So far I’m looking at the following:
- Introduction to Galois Theory – 3hrs
- Topics in Set Theory – 3hrs
- Real Analysis I – 3hrs
- QFT II – 3hrs
The Introduction to Galois Theory is basically going to be an Abstract II initially. It’ll be filling me in on Rings and Fields before going into the meat of the material. Probably going to use Gallian primarily and Artin as a supplement (hoping to avoid Fraleigh).
Topics in Set Theory will be part of a foundations in Mathematics, so to speak. The goal is to cover ZFC with choice, rigorously. Text comes from Lewin’s Analysis and personal course notes.
Real Analysis I won’t cover the traditional topics and will remain entirely in one dimension. There will be a period of background material including:Emergence of Rigor in Calculus, Mathematical Grammar, Proof Writing, Set Theory. The topics of the course will be roughly as follows: Real Number System, Topology of the Real Line, Limits of Sequences, Limits and Continuity of Functions, Differentiation, Exponential & Logarithmic Functions, Riemann Integration, Infinite Series, Improper Integrals, Sequences and Series of Functions, Integration of Functions of Two Variables. In honesty, I doubt we’ll cover them all…the expanded topics list in the text is considerably greater. The text is by Lewin
The course in QFT will really be finishing what I should have done last semester (whoops) and then continuing into more advanced material, hopefully I’ll move from Ryder to Peskin & Schroeder. There is a hidden piece of awesomeness though…I’ll be covering General Relativity (from the particle physicist’s perspective, of course) from Weinberg in parallel.
Besides the courses, I’ll also begin research in QCD…or so I’ve been told, we’ll see how that turns out, haha.