MATLAB Implementation of Monte Carlo Algorithm with Code Descriptions

This documentation presents a MATLAB-based implementation of the Monte Carlo algorithm utilized during my graduation project. The Monte Carlo algorithm is a computational method that employs random sampling to derive numerical solutions to mathematical problems. Key implementation aspects include: - Generation of pseudorandom numbers using MATLAB's rand() and randn() functions - Statistical sampling techniques for probability distribution modeling - Convergence analysis through iterative simulation runs - Result validation using variance reduction methods The algorithm finds extensive applications across multiple domains including computational physics (particle transport simulations), financial engineering (option pricing models), and engineering systems (reliability analysis). The name originates from the Monte Carlo Casino in Monaco, reflecting the random nature inherent in gambling games. The MATLAB implementation features modular code structure with separate functions for random number generation, simulation loops, and data analysis. Core functions include: 1. monteCarloCore() - Main simulation engine handling iterative calculations 2. setupParameters() - Configuration of simulation parameters and bounds 3. analyzeResults() - Statistical processing and convergence monitoring I welcome technical discussions regarding algorithm optimization, alternative sampling strategies, and potential applications in other research domains. The code architecture allows for easy modification of probability distributions and integration with larger simulation frameworks.