NP-Incompleteness
Sobolev Spaces
02 May 2026
Continuing with my exploration of understanding physics from first math principles (see previous post on functionals), I wanted to learn more about Sobolev spaces.
These are a type of vector space named after the Soviet mathematician Sergei Lvovich Sobolev (1908-1989), featured on the thumbnail.
[Book] Stream Processing with Apache Flink
28 Apr 2026
In this post I’ll share my notes on the book Stream Processing with Apache Flink by Fabian Hueske and Vasiliki Kalavri.
This book covers many aspects of the popular open-source Apache Flink, a stream processing engine.
Functionals
26 Apr 2026
I started reading the book The Theoretical Minimum by Leonard Susskind and George Hrabovsky. A lot of the math from the early chapters looked familiar, but in Chapter 6: The Principle of Least Action, they describe and derive the Euler-Lagrange equation, which I don’t recall seeing before.
I wanted to explore these equations and their derivation, but from a more mathematical point of view. This led me to a short rabbit hole around functionals and Sobolev spaces and since I like learning things from first principles, I decided to cover functionals first.
[Book] Complex Analysis
05 Apr 2026
In this post I’ll share a summary on the book Complex Analysis by Lars V. Ahlfors, and my journey in studying it.
I’ll start with the journey because I think it’s the more interesting. The second part is basically a link to all the posts I wrote from studying this book.
The Weierstrass ℘ Function
04 Apr 2026
In our post on Elliptic functions [2] we started with the simply periodic functions such as $\sin z$. We noted that $e^{2\pi i z} / w$ is the simplest of the periodic functions and that every single simply periodic function $f(z)$ of period $w$ can be written as a function of it: $f(z) = g(e^{2\pi i z} / w)$.
Then we introduced doubly periodic functions, also known as elliptic functions. One may ask if there is, analogously, the simplest elliptic function and whether it’s possible to write all elliptic functions as a function of it. The answer is yes! And this function is known as the Weierstrass ℘ function which we’ll study in this post.
Visit archive to see all posts...