Notes
A fun, nerdy way to spend time is to wrestle with an interesting mathematical problem. Sometimes, after the dust is settled, I find the outcome to be worthy of remembering (by no means, I am assuming that others should feel the same way); and therefore convert the drafty scribbles to a hopefully more readable digital file. On this page, you can find a list containing some of those files; it also includes some of my term papers/reports. (A đź”’ symbol indicates that the note will not be updated anymore.)
While studying quantum field theory (QFT for short), one faces many do-it-yourself calculations. In this file, I will try to do those calculations as clearly (at least to myself) as possible. [Last Update: Oct 2024]
🔒 This is the Persian report of my BS thesis (for the electrical engineering course) titled “Phase Transitions in the Community Detection Problem: An Information Theoretic Approach”. [Last Update: Jun 2021]
Here you can find a term paper that I wrote a while ago on the issue of rigid body motion in relativstic physics. [Last Update: Dec 2020]
This is a drafty version of many of my calculations in the field of general relativity. It contains most of my work for the Physics BS project I did in 2019. [Last Update: Dec 2022]
đź”’ While working on the Quasi-Inversion project, many little lemmas were proved; this is one of them. [Last Update: Feb 2021]
It is easy to make a paper cylinder but impossible to make a paper sphere. “What is the general rule here?” I asked Behzad, my high school friend, and he came up with a rather beautiful conjecture; this note is a proof for his (generalised) conjecture. There are a few open (at least for me) problems here as well (Cf. Problems tab). [Last Update: Apr 2019]
đź”’ This is a model that proves the poorer one is, the more decent he is as well. (Of course I am kidding!) [Last Update: 2017]
đź”’ I am interested in the sphere packing problem. In 2017, I published a Persian review here. This is a neater version. [Last Update: 2017]
đź”’ As a term paper for the course Quantum Mechanics II, I wrote this concerning the Lamb effect. [Last Update: 2017]
You are given a bunch of noisy data points in the form of many (say 1000) dimensional real vectors. But you know that they all lie on a possibly curved low dimensional (say 7) manifold. How would you estimate the true intrinsic dimension? This is one method that I developed in 2017. [Last Update: 2017]
🔒 As a term paper for the Fluid Dynamics course, I wrote this concerning Kolmogoroff’s 4/5 law.
🔒 On the first encounter, I found the numerical method “wag the tail” (as explained in Griffiths’ Quantum book) interesting and therefore applied it to solve the energy levels of a particle in an infinite triangular well. (here) [Last Update: 2015]