Introduction to Mathematical Physics

An introduction to the statistical mechanic of classical and quantum spin systems. Among the topics to be discussed are phase transitions, emergent structures, critical phenomena, and scaling limits. The goal is to present the physics embodied in the subject along with mathematical methods, from probability and analysis, for rigorous results concerning the phenomena displayed by, and within, the subject's essential models. The lectures start with a brisk review of what was covered in the course in Spring 2021, and then continue beyond that with a more extended, though still self contained, discussion of quantum systems.