The doctoral program provides an opportunity to gain deep expertise, conduct research and write a dissertation in the areas of computational algebra, cryptology, decision making under uncertainty, group theory, numerical analysis, optimization, partial differential equations (PDEs), reliability theory, and stochastic modeling under the guidance of world-class experts. Its main outcome is producing an original and significant result in mathematics and its applications. In addition to rigorous coursework, doctoral candidates are expected to explore and learn on their own, e.g., by attending and organizing seminars, and to build effective communication skills. The ability to conduct scientific research requires not only intimate knowledge of the chosen area of specialization but also qualities such as scientific curiosity, initiative, critical thinking, independence, and tenacity. Upon completion of the program, the students can pursue careers in academia, technology industries (pharmaceuticals, insurance, financial services, etc.), scientific and management consulting companies, and military and government research labs.