Blog (mostly math)

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

${ F = m a }$

The goal is to study “forces”. Can we quantify “forces”? Consider a wooden block on a smooth horizontal surface. Suppose the wooden block is initially moving from west to east with a velocity ${ \vec{v} . }$ i) Note that if no “force” acts on it, it will continue to move with this velocity indefinitely. ii) Suppose a constant “force” acts on... Read more

Mæth

Updated: 27/3/25 Link to Youtube channel: Mæth. The goal is to study Mathematics in an Inquiry based approach. \[{ \underline{\textbf{Reading List}} }\] Inquiry based approach. Mathematics and Data Science “Undergraduate Algebra” and “Undergraduate Analysis” by Lang. “Introductory Real Analysis” by Kolmogorov, Fomin. “Modern Geometry... Read more

Finite Abelian Groups

Updated: 22/2/25 Ref: “Undergraduate Algebra” by Lang. The goal is to study the structure of finite abelian groups. Let ${ (A, +) }$ be a finite abelian group. We can ask ourselves: Can we express ${ A }$ in terms of its subgroups? Note that for every integer ${ n \in \mathbb{Z} _{> 0} }$ there is a group homomorphism ${ \varphi _n : A \t... Read more

Differentiation-4

Link to previous part ROUGH NOTES (!) Regular points; Manifolds; Tangents and Normals Back to top. \[{ \underline{\textbf{Regular points}} }\] The goal is to study the zero sets of ${ C ^P }$ maps ${ f : U (\subseteq \mathbb{R} ^n \text{ open}) \to \mathbb{R} ^m . }$ Obs [Implicit function theorem for ${ C ^p }$ maps ${ \mathbb{R} ^n \t... Read more