A Theoretical Study of Modelling and Simulation in Mathematical Sociology: Future Directions and Challenges

Abstract

Mathematical Sociology was established as an interdisciplinary field of research concerned both with the use of mathematics within sociological research as well as research into the relationships that exist between maths and society. Mathematical sociology utilizes mathematical and computational tools to analyse social phenomena, providing valuable insights into complex social systems. It forms a complementary sphere from disciplines like the sociology of knowledge and science that tries to understand the social roots of mathematics as well as the impact of maths has imposed on the society. This paper provides a comprehensive review of recent developments and studies in the field of mathematical sociology. The review covers key areas of research, including social networks, collective behavior, social dynamics, and modeling approaches. Various studies are examined, highlighting their contributions and methodologies. The paper concludes with future directions and challenges for the field.