# Hello World!

September 16, 2011 1 Comment

For better or for worse, I’m done with the basic exam, and now have slightly more time for the things I want to do. That includes this blog. I want to start from the basics, and build up to some of the big ideas in mathematics. I hope this sounds interesting.

If there’s anything you really want to see, let me know. A few topics I want to cover eventually are

- Insolubility of general quintic equations (Abel-Ruffini Theorem)
- Cool theorems in Logic (Compactness, Gödel’s completeness, and incompleteness theorems)
- Basic Category Theory

I’m open to suggestions, so please make them. I really appreciate the comments.

My plan is to post 3-4 times per week. We’ll see how this goes.

So what’s first? Well, Galois Theory, but there’s a lot to be done before we get there. So we’re technically starting with linear algebra. Don’t worry. It sounds lame, but it turns out it’s really cool. Maybe on the way to Galois theory, we’ll prove some cool theorems.

So tomorrow we’ll start with fields. Woo!

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Would love to see anything on those topics:

1. p-adic numbers

2. algebraic geometry

3. homology