Galois, Lie and Me

I'd love nothing better than to go back to a University and get my PhD in Mathematics. However, right now I can't afford it, both in time and money. So to keep my brain from atrophying, I've researched a few different branches of Math that are beyond the scope of my previous education. I figured that if I could just get my mind working through one idea in Mathematics that I've never pursued before, that maybe just maybe, I'd shake these cobwebs from my brain. And that, in turn, would make me a better tutor, and quite frankly, also a happier person in general.

Some subjects just didn't interest me. The way my brain works, I think in terms of circles, curves and continuity. Binary thinking is harder for me to gasp. But it's fascinating how you can feel compelled, drawn towards certain problems. I stumbled upon Galois Theory, and Lie Groups several times, but felt convinced that I could not understand, well, even the basics. Still, there was something compelling me to look deeper, even though it felt like I was stumbling around in complete darkness. 

I looked through my usual sources: Wikipedia, Khan Academy, journal papers and a variety of other material online. Alas, I just didn't get it, so I put it aside. I started reading about Benford's Law, and discovered Zilf's work, applying it to letters and words, and its applications to cryptography. I can imagine that finding anomalies in large data sets might be interesting and useful. But this didn't fascinate me.

Then, a few days ago, I joined twitter, as @toopretty4math. I started following some of the extraordinary Math Professors I'd found on twitter as @girlmeetsbike. Yesterday @Mathematicsprof tweeted something that changed my mind about the inaccessability of Lie Groups:

 "Robert Gilmore has a clearly written book on Lie Groups online at goo.gl/cphAI "

 I went to Professor Gilmore's website, expecting the same jargon that had been used in Wiki and every other source (it seemed) that I'd scanned. This was different.

Under the heading of the first chapter, Professor Gilmore states:

"Lie groups were initially introduced as a tool to solve or simplify ordinary and partial differential equations."

Thank you Robert Gilmore. I understand more about Lie Groups from this one statement than I have ever understood before. It's clear concise, and it gets me motivated to know more, without using jargon.

I downloaded the first chapter of "Lie Groups, Physics, and Geometry", and started reading. I found myself thinking, "OOOH Oh, that's cool", then I realized that he was using math that was easy for me to understand. I looked at the rest of the chapters (that were available for download), and indeed, he has incorporated both math and language that I understand. For the first time in a long while, I can sit back, sift through, and totally enjoy reading a math textbook. And yes, I'm even going to attempt the problem sets.

Are you interested in Lie groups? If you are currently reading "Lie Groups, Physics, and Geometry" by Prof. Robert Gilmore (or have before) and have some insights, please comment, and let's discuss.