Boiled potatoes and jalapeno mayo. Great stuff. Read more 13 Mar 2026 - less than 1 minute read
[Link to previous post: Link] Ref: “Principles of Analysis” by Junghenn. Let ${ \mathscr{X} }$ and ${ \mathscr{Y} }$ be Banach spaces. Let ${ T : \mathscr{X} \to \mathscr{Y} }$ be a continuous linear bijection. Is the inverse ${ T ^{-1} : \mathscr{Y} \to \mathscr{X} }$ also continuous? Note that continuity of ${ T ^{-1} }$ is equivalent t... Read more 10 Mar 2026 - 6 minute read
Introduction to Programming Updated: 12/3/26 Link to Udacity subscription: Link. Link to Udacity course: Link. All rights of the (often wonderful) images found in these notes go to Udacity unless explicitly noted. We will learn the foundations of four of the most popular languages: HTML, CSS, Javascript, and Python. \[{ \underline{\textbf{... Read more 09 Mar 2026 - 4 minute read
Updated: 11/3/26 Note that \[{ \int _0 ^{1} \frac{1}{1+x ^2} \, dx = \frac{\pi}{4} . }\] This suggests studying inequalities of form \[{ \boxed{ \int _0 ^{1} \frac{P(x) ^2}{1 + x ^2} \, dx > 0 } }\] where ${ P(x) }$ is a polynomial, to get bounds on ${ \pi . }$ Ideally, we want ${ P(x) ^2 }$ to leave a constant remainder on dividing b... Read more 08 Mar 2026 - 3 minute read