Mastering Mathematical Modeling: From Problem Analysis to Solution

The core of mathematical modeling is to build a mathematical model that describes a problem. The process can be divided into two phases: the first constructs the model, the second analyzes and utilizes it.

In the model‑building phase, we first thoroughly analyze the problem: its objectives, existing conditions, needed information, and which factors are important or can be ignored. This analysis yields a simplified problem scenario, similar to a high‑school word problem with clearly stated conditions and requirements.

Based on the simplified scenario, we express the quantities using mathematical symbols to facilitate computation and organization. Leveraging our understanding of the problem and mathematical rules, we arrange these symbols into more complex structures such as equations, systems of equations, or functions—a process often called “mathematization.”

When we have constructed a mathematical structure capable of solving the problem, the model‑building stage is temporarily concluded.

Analysis and utilization of the mathematical model involve examining its characteristics, determining solution methods, and interpreting results to answer the original question.

Of course, solutions are often not achieved in a single step; during model construction we may encounter excessive variables, infeasible solutions, unreasonable results, or other issues, prompting us to revisit and adjust earlier steps. Below is a visual illustration of the mathematical modeling process: