A Comprehensive Overview of Calculus A Comprehensive Overview of Calculus: Foundations, Formulas, Applications, and Future Prospects Calculus is a cornerstone of mathematics that deals with change and motion, providing tools to analyze quantities that vary continuously. Developed independently by Sir Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, calculus has become indispensable…
Statistics and probability form a critical branch of mathematics that deals with collecting, analyzing, interpreting, and making decisions based on data, as well as modeling uncertainty and randomness. These fields are foundational to understanding patterns in data and predicting outcomes in uncertain environments. These notes provide a comprehensive overview of statistics and probability, their significance,…
Linear algebra is a foundational branch of mathematics that studies vectors, matrices, linear transformations, and systems of linear equations. It is a cornerstone of both pure and applied mathematics, with extensive applications across numerous fields, from computer science to physics to economics. These notes provide a comprehensive overview of linear algebra, its significance, research areas,…
Prime Number Theorem (PNT) – A Short Note Introduction The Prime Number Theorem (PNT) describes the asymptotic distribution of prime numbers among natural numbers. It states that the number of primes less than a given number nn is approximately nln(n)\frac{n}{\ln(n)}. This result provides a deep insight into how primes are distributed across large numbers. Statement…
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