- Introduction to Mathematical Modeling

Over the last several decades, mathematical modeling has been playing a major role in understanding and solving many real-life problems, under certain conditions. Most mathematical models have been like individual works of art that reflected the scientific views and personal characteristics of the modeler. However, many attempts are being made to unify the mathematical models in order to provide a standardized and reliable method of investigation accessible for every scientist. Modeling is a multistep process involving the following: i. Identifying the problem ii. Constructing or selecting the appropriate model iii. Figuring out what data need to be collected iv. Deciding the number of variables and predictors to be chosen for greater accuracy v. Analytically or numerically computing the solution and testing the validity of models vi. Implementing the models in real-world situations Usually, modeling is an iterative process in which we start from a crude model and gradually refine it until it is suitable for solving the problem, and modeling enables us to gain insight into the original situation. The purpose of the model is to understand the underlying phenomenon and perhaps to make predictions about future behavior. If the predictions do not compare well with reality, we need to refine our model or formulate a new model and start the cycle again.