The advent of social media has catalyzed a paradigm shift in the way information is disseminated and consumed, giving rise to novel phenomena such as viral trends and information diffusion. This review article provides an in-depth scholarly examination of network science as applied to social media analysis, focusing on the mathematical formulations, algorithmic techniques, and interdisciplinary methodolo-gies that underpin the field. By exploring graph theory, community detection, scale-free networks, centrality measures, machine learning applications, and cultural influences, this study offers a comprehensive and nuanced understanding of network structures and dynamics. As a top-tier contribution to the field of computer science, this review serves as a nexus for the interdisciplinary study of network science, providing valuable insights and directions for future research in the analysis of information diffusion and viral trends within social media platforms.
This paper delves into the application of informatics and logic-based solutions to solve Problem 5 of the 2023 International Mathematical Olympiad (IMO). The problem, known as the Japanese Triangle Problem, presents a unique challenge that can be addressed using various informatics techniques , combined with structured logical reasoning.
This paper offers a comprehensive examination of Fermat's Last Theorem , a statement in number theory that captivated mathematicians for over 350 years until its proof by Andrew Wiles in 1994. Beginning with historical context surrounding Pierre de Fermat and the theorem's formulation , the paper meticulously reviews the mathematical foundations underlying the theorem, including Diophantine equations, modular forms, and elliptic curves. Special attention is given to Wiles' groundbreaking use of the Taniyama-Shimura-Weil conjecture and Ribet's theorem to provide a complete proof, including the resolution of an initial flaw in the proof. Furthermore, the paper explores the theorem's far-reaching implications in number theory, algebraic geometry, cryptography, and computer science. The study reveals that Fermat's Last Theorem is not just an isolated mathematical problem but a testament to the depth, beauty, and inter-connectedness of mathematics, with broad impact across various scientific disciplines.