Saturday, August 1, 2009

Introduction

When you are collecting mushrooms, you only see the mushroom itself. But if you are a mycologist, you know that the real mushroom is in the Earth. There's an enormous thing down there, and you just see the fruit, the body that you eat. In mathematics, the upper part of the mushroom corresponds to the theorems that you see, but you don't see the things that are below, that is: problems, conjectures, mistakes, ideas, etc.
V. I. Arnol'd, "From Hilbert's Superposition Problem to Dynamical Systems",
In The Arnoldfest, Fields Institute Communications 24 (1999) pages 1–18

What is this Blog?

This is my collection of notes, arranged in probably an erratic manner. For this reason, I am using a table of contents type widget at the top of the page, and to double check I am not overlooking anything I have the archive at the bottom.

Who am I?

I'm all things to all people. The physicists call me a mathematician, the mathematicians call me a physicist. I'm a pariah I guess ;)

Format of Blog

This blog is probably going to be a collection of my math notes, I was thinking of following Bourbaki's lead and have this blog be as self-contained as possible. That means that I'll be linking to my own blog a lot, and as I write more you may find more links in older posts to recent material. Unlike Bourbaki, I'll try to avoid writing grocery lists of definitions, theorems, proofs. I'll be giving some intuition, some examples, and some basic procedures carried out in explicit details.

(And just a spoiler: category names like Set are usually links except when they are first defined -- go ahead and look, that really is a link I just made despite its appearances!) I'll also try to refer to open source, freely available technical materials too, when possible.

It should be read in the order as specified by the table of contents, of course; I've even numbered it and everything ;)

I've just discovered the "object oriented" approach of category theory, and have fallen in love with it. I'm about to take the abstract algebra series at my university, so this seems like the ideal time to practice such an approach to math. This blog will probably be my notebook for abstract algebra, among other things. So make the most of it.

(One last thing, I might have an entry up that's not on the table of contents that is changing every so often. It's an entry I'm working, which is why it's changing, and it's not quite finished, which is why it's not on the table of contents. It'll show up soon enough though...)

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