Mathematical modeling is a process of describing actual phenomena with mathematical language. The actual phenomena here include both concrete natural phenomena, such as free fall, and abstract phenomena, such as customers' value tendency to a certain commodity. The description here includes not only the description of external form and internal mechanism, but also the prediction, experiment and explanation of actual phenomena.
We can also intuitively understand this concept: mathematical modeling is a process that makes pure mathematicians (mathematicians who only study mathematics and don't care about its application in practice) become physicists, biologists, economists and even psychologists.
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A mathematical model is generally a mathematical simplification of actual things. It often exists in an abstract form close to the real thing in a sense, but it is essentially different from the real thing. There are many ways to describe an actual phenomenon, such as recording, video recording, metaphor, rumors and so on.
In order to make the description more scientific, reasonable, objective and repeatable, people use a generally accepted strict language to describe various phenomena, which is mathematics. What is described in mathematical language is called a mathematical model. Sometimes we need to do some experiments, but these experiments often use abstract mathematical models as substitutes for actual objects and carry out corresponding experiments. The experiment itself is also a theoretical substitute for the actual operation.