FunnyOriginally Posted by topsquark
What is a physicist doing in the realms of Abstract Algebra
The book I have is by,
John B. Fraleigh called "A First Course In Abstract Algebra".
Great Book, well written.
I am taking a "strategic retreat" in my program of study. My Algebra text is actually a graduate book, and I evidently don't have enough experience with the basics to really grasp what I need to do with it.
I have a low-level undergrad book that focusses mainly on geometric constructibility. I've learned alot from that, but the author confesses that many of the details aren't in the book. I found the going very easy with that one, but obviously the gap between it and the graduate text is rather broad.
So I am looking for a more "fundamental" text, that would correspond maybe with advanced undergraduate level or so? My ultimate goal with this is to be able to at least understand Galois theory. I figure if I can do that I'm probably set with anything Algebraic I encounter in Quantum Field Theory.
Thanks for the tip!Originally Posted by ThePerfectHacker
My current goal is to learn String Field Theory, a rather abstract and certainly heavily Mathematical field of study. Most of the theoreticians doing it, whether they want to admit it or not, are essentially Mathematical Physicists.
I had a conversation with one of my professors once when I was at Purdue studying for my PhD. (I had to leave the program uncompleted, unfortunately, due to health reasons.) He was slightly bemused that I was taking Partial Differential Equations from the Math department and he asked me why? I told him that I was interested in knowing why the techniques I had been using to solve them work, and that if I came across a type of equation I hadn't seen before I wanted to know the general theory so I would know what to do to solve it. His reply? "We'll teach you everything you need to know."
Pffl! They don't.
So, I'm currently out of both work and school and with a great deal of time on my hands. I've set myself the goal of trying to learn String Theory on my own, which is VERY heavily Mathematical. I know most of the Physics involved, but the Math is difficult to follow using my current knowledge base. So I decided to start learning the topology, group theory, geometry, and algebra that I will need. It's a big shopping list, but fortunately I doubt I'll have to master any of them...I suspect that a knowledge of the basics of each will probably do to get me into the subject and I can then pick up whatever else I'll need later on.
So that's what a mere Physicist is doing mucking about in the "realms of Abstract Algebra.
Besides, do you know how many Physics chicks are impressed by my being able to solve cubic equations by hand?
I didn't like the first two editions with their habit of referring to "the literature" for proofs of some key results. I believe the third edition is better.Originally Posted by ThePerfectHacker
Personally I would recommend Saunders and MacLane Survey of Modern Algebra or Herstein Topics in Algebra.
Things have obviously changed from when I was an undergraduate. ThereOriginally Posted by topsquark
was only the one "Physics chick" in our year.
Though there were a significant number of "Astrophysics chicks" by the time
I got around to studying Astro seriously.