MATHEMATICAL FOUNDATIONS FOR SECURE COMPUTING, DATA SCIENCE AND AI: APPLICATIONS OF ALGEBRA, DIFFERENTIAL EQUATIONS, NUMERICAL METHODS AND OPTIMIZATION

Abstract

This paper presents a comprehensive study of the fundamental mathematical principles that support secure computing, data science, and artificial intelligence (AI). By exploring algebraic structures such as groups, rings, and fields, the paper highlights their critical role in cryptographic algorithms that safeguard data privacy and integrity. It further examines the application of differential equations in modeling dynamic systems relevant to network security and signal processing. The use of numerical methods is discussed in the context of approximating solutions to complex problems where analytical methods fall short, enhancing computational accuracy and efficiency. Lastly, the paper emphasizes optimization techniques that drive machine learning models and resource allocation strategies, thereby improving the robustness and performance of AI systems. This multidisciplinary approach underlines the indispensable role of mathematical foundations in advancing secure and intelligent computational technologies.