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Tuesday, January 05, 2016

Counting on applications by Dr Liew How Hui

Photo: Liew How Hui
Dr Liew How Hui, assistant professor with UTAR’s Department of Mathematical and Actuarial Sciences summarizes, "The advancement of technology depends very much on mathematical inputs and solutions."

IT may not be so straightforward to explain the applications of mathematics to a non-science background layman because the mathematical theory of an engineering product is quite complicated.

For example, the mathematical theory behind a computer and a smart phone is Boolean algebra and state machines. It will take time and knowledge to understand the details of the theory.

Interestingly, countries such as USA, Korea, Japan and China are able to develop advanced engineering products, and one of the main reasons is that they have many experts with strong mathematical knowledge.

The USA has the largest number of mathematicians in the world. Knowledge and understanding in Mathematics is key to many applications in life especially in the field of engineering, information technology, software development and many more.

Fast Fourier transform, wavelet transform, error detection and correction techniques are all about mathematics. They are behind modern digital audio, picture and video compression technology. We are enjoying MP3, JPEG, and MP4 all because of these signal processing mathematical knowledge.

Diagram 1: Various Waveforms

Two mathematical subjects – Probability Theory and Statistics – are used in many places including the insurance industry, health and medical industries and marketing survey industries. The statistical analysis of public health data is the foundation for national health management.
National health institutes will normally carry out a survey on the lifestyle of the general public to learn how our lifestyles are affecting our health or to learn the distributions of certain diseases.

With the outcomes from the data analysis, our government can implement national health budget and control by allocating the right amount of budget in support of public health.

In medical industries, sophisticated design and experimental techniques from statistics are required to make sure the new medicines are effective with minimal experiments.

To understand how a medicine works, for example in the medication for suppressing HIV viruses, sometimes very complicated dynamical system modelling involving differential equations may be used.

Even graph theory, a mathematical subject considered to be “pure”, has been applied to kidney matchmaking and have saved many lives.

Diagram 2: Basic components of Hodgkin–Huxley-type models.

Mathematics is not only employed in engineering and medical industries, but also in environmental science to study the distribution of species, the changes in climates and modelling the propagation of pollution.

With more and more human activities, pollution and deforestation, statistical analysis shows that many subspecies have gone extinct and many species are on the brink of extinction.

Scientists are trying to build more accurate models to understand the dangers of pollution, global warming and the deforestation to human population growth and economic growth.

So far, there are very few results because the mathematical models are either too complicated or too simple to provide proper predictions.

The current engineering practice does not take environmental issues and sustainability into account as yet.

Source: The Star Online 

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