Blog (mostly math)

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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

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

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