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 22 Feb 2026 - 2 minute read
Updated: 22/2/26 Ref: Functional Analysis lectures by Casey Rodriguez. Lecture on the Open Mapping Theorem. Link to the lecture: Link. “Introductory Functional Analysis” by Kreyszig. Let ${ B _1, B _2 }$ be Banach spaces. Let ${ T \in \mathcal{B}(B _1, B _2) }$ be a continuous linear operator. Suppose ${ T }$ is biject... Read more 19 Feb 2026 - 5 minute read
Ref: UPenn Coursera courses on Business. Link to UPenn Coursera page: Link. Link to UPenn MBA curriculum: Link. Link to UPenn Finance courses: Link. ROUGH NOTES (!) Updated: 23/2/26 Course-2: Introduction to Corporate Finance Instructor: Prof. Michael Roberts. Book: “Corporate Finance” by Berk, DeMarzo. Time Value of Money. Link to off... Read more 16 Feb 2026 - less than 1 minute read
Ref: “Discrete-Time Markov Chains and Monte Carlo Methods” by Jem Corcoran. Link to the Course: Link. ROUGH NOTES (!) Updated: 3/2/26 A stochastic process is a time indexed collection of random variables. For example, ${ X _0, X _1, X _2 \ldots . }$ For now, we will consider discrete time and discrete random variables. The random variable... Read more 03 Feb 2026 - 6 minute read
Ref: “Introduction to Hilbert Spaces” by Debnath, Mikusinski. Link to James Cook’s video lectures: Link. ROUGH NOTES (!) Updated: 4/2/26 \[{ \underline{\textbf{Lebesgue Integral}} }\] Sections: Read more 29 Jan 2026 - less than 1 minute read