This is the first semester of a two semester sequence on Concepts of Mathematical Physics. This sequence is part of the core curriculum for graduate students in Physics. It is impossible to neither study nor do research in Physics without the use of Mathematical Methods and Concepts. This course is designed to give an introduction (or review) to some of those concepts.
It is not a “mathematical course” in a sense of rigorousness and completeness. In fact, any of the “topics” mentioned below can easily take one or two semesters in the form of a regular mathematical course. Instead: motivation will be given for some of the methods showing its necessity to solve problems, and secondly technicalities of the method will be introduced, and then applied to solve more problems.
To introduce Physics graduate students to fundamental techniques of classical and quantum mechanics at a theoretically sophisticated level
To demonstrate usefulness of this techniques in real-life application problems, thereby helping students to master other core subjects (classical mechanics, electrodynamics, optics, quantum mechanics, etc.)
To develop problem solving skills and research attitude.
To prepare students for the Ph.D. qualifying exams at some of the University.