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Ask people about their experience with mathematics in school, college or university, and they’ll probably say they loved it or hated it. It’s one of those topics that has no grey area for many people, seemingly because it takes many hours of studying to understand. Yet, regardless of people’s feelings towards it, there’s no denying that mathematics has played a significant role in the world.

Like many subjects mathematics has several branches, with applied mathematics being one of them. By definition, applied maths consists of the application of mathematics to problems found in areas such as engineering, science and other diverse fields. It also encompasses the study of mathematical models that can be used in practical situations.

Throughout history, practical applications have spurred the development of mathematical theories; these then become a study topic in pure mathematics. In this way, the subject becomes a point of interest to students and professionals alike, including Othman Louanjli, a private banker who works in the United Arab Emirates.

A Bit of History

In the early days, applied mathematics was made up of methods such as differential equations, applied probability and approximation theory. These areas had a direct relation to the progress of Newtonian physics, keeping in mind that the difference between physicists and mathematicians was not quite clear before the middle of the 19th century. Also, subjects such as classical mechanics were often taught in applied math departments at universities in the United States instead of physics departments. However, over the centuries applied mathematics has gained a clearer definition, and includes subjects such as mathematical finance and related topics taught in computer science and engineering departments.

Around the world, there is no consensus on the specific branches of applied mathematics – partly because of the way science and mathematics change over time – or how academic institutions organise their courses and departments. The term “applied mathematics” is therefore often used in a broad sense that includes some of the traditional areas mentioned, but also fields that apply mathematics heavily such as cryptography, even though they may not be considered part of applied mathematics per se. This view has led to some divisions within the field of mathematics, with some mathematicians denying “applied mathematics” as a field and claiming there are only applications of math.

The growth of technology has brought about new applications including the study of computer technology (computer science) to study issues that arise in other scientific areas (computational science) and the mathematics of computation (for example, numerical analysis and computer algebra). Statistics is perhaps the most widely used mathematical science, but there are other areas of mathematics such as economics that are highly useful in the modern world.

Pure Vs. Applied Mathematics

If you’re studying mathematics, there might come a point where you’ll choose between pure and applied mathematics. One of the easiest ways to differentiate between the two is to think of pure maths as mathematics “done for its own sake,” while thinking of applied math as mathematics which has a practical use. At a more detailed level, however, even abstract mathematical methods can be applied practically. For example, number theory, once considered relatively useless in mathematics, is a vital aspect of computer encryption.

Status in Academia

As mentioned, academic institutions are notoriously inconsistent in the way they consider applied mathematics in their degrees, programs and courses. Some schools have a single mathematics department, while others will have separate departments for Pure Mathematics and Applied Mathematics. Similarly, Statistics departments tend to be separate at institutions with graduate programs, but those with undergraduate-only programs tend to have statistics within a larger mathematics department.