Historical Problems from China Undergraduate Mathematical Contest in Modeling with MATLAB Code Solutions

The China Undergraduate Mathematical Contest in Modeling (CUMCM) has consistently served as a prestigious platform for mathematical talent development over numerous years. Throughout its history, the competition has attracted exceptional students who demonstrate advanced problem-solving capabilities through complex mathematical modeling challenges. MATLAB has emerged as a critical computational tool for participants, providing robust environments for implementing numerical algorithms, statistical analysis, and optimization techniques. Competitors frequently utilize MATLAB's specialized toolboxes including Optimization Toolbox for constraint handling, Statistics and Machine Learning Toolbox for data pattern recognition, and Symbolic Math Toolbox for analytical computations. Typical implementations involve matrix operations for linear algebra problems, finite difference methods for differential equations, and graph theory algorithms for network optimization. The programming environment enables efficient data visualization through plotting functions and supports algorithm validation through Monte Carlo simulations. The integration of MATLAB in CUMCM has significantly enhanced participants' technical capabilities, fostering deeper understanding of computational mathematics and promoting cross-disciplinary applications. This synergy between mathematical theory and programming practice has contributed substantially to the competition's academic rigor and continuous innovation in problem-solving methodologies.