Blog (mostly math)

Udacity-1 Intro Programming-1 Intro Web Dev

Introduction to Programming Updated: 25/2/26 Link to Udacity subscription: Link. Link to Udacity course: Link. We will learn the foundations of four of the most popular languages: HTML, CSS, Javascript, and Python. \[{ \underline{\textbf{Introduction to Web Development}} }\] Sections: The Web and HTML; [The Web and HTML] HTML is used to ... Read more

Closed Graph Theorem

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

Udacity Courses

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

Post

Grothendieck on being alone. Link to the writing: Link. Read more

Baire Category Theorem

Ref: “Introductory Real Analysis” by Kolmogorov, Fomin. Link to Stackexchange post: Link. Def [Nowhere dense sets] Let ${ (X, d) }$ be a metric space. Let ${ A \subseteq X . }$ We say ${ A }$ is nowhere dense if for every open ball ${ B }$ the set ${ A \cap B }$ is not dense in ${ B . }$ Let ${ (X, d) }$ be a complete metric space. How la... Read more