This is a kind of longish post on algebraic sets. I bought Hartshorne, then ended up studying from Fulton’s “Algebraic curves”. I will focus on the geometric aspects of algebraic sets. So what are algebraic sets? They could be points, curves, surfaces. But if they are curves, they have to be infinitely long curves onContinue reading “Algebraic sets”

# Monthly Archives: July 2014

## A little something about the two equivalent definitions of compactness in a metric space

The two statements are equivalent in a metric space: 1. Every infinite sequence has a convergent subsequence. In other words, there is an accumulation point for every infinite sequence. 2. The metric space is convergent. Proving (2) from (1) follows the standard practice of deducing that any open set containing the accumulation point contains allContinue reading “A little something about the two equivalent definitions of compactness in a metric space”

## My new project

When we learn mathematics while young, we are taught numbers using pictures and other kinds of visual devices. That is what helps us learn those concepts. Had they been taught as axiomatic constructs, children would find it exceedingly difficult to learn them. This is not substantiated, but something I truly feel. The things that IContinue reading “My new project”

. Just a small note. I am exactly like this guy. EXACTLY. Will Mackenzie. Kinda bad looking. Bad teeth. Unremarkable complexion. High morals which have been discarded only too often. And an idealism-fuelled self assurance. I used to think I was a lot like my girlfriend. But I think everyone knows she’s too goodContinue reading

## A continuation of the previous post

Let be an n-dimensional vector space, and let be a surjective linear mapping. If is m-dimensional, then is a matrix of order . Is it possible that ? Let us assume that it is. Then has a basis , all of which are mapped to by distinct vectors in . Moreover, these vectors have toContinue reading “A continuation of the previous post”

## Dual spaces- An exposition

Studying Dual Spaces can be confusing. I know it was for me. I’m going to try to break down the arguments into a more coherent whole. I am following Serge Lang’s “Linear Algebra” (the Master is my favourite author). However, I am not strictly following the order he follows to develop the theory. Say weContinue reading “Dual spaces- An exposition”