Pure Mathematics, as part of the mathematical sciences, is a focus of study that focuses on the study of mathematics abstractly and theoretically, without considering practical applications in the real world. This group includes various fields of study, such as algebraic structure, topology, geometry, and number theory, where pure mathematics is used as a tool to understand fundamental concepts in the mathematical world. The main goal of pure mathematics is to develop a deeper understanding of mathematical structures, identify relationships between various mathematical concepts, and solve theoretically difficult problems. At a higher level, pure mathematics tries to answer fundamental questions and look for patterns underlying various mathematical phenomena. Pure mathematics also plays an important role in forming the conceptual foundation for various sciences and technologies. The abstract concepts developed in pure mathematics often provide a strong theoretical foundation for research and innovation in computer science, physics, economics, and many other fields.

Statistics, as a subfield of mathematics, addresses the study of data collection, analysis, and interpretation. Its main focus is on the development of methods and techniques that enable the formulation and testing of hypotheses, model building, prediction of phenomena, and identification of patterns in data. Statistics has wide and deep applications in areas such as science, business, health, social sciences, economics, and many more. One of the key aspects of statistics is data collection, which involves methods to gather relevant and representative information. Once the data is collected, statisticians use various techniques to analyze and understand the patterns and information contained in the data. These include central measures (such as mean, median, mode), calculations of variation (such as standard deviation), and data visualization (such as charts and graphs). Statistics also plays a role in developing mathematical models to represent and predict phenomena. These methods include the use of probability distributions and probability theory to assess the level of confidence in predictions. Regression analysis, time series analysis, and statistical inference methods are examples of techniques used to apply mathematical models to data.

Operations Research, as a subfield of applied mathematics, has a primary focus on the application of mathematics to solve various problems and improve the efficiency of operations in various organizations and industries. Studies in this area include the development of mathematical models, quantitative analysis techniques, and the utilization of specialized software to design optimal solutions to the challenges at hand. One important aspect of Operations Research is the development of mathematical models. These models reflect situations and problems encountered in areas such as manufacturing, transportation, logistics, finance, and healthcare. The models are designed to represent the processes involved and the variables that influence decisions within them. In addition, quantitative analysis techniques are the cornerstone of Operations Research. The application of mathematical and statistical methods helps in the analysis of relevant data and making more informed decisions. The use of algorithms and optimization techniques helps to find the best solution in the context of specific constraints and objectives. The main goal of the Operations Research discipline is to improve organizational performance and efficiency by using data and mathematical methods to optimize business decisions. Engagement with experts in other fields is essential, as the problems faced are often complex and require an interdisciplinary approach to create the most effective solutions.

Computational mathematics focuses on the use of computers and information technology to solve mathematical problems. It involves the development of algorithms, computer programming and simulation techniques to tackle complex and challenging mathematical problems. One of the key aspects of mathematical computing is algorithm development. Algorithms are structured steps or procedures designed to solve a specific mathematical problem. By developing efficient algorithms, mathematicians can create faster and more accurate solutions to a variety of complex problems. Computer programming is also an element of this scientific group. Through programming, mathematicians can implement mathematical algorithms and methods into machine language that can be executed by computers. This makes it possible to solve problems that require large and complex calculations. The main goal of this scientific group is to speed up the solution of mathematical problems that are difficult or even impossible to do manually. Mathematical computing also aims to create new solutions that may not have been thought of before.