Calculus is often seen as a subject full of complex symbols and formulas, but at its core, it’s about understanding change. While derivatives help us measure how things change, antiderivatives do the reverse—they help us reconstruct the original function from its rate of change. In other words, if differentiation is breaking things down, antidifferentiation is putting them back together. What is an Antiderivative? An antiderivative of a function \(f(x)\) is another function \(F(x)\) such that when we take its derivative, we get back \(f(x)\).

Exploring Monte Carlo simulations has always intrigued me because of their real-world applications in areas like physics, finance, and artificial intelligence. And what better place to start than with estimating \(π\)? This seemingly abstract number, 3.14159…, holds a special place in mathematics and everyday life, and Monte Carlo simulations give us an intuitive, probability-based approach to approximate it. And here it is, the journey from the math to the code, with everything in between!

In the world of data science, dealing with uncertainty is a constant challenge. Predicting outcomes, modeling trends, or making decisions based on incomplete data all boil down to one thing: how confident are we in the predictions we make? This is where Bayesian Inference comes into play. It provides a framework for updating our beliefs about a hypothesis as we gather new evidence, allowing us to model uncertainty in a probabilistic and flexible manner.