Pure Mathematics is a discipline of mathematics that emphasizes the abstract and theoretical study of fundamental mathematical concepts. This group includes the study of algebraic structures, topology, geometry, number theory, and other high-level mathematical concepts. The main goal of pure mathematics is to understand mathematical structures more deeply, identify and understand the relationships between various mathematical concepts, and solve complex mathematical problems theoretically. The study of pure mathematics is often abstract, without considering practical applications in everyday life. Pure mathematicians are interested in logic and mathematical deduction, and develop theorems that form the basis of modern mathematics. The thinking and research in pure mathematics led to profound and fundamental new discoveries, which often became the foundation for the development of further mathematical theories. The contribution of pure mathematics to the advancement of science and technology cannot be ignored. Although its study is initially more theoretical in nature, its results often have wide applications in many fields, including physics, engineering, economics, and informatics. Discoveries in pure mathematics can pave the way for the development of new technologies, optimization of industrial processes, and solving complex problems faced by society.

Statistics, as a subfield of mathematical science, delves into the collection, analysis, and interpretation of data. This field allows us to investigate phenomena by collecting data, analyzing emerging patterns, and making predictions based on the results that have been obtained. It also involves developing various statistical methods, techniques, and models to formulate and test hypotheses, identify hidden patterns, and make reliable estimates. One important aspect of statistics is its widespread use in various fields. In the world of science, statistics help researchers analyze the results of experiments and scientific studies. In business, statistics are used to analyze market trends, consumer behavior, and operational efficiency. In the health sector, statistics help analyze clinical data and medical research to improve diagnosis, treatment, and health policy. Additionally, in the social sciences, statistics are used to analyze human behavior, public opinion, and social trends. A strong understanding of statistics enables better and more accurate decision-making. It helps in planning effective strategies, identifying risks, and measuring the efficiency of actions taken. In addition, statistics play an important role in scientific research and experimentation, providing a foundation for data-backed generalizations and conclusions.

Operations Research, as an important subfield of mathematical sciences, focuses on the application of mathematical concepts and techniques to solve problems and improve operational efficiency in various organizations and industries. The group plays a key role in developing mathematical models, applying quantitative analysis techniques, and utilizing specialized software to design optimal solutions. The primary goal of Operations Research is to maximize the efficiency and productivity of organizations, including business, manufacturing, transportation, logistics, finance, healthcare, and many other sectors. Through the application of mathematics, they design systems that can manage resources more efficiently, minimize costs, optimize distribution, and plan the best strategies. One important application example is supply chain management. Research Operations helps plan shipments, devise efficient warehousing strategies, and optimize logistics so that products reach consumers with minimal time and cost. In finance, they help in risk management, portfolio allocation, and investment optimization.

Computing in mathematical sciences takes mathematics to a new level by harnessing the power of computing and information technology to solve complex mathematical problems. It combines mathematics with computer programming, algorithms, and simulation techniques to formulate efficient and effective solutions. One of the main goals of this subfield is to accelerate the solution of mathematical problems that are difficult or even impossible to solve manually. Computers enable extremely fast and high-precision calculations, allowing scientists to better explore vast and complex solution spaces. This is especially important in cases where manual calculations would take days or even months. Applications of mathematical computing are very diverse. One prime example is data analysis, where computation is used to extract patterns and valuable information from large data sets. Physics modeling is another very important application, where computing helps in understanding complex physical phenomena by simulating the behavior of physical systems with a high degree of accuracy.