A COMPREHENSIVE METHODOLOGY FOR DEVELOPING MATHEMATICAL MODELING AND ALGORITHMIC THINKING THROUGH OPTIMIZATION AND COMBINATORIAL ANALYSIS

This article proposes a comprehensive methodology for developing mathematical modeling and algorithmic thinking skills through optimization problems and combinatorial analysis. The approach integrates algebraic structures, elementary calculus, and discrete mathematical methods to enhance students’ ability to analyze complex systems and construct optimal solutions. Special emphasis is placed on step-by-step modeling, functional analysis, derivative-based optimization, and combinatorial enumeration without the use of graphical tools. The methodology provides a structured framework for teaching, including algorithmic decomposition, recursive reasoning, and logical generalization. The effectiveness of the approach is demonstrated through theoretical explanations and practical applications in education.