Ref: “A simple proof that ${ \pi }$ is irrational” by Niven. Link to paper: Link. Math StackExchange posts here, here. Updated: 15/3/26 Belated Happy ${ \pi }$ Day! [Inner product of a polynomial with ${ \sin(x) }$] Let ${ P(x) }$ be a polynomial. Note that \[{ \small {\begin{aligned} &\, \underline{\int P(x) \si... Read more 15 Mar 2026 - 2 minute read
Ref: “Linear Algebra” by Lax. ROUGH NOTES (!) Updated: 15/3/26 We will study \[{ \boxed{\textbf{Convexity}} }\] \[{ }\] \[{ \underline{\textbf{Convex Sets}} }\] Def [Line Segment] Let ${ X }$ be a (real) vector space. Let ${ x, y \in X . }$ The line segment with endpoints ${ x }$ and ${ y }$ is \[{ [x, y] = \lbrace x + a ( y - ... Read more 15 Mar 2026 - 4 minute read
Esse quam videri. “To be, rather than to seem”. Read more 14 Mar 2026 - less than 1 minute read
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