Learn You Some Algebras for Glorious Good!

This is a math book. We aim to take a logically rigorous, yet informal approach to math.

The title (and content) is inspired by Miran Lipovača's Learn You a Haskell for Great Good! If you want to learn the Haskell programming language, we recommend that book.

I have observed that most math (and science) books nowadays seem to take an approach wherein it's more important to keep an academic tone than it is for the reader to understand the material, and, more importantly, enjoy reading the book. We take the opposite approach. We want to create a book that is fun to read, easy to understand, while still addressing the more advanced concepts in math.

If you like chatting on IRC, come see us in #learnmath on FreeNode. If you don't know what IRC is, or you don't have a client set up, you can connect through FreeNode's webchat. You can email me (pharpend) at pharpend2@gmail.com. I don't check that email very often, so IRC is better. I'm pharpend in the channel.

You are more than welcome to contribute, but please read the contributing guide first. (Sorry, we know how annoying those are.)

If you notice any errors, don't be shy to report then in the issue tracker. If you have any suggestions for improving LYSA, also post them in the issue tracker (or bring them up in the IRC channel).

If you have any questions about LYSA (or math), feel free to ask in the channel, or in the issue tracker.

Excerpt

If you want an idea of what the book might look like, here's an excerpt from the previous attempt.

Introduction

This book is about Commutative Algebra - a fun area of math. That statement is a bit redundant - is there an area of math that isn’t fun? Of course not! Now let’s get started!

Everything is a toy if you play with it.

– Chris Pratt, Parks and Recreation

So what is Commutative Algebra?

Simply put, Commutative Algebra is the study of things called icommutative rings. There are two words there, “commutative,” and “ring.” Before we can get to those words, you have to understand some other words first.

Sets and elements

Imagine a bunch of things. These things all have some property in common. Congratulations! You just intuited a iset! See, you’re getting this!

For example, look at iintegers. You may have heard of “whole numbers,” numbers that don’t have a decimal point. Whole numbers are \(\{0, 1, 2, 3, \ldots\}\). Integers are the same, but they include negative numbers. The integers are \(\{\ldots, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, \ldots\}\)

Notation

Did you see that I cleverly tricked you into understanding some notation there? I’m also guessing you understood it! The notation I used is the brace notation for sets, as well as set extrapolation. Those words are a bit confusing.

The “brace notation” simply means I use curly braces (these things - \(\{\) and \(\}\)) to express a set. Everything between those two braces is in the set. I also used commas to differentiate between the various things in the set. See, this math stuff isn’t hard!

I also used this thing called “assumed extrapolation.” That was what you did when you saw the ellipsis (the three dots - “\(\ldots\)”). See, you’re getting this stuff without even thinking about it! The ellipsis basically means “I think you’re smart enough to figure out what I’m going to put here.” And you are! Just look at how far you’ve gotten all on your own!

My Calculus teacher in high school was rather emphatic that mathematical notation is all about being lazy. That idea stuck with me. I think you’ll learn very quickly is that mathematicians are lazy. Really lazy. We are so lazy that we can’t even bear to type the word “integer.” So, instead, we use letters to express these words. We use a large fancy Z, instead of writing “integers.” We really are that pretentious. So, whenever you see \({\mathbb{Z}}\), you can think “oh, he’s just a lazy jerk who can’t be bothered to type the word ‘integers’.” And you’ll probably be right.

Links and other stuff.

• Come see us in #learnmath IRC channel on FreeNode. We don't have any formal rules in the channel yet, so please just use common sense. If you don't know how to use IRC, you can use FreeNode's qwebirc client to connect.
• I previously took a stab at a similar idea here.
• A preliminary outline.
• The source for this site.
• The issue tracker.
• Contributing guide

License

LYSA is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. This means many things, but here's the gist of it:

• You are free to read this book, redistribute it, change it, sell it, what-have-you. There are a minimum of strings attached.
• The first string - you have to give us credit. You can't claim that you wrote this book all on your own.
• The second thing - you are welcome to make changes, but, if you publish your changes, you must publish your changes under the same license. This ensures that we can then integrate your changes back into the main work.

If you want to know the details, read the legal code.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.