About Applied Math

There can be a common misconception about the phrase “applied math”. Contrary to the prevalent belief that applied mathematics involves the application of mathematics to other fields, it is actually the reverse. In reality, applied mathematics involves using concepts and methods from other disciplines within the framework of mathematics. This is better understood when considering the difference between the terms ‘applied math’ and ‘mathematical application’. The former implies a broader scope where external concepts are integrated into mathematical contexts, while the latter suggests a more limited view where mathematics is merely applied as a tool in various fields.

One clear example of this integration in applied mathematics is the visualization of solution sets. These visual representations significantly aid in understanding the qualitative behavior of solutions to equations, be they algebraic or differential, which would be otherwise quite challenging to comprehend quantitatively. Through visualization, abstract mathematical concepts become more tangible, allowing for a deeper and more intuitive understanding. This is not just about applying mathematical techniques elsewhere; rather, it is about bringing in elements from fields like graphic design and computer graphics to enrich the study of mathematics.

Another example is the use of algorithms and machine learning to optimize mathematical problem-solving. Here, computational and statistical methods are employed to tackle mathematical challenges, demonstrating a fusion of computer science, statistics, and mathematics. This synergy is not about using mathematics to enhance computing or statistics, but rather about utilizing computational power and statistical techniques to achieve better results in mathematical problems. This integration shows how applied mathematics is not a one-way street of applying mathematics to other areas, but rather a collaborative intersection where various disciplines contribute to and enrich the field of mathematics itself.