Blog (mostly math)

Entropy Power Inequality

Ref: “On the similarity of the Entropy Power Inequality and the Brunn Minkowski inequality” by Costa, Cover. “The Convolution Inequality for Entropy Powers” by Blachman. “Simple Proof of the Concavity of the Entropy Power with respect to added Gaussian Noise” by Dembo. “Stochastic Models, Information Theory, and Lie Groups, Vol 1” by Ch... Read more

Cartan-Dieudonne

Ref: Marc van Leeuwen’s answer here: Link. Let ${ E }$ be an ${ n }$ dimensional Euclidean space. What are the origin and distance preserving maps ${ f : E \longrightarrow E }$? Obs: Let ${ E }$ be an ${ n }$ dimensional Euclidean space. Let ${ f : E \longrightarrow E . }$ Then the following are equivalent: ${ \lVert f(x) - f(y) \rVe... Read more

Theoretical Minimum

Link to Courses: Link. ROUGH NOTES (!) Updated: 4/4/25 The Milky Way Galaxy. Read more

CS50

Link to Course: Link. ROUGH NOTES (!) Updated: 5/4/25 Week 0. Scratch. What is Computer Science? Computer Science is the study of information. How we represent it, and how we process it. What is Problem Solving? \[{ \text{Input} \to \blacksquare \to \text{Output}. }\] Can we represent the inputs and outputs? Eg: Consider counting, repr... Read more

Book Series

Updated: 24/7/25 Mathematics Serge Lang’s books. “Mathematical Analysis, Vols 1 and 2” by Zorich. “Elements of Mathematics, Vols 1 to 12” by Bourbaki. “Treatise on Analysis, Vols 1 to 8” by Dieudonne. “Analysis, Vols 1 to 4” by Godement. “Analysis, Vols 1 to 3” by Amann, Escher. “Analysis, Vols 1 and 2” by Tao. Baby Rudin, Papa... Read more