To understand the usefulness of "applied mathematics," one needs to know what that simply means.
This is the type of mathematics that uses the abstract to solve concrete problems in sciences, businesses, and other areas. In short, applied mathematics is "social mathematics." There are many different fields of applied mathematics. One should not be thinking about the board term.
One should think about the usefulness of the different fields of applied mathematics.
The following fields of applied mathematics are: mathematical physics, mathematical fluid dynamics, numerical analysis, optimization, probability theory, statistics, financial mathematics, and game theory.
Mathematical physics is defined as: the scientific discipline interfacing mathematics and physics.
This uses mathematics to solve problems in physics. It uses mathematics for formulas in physical theory.
With that said, mathematical physics combines math and physics. One could ask: How useful would mathematical physics be? It is quite useful as it is important for various fields of physics such as: mechanics, elasticity theory, acoustics, thermodynamics, electricity, and so forth. If you are going into physics, mathematical physics has very valuable uses.
Mathematical Fluid Dynamics or "Fluid Mechanics" is the study of how fluids move and the forces on them. In mechanics, this type of applied mathematics is quite useful.
Numerical Analysis can be used in using numbers to predict the weather. It could use numbers to predict a sunny day, a drought, a heat haze, a hurricane, a tornado, rainy weather, snowy, weather and so forth. Hedge funds also depend on the use of numerical analysis. Airline companies also rely on this type of applied mathematics.
Optimization is the study of problems to minimize or maximize a real function. This type of applied mathematics comes in very handy.
If you are purchasing something, you want to optimize it. In short, you want to get the biggest bang for the buck. If you are prepared for some possible damage, you want to reduce the blow as possible. One could compare that to getting hammered at the bar while trying to reduce the hangover effect the next day.
Probability Theory analyzes random phenomena. This is a type of mathematics that is used in just about everyday life. So far, many gamblers let alone mathematicians rely on this type of applied mathematics when going to the casino. They use this to win big on card games like poker and blackjack.
Many professional card players are known programming experts and mathematicians.
Statistics is the science of collecting, analyzing, interpreting, explaining, and presenting data.
In short, it deals in data. This is one type of applied mathematics that one will use in everyday life. What is the use of statistics? There are many different uses. One example would be political polling in which pollsters interview people and collect information on a variety of subjects. Political campaigns keep track of the different polls. If you are doing business, you have to research the statistics.
Statistics play a major part of everyday life.
Financial Mathematics has many uses. This deals with the financial markets and financial economics. If you are dealing in business, you will have to use financial mathematics. If you are a chief financial officer (CFO) of a business, you will have to use financial mathematics. If you play the stock market, you will have to use financial mathematics.
Game Theory has many uses.
Perhaps this could be one of the most useful of all applied mathematics. This is applied mathematics used in social sciences. In short, this could be called "social mathematics." It is quite the valuable type of applied mathematics in which it attempts to use mathematics to capture behavior in strategic situations.
It has its uses in politics, economics, businesses, philosophy, and so forth. While I do not like mathematics much, I have come to appreciate the use of game theory. This is the type applied mathematics that I employ a whole lot. With the information, variables, and constants given to me, I am able to make near perfect predictions and take highly calculating risks.
The most calculating of individuals would enjoy employing this method of applied mathematics.
When you look at everything, applied mathematics has its many uses. In fact, applied mathematics has its vital uses in everyday life.
Without using some form of applied mathematics, we would not be able to function in today's world.