👉 The document outlines several key mathematical principles and theorems, including the foundational concepts of calculus, linear algebra, probability theory, and number theory. Calculus, particularly differential equations, is used extensively to model dynamic systems and understand rates of change and accumulation. Linear algebra provides the framework for solving systems of linear equations, eigenvalue problems, and vector spaces, which are crucial in fields like data science and machine learning. Probability theory underpins statistical analysis, risk assessment, and decision-making under uncertainty, while number theory explores properties of integers and has applications in cryptography and algorithm design. The document also delves into discrete mathematics, including combinatorics and graph theory, which are essential in computer science and optimization problems. Each of these areas is supported by rigorous mathematical proofs and theorems, ensuring a robust theoretical foundation for their applications.
