# Art of Modelling in Mathematics

Mathematics is a very precise language with well-defined rules for manipulation. As like other languages we can express the real-world problems we are facing in a mathematical language which is retermed as Mathematical Modelling. **Mathematical modelling** is the art of framing a tractable **mathematical** relation which leads to solution, answers, analysis, and prediction to real world problems. It is a vast multidisciplinary field that leads to solution starting from a small, simpler problems to large kind of problems. Mathematical modelling plays a significant role in our technology-based world starting from weather prediction, moving to high-speed computers, simulation, and design of control systems, predicting the biological processes, for scientists in space research, launching satellites, compounding the money in business etc.,

In this pandemic situation, basic SIR Model (number of susceptible, infectives and removed) along with the inclusion of other factors is used widely. Mathematical modelling helps Centers for Disease Control and Prevention (CDC) respond to the COVID-19 pandemic by informing decisions about pandemic planning, resource allocation, and implementation of social distancing measures and other interventions. You can see this information in the official website: https://www.cdc.gov/coronavirus/2019-ncov/covid-data/mathematical-modeling.html

Engineers without basic Mathematical knowledge in certain areas will not be able to find solution to the problems in their field. To frame a Mathematical model for a particular problem, one should understand the problem clearly, know the mathematical concept underlying in it, have a knowledge on mathematical part and then only able to develop a model.

Most of the models in Science and Engineering involves differential equations which involves laws in Physics. To solve differential equations of higher order, we are using eigen values and eigen vectors which needs the support of linear Algebra. So, mathematical model links different areas of mathematics with respect to different fields.

Another simple example for you. Water pollution is happening in more places. If three to four ponds are interconnected and let one pond be polluted. What happens to the remaining ponds if the water flows from one pond to another and how much each pond will be polluted? A simple mathematical model involving differential equations will give solution to the above issue.

Intelligence is the ability to adapt to change