Mathematical modeling is the process of creating a mathematical representation of a real-world scenario to make a prediction or provide insight. It involves translating beliefs about how the world functions into the language of mathematics. Mathematical models are used in applied mathematics, natural sciences, engineering disciplines, and social sciences. The process of developing a mathematical model involves identifying the problem, selecting variables, and creating equations that establish relationships between the variables. Mathematical modeling can be used to develop scientific understanding, make predictions, and provide solutions.
Some key features of mathematical modeling include:
- Precision: Mathematics is a very precise language, which helps to formulate ideas and identify underlying assumptions.
- Conciseness: Mathematics is a concise language with well-defined rules for manipulations.
- Computational power: Computers can be used to perform numerical calculations.
- Open-endedness: Real-world problems are often open-ended, which can make mathematical modeling challenging but also allows for creativity, innovation, and problem-solving skills to be developed.
It is important to note that while mathematical modeling uses mathematical concepts and language, it is not itself a branch of mathematics and does not necessarily conform to any mathematical logic, but is typically a branch of some science or other technical subject, with corresponding concepts and standards of argumentation.
