The Doctor of Philosophy (PhD) in mathematics is the highest degree offered by our program. Graduates will have demonstrated their ability to conduct independent scientific research and contribute new mathematical knowledge and scholarship in their area of specialization. They will be well prepared for research and faculty positions at academic institutions anywhere in the world. Owing to their independence, analytic abilities, and proven tenacity our PhD graduates are also sought after by private and government employers. Our PhD program offers two tracks, one for Theoretical Mathematics and one for Applied Mathematics. The tracks differ only in the course and qualifying requirements during the first two years. Specifically, the qualifying requirements for the theoretical track consist of our Abstract Algebra (Math 6111, Math 6112) and Real Analysis (Math 6211, Math 6212) course sequences that can be fulfilled by passing each with at least an A- (or a respective examination). Those for the applied track combine a mandatory Scientific Computing (Math 6601) course, one of the algebra and analysis courses, three additional courses from Math 6602, Math 6411, and Math 6451, as well as the algebra and analysis courses. The breadth course requirements in the applied track, as compared to those in the theoretical track, offer more flexibility but also include a mandatory graduate course in a non-math STEM department from an approved list.