MATHEMATICAL MODELING AND ITS REAL-WORLD APPLICATIONS
Keywords:
Mathematical modeling, machine learning, artificial intelligence, data-driven models, optimization, predictive modeling, multiscale modeling, stochastic models, real-time systems, quantum computing, interdisciplinary collaboration, environmental modeling, healthcare modeling, big data analytics, deep learning, epidemiology, sustainability, artificial life, evolutionary algorithms, social systems modeling, personalized medicine.Abstract
Mathematical modeling is a powerful tool used to represent real-world systems and phenomena through mathematical formulations. It allows for the analysis of complex processes in various fields such as engineering, economics, medicine, and environmental science. This article provides an overview of the fundamentals of mathematical modeling, its real-world applications, challenges faced in model development, and emerging trends in the field. By exploring different types of models and their applications, the paper highlights the critical role of mathematical modeling in solving contemporary problems and optimizing decision-making processes.
References
1. Rasmussen, S. & Toft, P. (2020). “Mathematical Modelling in Science and Engineering.” Springer.
2. Gershenfeld, N. (2016). “The Nature of Mathematical Modeling.” Cambridge University Press.
3. Stewart, J. (2019). “Mathematics of Modeling and Simulation.” Wiley & Sons.
4. Cohen, A. & Martin, B. (2018). “Data-Driven Models and Mathematical Techniques.” Oxford University Press.
5. Nocedal, J., & Wright, S. (2006). “Numerical Optimization.” Springer.
6. Kou, G., & Shi, Y. (2021). “Machine Learning in Mathematical Modeling: Approaches and Applications.” Springer.
7. Zhang, L., & Li, X. (2020). “Predictive Modeling and Machine Learning in Healthcare.” Elsevier.
8. Angus, D., & Zhang, Z. (2017). “Optimization Methods and Mathematical Models.” Wiley-Blackwell.
9. Liu, L., & Wang, Y. (2019). “Multiscale Modeling: Techniques and Applications.” Cambridge University Press.
10. Bryson, A. E. (2017). “Control and Optimization in Mathematical Models.” SIAM