Introduction

Hello, and welcome to Dihedral Soup. I started this blog with a few goals in mind. First, I'd like to chronicle some of my own learnings and ventures through the world of mathematics. I spend quite a bit of time reading and studying math and often the best way to check my understanding is to try and explain it to someone else. Secondly, I hope to eventually attract other mathematicians to my site and maybe meet some people that are on the same mathematical level that I am. Anyone and everyone is welcome, though, so regardless of your mathematical training or your age and skill level, please feel free to comment and share your thoughts about math, about life, or about anything you'd like. However, if you'd like more of a non-mathematical view into my life, please feel free to visit my personal blog, Breathing is Easy - I hope to keep both of them updated regularly. Finally, the biggest reason that I started this site is because I love math and I want everyone to love it the way I do. I hope that I can share a little bit of that and I insist that you ask questions if you have them. There are no stupid questions - especially when you're learning - but if you don't feel comfortable commenting, feel free to email me or instant message me on AIM - my email address and screen name are on the sidebar on the left.

It is my intention to keep my writing style as informal as I possibly can. I feel like something that deters a lot of people from math is the enormous amount of detail and procedure that is naturally embedded in it. While this is certainly necessary in the development of the theory and in convincing ourselves of our rigor, I do admit that cumbersome proofs and fiddling at length with gigantic equations can be daunting and discouraging. There is certainly a time and a necessity for such things, but an online blog is neither of those. A certain amount of proof is required even if only to convince you that I'm not lying to you or just because sometimes proofs are cool as hell, but I have no plans on writing a textbook.

For those of you that are new to the world of theoretical mathematics, you may be asking yourself what I mean by a "proof." I need to preface this entire journaling endeavor with one very important fact, and that is that the sort of math that I do does not use numbers in the way that most people expect. My particular branch of mathematics concerns itself with a lot of abstract objects and a whole different sort of "universe" than the real numbers that most of us associate with mathematics. I will often start out with a few definitions and then use those definitions (along with things that we may already know) to develop rules, relationships, and consequences of these definitions. These rules are called theorems and a proof is the argument that shows a theorem to be true.

Please enjoy, and remember to give me feedback on what you like, what you don't like, what you don't understand, and what you'd like to know.