João Victor · Aug 9, 2023
Nowadays, with the popularization of computers, mathematical problems that were once difficult to solve have become easy with the use of programming and computational applications. We take as an example the use of computational methods in numerical calculus. With the fast processing of computers, all areas of science have been using computational methods and techniques in problem-solving.
Computational mathematics introduces how to solve some mathematical problems numerically, that is, without seeking an analytical solution, either because one does not exist, or because it is not easily obtained. It is also important to note that there is both theory and practice in computing, as well as mathematics. It is not enough to only understand how to solve problems with the computer, but also what limitations are imposed by the computer.
The use of computational mathematics brings many benefits, such as the use of software to simulate production, when used in machine parts to measure for printing, avoiding excessive spending and waste of residues. Also, it can be used to calculate a possible outcome of a betting game or a car crash to analyze the architecture and structure of the car.
Programming for mathematical purposes is not a recent thing anymore, since the late 90s it has been used to solve many problems. Many of the things written today in several advanced fields of mathematics, physics, and engineering use these tools. On the other hand, these languages are reasonably more complicated to use, and nowadays we have several programming languages that are focused on or facilitate the development of mathematical software. An important characteristic of these languages is that they are high-level, that is, they are easier to use and read.
For example, we have the Scilab language, which is a high-level programming language oriented towards numerical analysis. The language features an environment for interpretation, with several numerical tools. Complex algorithms can be created in just a few lines of code. Another widely used language is Python, which is a programming language widely used in web applications, software development, data science, and machine learning (ML).
In today's world, the field of machine learning and data science is an excellent result of years of computational mathematics. We have the direct impact of its applications in our daily lives with autonomous programs, statistics, accurate predictions, and even autonomous cars.
Therefore, the use of programming in the mathematical field is very important and useful for solving problems previously seen as impossible or impractical. Its use has had a significant impact on our current world and has resulted in a more developed society with the benefits of its application in daily life.
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