What is Computational Math, and How Does it Work?

Computational math is a branch of math concerned with the application of math to computer technology. Computational math is the study of math in areas of science and engineering where computing plays a central role. There are seemingly infinite ways to apply computational math to computer science because so much of the programming and hardware world is based on mathematical operations. Computational math is intertwined with a number of other branches of math, as a better mathematical understanding of a problem frequently leads to novel numerical techniques.1

What are the Applications of Computational Math?

Computational math entails the investigation of problems with applications in engineering, operations research, medicine, and other fields of science. Many issues that affect our daily lives are included, ranging from Internet security and telecommunication networking to school bus and delivery company routes, scheduling tables, and so on. Researchers have recently applied computational methods in a variety of fields, and while summarizing them in a few paragraphs is difficult, the main themes of these works are applications in industry or technology.2

The use of logic gates, which are found on every microprocessor, is one of the most basic examples of computational math’ power. The logic gates are the operational pathways of the computer, directing circuit board activity and allowing for all computations based on inputs. Computational math can be seen as a primary example of mathematical models applied to logic gates, but scientists also apply mathematical concepts to computer science in a variety of ways.1 Other topics include the development of accurate and efficient numerical methods for solving physical or biological models, the analysis of numerical approximations to differential and integral equations, the development of computational tools to better understand data and structure, and so on. Stochastic methods and models, symbolic computation, encryption modeling are some examples of specific methodologies using computational math.3

Computational math has varied applications across different domains and some of its applications are as follows:

• Areas where mathematical and computational advances can be applied to other sciences and, as a result, industrial or technological advancements can be derived: From categorical algebra to formal context analysis, from numerical methods to computer science, and from lattices to relational theory, there is something for everyone.2
• Bioinformatics is a new field that is rapidly developing, thanks to advances in computer science and mathematical methods. In this context, computational math employs machine learning techniques to predict a specific health problem in humans, as well as another that employs pattern analysis to manage a database of leukemia patients.2
• Parallelization and other computational methods contribute to the advancement of other disciplines. Examples of this can be coding theory, partial differential equations, and acoustic analysis.2
• Direct application in industry or technology, such as the creation of a new geomechanical quality index, the production of electricity in hydro plants, the improvement of vine leaf harvesting, or the forecasting of environmental models.2

Computational math is a source of inspiration for gaining a better understanding of the real world. Along with the use of technology and engineering, it has been an undeniable benefit in the development of theories to guide scientific exploration while also resulting in significant advances in the quality of life.

References:

1. What is Computational Mathematics? – Definition from Techopedia. (n.d.). Retrieved June 20, 2022, from https://www.techopedia.com/definition/32721/computational-mathematics
2. Alharbi, A. (2016). COMARA: Computational Mathematics in Real-life Applications Special session at. ADVCOMP. http://www.iaria.org/conferences2016/ProgramADVCOMP16.html
3. Computational Mathematics | Department of Mathematics. (n.d.). Retrieved June 20, 2022, from https://math.duke.edu/research/computational-mathematics