[Link to Stackexchange post: Link] Ref: “A Course of Pure Mathematics” by Hardy. [Product to Sum] Note that computing sums is easier than computing products. Can we have a nice bijective function ${ f : (0, \infty) \to \mathbb{R} }$ such that equations “${ x y = z }$” in ${ (0, \infty) }$ give equations “${ f(x) + f(y) = f(z) }$” in ${ \... Read more 29 Mar 2026 - 5 minute read
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: 17/3/26 We will study \[{ \boxed{\textbf{Convexity}} }\] \[{ }\] In theorem statements, often the vector spaces considered are finite dimensional. \[{ }\] \[{ \underline{\textbf{Convex Sets}} }\] Def [Line Segment] Let ${ X }$ be a (real) vector space. Let ${ x, y \in X . }$... Read more 15 Mar 2026 - 10 minute read
Esse quam videri. “To be, rather than to seem”. Read more 14 Mar 2026 - less than 1 minute read