This course is designed to introduce first-year graduate student to mathematical concepts and tools needed for research, and more advanced math courses. The subject exposes the students to the level of mathematical rigor required for doctoral research. It helps students acquire the mathematical methods and tools for other graduate course (particularly E&M, QM and SM), necessary research while earning their Ph.D.'s, and understanding journals and papers (e.g. PRLs) necessary for their study. This course also introduces the students to the mathematical tool, Mathematica.
The course provides exposure to the following topics: