MODERN APPROACHES TO MATHEMATICAL MODELING IN PROBLEM SOLVING

Abstract

This article provides a comprehensive overview of modern approaches to mathematical modeling applied in solving complex problems in various scientific and practical fields. It examines four primary modeling methodologies: analytical modeling using differential equations, statistical modeling through regression and probabilistic methods, computer-aided simulations including agent-based models, and advanced artificial intelligence techniques such as neural networks and machine learning. The study discusses the theoretical foundations of these methods and illustrates their practical applications with examples from economics, ecology, engineering, and medicine. Furthermore, the article highlights the significance of developing mathematical modeling competencies among university students to enhance their critical thinking and problem-solving abilities. Challenges related to computational resources and data quality are also addressed. Finally, recommendations are provided for integrating these modern modeling techniques into higher education curricula to foster more effective learning and prepare students to tackle real-world multifaceted problems.