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Are mathematical modeling and mathematical model the same?
It's different!

Mathematical modeling is to solve practical problems with mathematical models.

Mathematical model is the product of mathematical abstraction, and its prototype can be concrete objects and their properties and relationships, or mathematical objects and their properties and relationships. Mathematical models can be divided into broad sense and narrow sense. In a broad sense, mathematical concepts, numbers, sets, vectors and equations can all be called mathematical models. In a narrow sense, mathematical models can be roughly divided into two categories: (1) deterministic models that describe the inevitable phenomena of objects, and their mathematical tools are generally algebraic equations, differential equations, integral equations and difference equations, (2)