English
Analysis and calculus
Notes on the core ideas of mathematical analysis and calculus — limits, continuity, differentiation, integration, and infinite series. Each post unpacks not just the mechanics but the intuition behind why things work the way they do. Expect rigorous reasoning alongside concrete examples, with a focus on understanding over memorization. Topics range from foundational concepts to subtler results that often trip people up.
Calculus rarely brings police reports to mind — yet that is exactly what inspired one of the most memorable theorems…
"One could just as well provide Kolmogorov's function."
Yes, such series exist — and there are plenty of them. To understand why they can't be regularized, we first…
Cambridge, January 1913. A parcel from distant Madras arrives on the desk of 36-year-old G. H. Hardy. The sender is…
Mathematics is not just equations and graphs — it is entire universes where simple rules give rise to complex, self-regulating…
Imagine a tool that doesn't just measure speed or acceleration, but "remembers" everything that happened up to the current moment.…