Mathematical Modeling
Mathematical modeling is the use of sophisticated mathematics to analyze and explore real-world problems. Models can range in complexity from simple algebraic equations to complex numerical simulations involving millions of variables and millions of calculations. From physics and engineering to economics and finance, mathematicians strive to use their models to accurately portray reality.
To understand how mathematician use mathematical modeling, let’s look at an example from engineering. Consider an airplane wing. The lift of a wing is determined by a number of factors including its shape, surface area, and air velocity. To determine the optimal wing design, mathematicians create models to simulate the various forces acting on the airplane and predict how it would behave in the real world. The model may consider wing shape, air velocity, and a multitude of other parameters to come up with a solution. The result of the analysis can then be used to design a wing that is optimized for maximum lift.
Mathematical models can also be used in economics, helping governments and businesses balance their budgets and make sound financial decisions. For example, economists may use mathematical models to predict how changes in taxes, interest rates, and other policies will affect a nation’s economy. Companies may also use models to forecast their profits and losses over time based on their production costs and other factors.
In addition to measuring tangible economic parameters, mathematical models are also used to measure intangible concepts such as public opinion and societal trends. By asking survey questions and then analyzing the data with mathematical models, researchers can pick up on subtle trends in things like consumer sentiment and public opinion. This can help companies better understand the needs of their customers and make more informed decisions.
Mathematical modeling is also used to explore complex scientific and biological questions. In astronomy, for example, mathematical models can be used to analyze the movements of celestial bodies and predict the future positions of planets and stars. In biology, mathematical models are used to study the behavior of populations, the spread of disease, and the evolution of species.
No matter the field it is used to explore, mathematical modeling can be a powerful tool for understanding and exploring the world around us. From predicting economic trends to forecasting the future positions of planets, mathematicians are using their models to uncover the mysteries of the universe.
