What is mathematical modeling?

Mathematical modeling is the art 

of translating problems from an application

 area into tractable mathematical 

formulations whose theoretical 

and numerical analysis provides i

nsight, answers, and guidance useful 

for the originating application.

Mathematical modeling is indispensable in many applications, successful in many further applications, gives precision and direction for problem solution, enables a thorough understanding of the system modeled, prepares the way for better design or control of a system, allows the efficient use of modern computing capabilities. 

Tasks such as:

Maja has 5 balls, 2 given to Jovan. How much balls does Maya have now?

They are not solved by mathematical modeling.

But tasks like:

You go on vacation with your family. How many towels should you bring with you?

They require more extensive thinking and more things to keep in mind.

-How many members are in the family?

-How much of them will go on vacation?

-How many towels does each one need?

-Will anyone else come with them in the coming days?

and many other issues.

One possible solution:

-There are 6 members in the family.

-4 of them will go on vacation.

-Two of them need 2 towels.

On day 3 they will be joined by the other two family members who need one towel.

This means that they need 8 towels.