## Of ellipses, hyperbolae and mugging

For as long as I can remember, I have had unnatural inertia in studying coordinate geometry. It seemed to be a pursuit of rote learning and regurgitating requisite formulae, which is something I detested. My refusal to “mug up” formulae cost me heavily in my engineering entrance exams, and I was rather proud of myselfContinue reading “Of ellipses, hyperbolae and mugging”

Let be a mapping. We will prove that , with equality when is injective. Note that does not have to be closed, open, or even continuous for this to be true. It can be any mapping. Let . The mapping of in is . As for , it may overlap with , we the mappingContinue reading

## Proofs of Sylow’s Theorems in Group Theory- Part 1

I will try to give a breakdown of the proof of Sylow’s theorems in group theory. These theorems can be tricky to understand, and especially retain even if you’ve understood the basic line of argument. 1. Sylow’s First Theorem- If for a prime number , , and , then there is a subgroup such thatContinue reading “Proofs of Sylow’s Theorems in Group Theory- Part 1”

Today, I will discuss this research paper by Javed Ali, Professor of Topology and Analysis, BITS Pilani. What exactly is a proximinal set? It is the set of elements in which for any , you can find the nearest point(s) to it in . More formally, for each such that . This article says aContinue reading

## Why I have nothing better to do than blog :(

After trying to follow blogs by various mathematicians, I have concluded that having a digital presence is pretty darned cool and useful in academia! Hence, in my pursuit of the forever-elusive elixir of “cool”, I have decided to record my progress in Algebraic Geometry through this blog. I’m no expert. But I feel trying to explain conceptsContinue reading “Why I have nothing better to do than blog :(“