Posted on Sat 25 December 2021 in Mathematics • Tagged with Mathematics
$\newcommand{\cE}[2]{\mathbf{E}(#1\ |\ #2)}$$\newcommand{\cP}[2]{\mathbf{P}(#1\ |\ #2)}$$\renewcommand{\P}[1]{\mathbf{P}(#1)}$$\newcommand{\E}[1]{\mathbf{E}(#1)}$$\newcommand{\F}{\mathcal{F}}$$\newcommand{\G}{\mathcal{G}}$$\newcommand{\ind}[1]{\mathbf{1}_{#1}}$ To motivate this note, I’ll pose the following …
Posted on Fri 03 December 2021 in Mathematics • Tagged with Mathematics
$\newcommand{\triple}{(\Omega, \mathcal{F}, \mathbf{P})}$$\newcommand{\P}{\mathbf{P}}$ This note on random variables follows as a result of confusing notation in several math textbooks. I'll explain random variables (in measure theoretic terms) as verbosely as I can, and then prove some results. This article assumes that the …
Posted on Wed 12 May 2021 in Mathematics • Tagged with Mathematics
I'll begin this article by brushing up a few definitions:
A function is a mapping between two sets: the domain D and the codomain C.
It's very important to note here that the function is the mapping itself, and not an element in the codomain or the domain. The function …
Posted on Fri 29 January 2021 in Mathematics • Tagged with Mathematics
$\newcommand{\pdv}[2]{\frac{\partial{#1}}{\partial{#2}}}$ $\newcommand{\ah}{\pmb{a} + \pmb{h}}$ $\newcommand{\a}{\pmb{a}}$ $\newcommand{\h}{\pmb{h}}$
Consider a function that maps reals to reals, $f:\Bbb{R} \to \Bbb{R}$. The linear approximation of this function is given by $$f(a …
Posted on Fri 16 October 2020 in Mathematics • Tagged with Mathematics, Programming
Just after 10th and as I was beginning my JEE Preparation, I felt the need for an extensible note-taking apparatus. Online notes would be too much trouble and would keep me hooked to the computer. Notebooks were also difficult, as I wanted my notes to be extensible; adding pages in …
Posted on Fri 11 September 2020 in Mathematics • Tagged with Mathematics, JEE
This beauty came in the 2nd September shift 2 paper:
Let $A = \{ X = (x, y, z)^T : PX = 0 \text{ and } x^2+y^2+z^2=1 \}$, where $$P = \left[ \begin{array}{l l l}1&2&1 \\ -2&3&-4 \\ 1&9&-1 \end{array}\right]$$ then the …
Posted on Fri 14 August 2020 in Mathematics • Tagged with Mathematics, Math Notes
This is a small set of posts that come into the category of "notes": self-explanations of concepts that I have recently picked up and found interesting.
Lagrange Interpolation is a concept that allows us to find a polynomial of least degree passing through a given set of points …
Posted on Sun 26 July 2020 in Mathematics • Tagged with Mathematics
My old man always used to say that there are two ways to solve a problem: there's the horse way, and there's the donkey way. The donkey way involves tedious calculations, whereas the horse way 'cuts' through the problem. Take this problem as an example:
For each positive integer $n …
Posted on Sat 11 July 2020 in Mathematics • Tagged with Mathematics, ISC, Data Science
The ISC Exam results were released on 10th June, 3 PM IST. In this article, I'll be analyzing the results of the 117 students in the science stream of my school and showing how they performed. I'll also weave a story with the data and point out things that could …
Posted on Thu 09 July 2020 in Mathematics • Tagged with Mathematics
A long time ago, I gave my friend (Let's call him C) an integral to solve. He came back to me a few days later and the conversation went something like this:
C: Debu, I couldn't solve that African integral you gave me.
Me: Ok, but why are you calling …