Updated: 16/11/25 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 “Foundations of Applied Mathematics” by Humpherys, Jarvis “Undergraduate Algebra” and “Undergraduate Analysis” by Lang. “Introdu... Read more 13 Mar 2025 - 1 minute read
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 05 Feb 2025 - 11 minute read
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 11 Oct 2024 - 78 minute read
Link to previous part ROUGH NOTES (!) Second derivative; Third derivative; Higher derivatives; Taylor’s theorem; Inverse function theorem; Implicit function theorem Back to top. \[{ \underline{\textbf{Second derivative}} }\] Def [${ C ^2 }$ maps]: Let ${ E, F }$ be complete normed spaces, and ${ f : U (\subseteq E \text{ open}) \to F .}$... Read more 31 May 2024 - 84 minute read
Link to previous part ROUGH NOTES (!) Integration of maps ${ f : [a, b] \to E }$; Mean value theorem Back to top. \[{ \underline{\textbf{Integration of maps } f : [a, b] \to E} }\] The goal is to study integration of maps ${ f : [a,b] \to E }$. Recall if a map is uniformly continuous and into a complete space, the domain of definition c... Read more 31 May 2024 - 51 minute read