Blog (mostly math)

Open Mapping Theorem

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 bijective. Is ${ T }$ a ... Read more

Business-2 Finance-2

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: 16/2/26 Course-2: Introduction to Corporate Finance Instructor: Prof. Michael Roberts. Read more

Post

Speculation. The Brain partly runs a supervised learning algorithm. Having role models is beneficial. Read more

Markov Chains

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

Lebesgue Integral

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