Ref: Functional Analysis lectures by Casey Rodriguez. Lecture on the Hahn-Banach theorem. Link to the lecture: Link. Updated: 5/3/26 For a normed space ${ V , }$ let ${ V ^{’} }$ denote ${ V ^{’} = \mathcal{B}(V, K) . }$ Q) Given a general nontrivial normed space ${ V , }$ how large is ${ V ^{’} }$? Is it ${ V ^{’} = \lbrace 0 \rbrace }$... Read more 03 Mar 2026 - 5 minute read
How do we know if everything is secretly already determined and unfolds to the T, or if there is randomness in the World? Is randomness an illusion? Does God play dice? Instinctually: Randomness exists in the World. Can we prove it? Read more 26 Feb 2026 - less than 1 minute read
Introduction to Programming Updated: 9/3/26 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{I... Read more 25 Feb 2026 - 17 minute read
Updated: 25/2/26 Ref: Functional Analysis lectures by Casey Rodriguez. Lecture on the Closed Graph Theorem. Link to the lecture: Link. Obs [Product of Banach spaces] Let ${ B _1 , }$ ${ B _2 }$ be Banach spaces. Then ${ B _1 \times B _2 }$ under \[{ \lVert (b _1, b _2) \rVert = \lVert b _1 \rVert + \lVert b _2 \rVert }\] is a Banach s... Read more 25 Feb 2026 - 2 minute read
Link to Udacity page: Link. List of some Udacity courses: Programming: Introduction to Programming. Data Structures and Algorithms. Front End Web Developer. Backend Developer with Python. Artificial Intelligence: AI Programming with Python. Statistics for Data Analysis. I... Read more 24 Feb 2026 - less than 1 minute read