moment around the globe. The rate of growth of new creations is so rapid that, at times, the human mind is unable to cope with the latest developments. As a result, every society seems to be under the illusion that the coming generations are becoming poorer in terms of their intellect. However, one demerit of the scientific advances mainly made by the developed countries is very much visible: the younger generation is becoming so much dependent on calculating gadgets (including computers) that they fail to sharpen their own mental ability and intellect. The younger generation prefers to use the electronic calculators even to do simple sums. This unfortunate aspect of their dependence on calculating machines must be discouraged in order to sharpen their own intellect. 4. Now I propose to highlight curricula programme: The simple principles of Arithmetic, Algebra, simple geometrical diagrams of straight lines, planes and solids should be taught at the primary level of 5 years schooling. Elementary concepts of Sets, Trigonometry, Coordinate Geometry (of 2-dimensions), Mensuration of Planes and Solids may be introduced in the first 3 years of secondary education. More advanced topics of these subjects and Coordinate Geometry of 3-dimensions, Vectors, Mechanics, Concepts of differentiation of simple functions (so-called Calculus) may be introduced in the last 2 years of secondary education. Most countries, even in the developing world (especially in the African and Asian continents), do include Integral Calculus, Abstract Algebra and some topics of Linear Algebra such as Determinants and Matrices in their Higher Secondary curricula. By the time the student reaches the tertiary level of education one must be familiar with these subjects. At the tertiary level, more advanced concepts of Calculus, Differential Equations and their applications to Laplace Transforms, Numerical Analysis, Operations Research, and many topics in Statistics may be taught in depth. More advanced disciplines of Mathematics such as Real and Complex Analysis, Metric and Vector Spaces, Homological Algebra, Topology, Special Functions, Number Theory, Graph Theory and its applications, Differential Geometry, Theory of Manifolds etc. are usually taught at postgraduate level but some of the universities in the Middle East, Africa, Asia and Latin America offering 3 to 4 year degree programmes do include some of the above subjects in their degree programmes as well. 5. Our Department basically offers service subjects in Mathematics and Statistics in order to cater for the needs of Engineering and other students. It also offers 2-year Diploma Programme and subsequent (2-year) Degree Programme in Computer Science. There is a dire need for qualified teachers to handle a number of mathematics courses. The Department has only 10 teachers (5 PNG nationals and 5 expatriates including the speaker) in Mathematics and 3 (2 PNG nationals and one expatriate) in Computer Science. It is a heavy load teaching around 33 subjects to nearly 1500 students with such meagre manpower. In order to start postgraduate programmes the Department needs more qualified staff. However, we are hopeful to start some postgraduate courses in Mathematics in Diploma Programme in the coming years. 6. The past century has witnessed tremendous explosions and revelations of knowledge especially in terms of the marvellous development in the field of Computer Science. It is well established now that the exploration in the field of Internet has surpassed all the frontiers of knowledge. It is highly desirable that an introductory course on Computers be taught at the Higher Secondary level. It is heartening to note that the Unitech is already offering CISCO-UNIX Certification course to the job-oriented learners. 7. In my concluding remarks I wish to emphasize that some innovations are immortal and they gain no age. Of late, British schools started teaching some principles of “Vedic Mathematics” which were propounded by ancient Indian scholars many thousand years back. The oldest book ever written by mankind on this planet, the Rigveda, deals with 16 computing formulae, so-called “Sulba Sutras”. The first of these called “Ekadhiken Poorven” magnificently describes the simplest way to get the accurate value of the fraction 1/19 (up to 18 decimal places) without carrying out actual division process: 1 / 19 = ·0526 3157 8947 3684 21. Remarkably enough, the above “Sutra” (the formula) was given by an intellectual brain. Surprisingly, it gained the attention of the scholars of the Western world so late. In the end, I thank the audience for patiently listening to the exposition of one of the most challenging disciplines. Unitech, Lae (PNG): 28.08.2008 Prof. Dr. R.B. Misra PAGE 4