### Ph.D. Mathematical Sciences

### Summary

The Mathematical Sciences Ph.D. program is designed to prepare students for advanced independent research in the mathematical sciences that is directed to the solution of modern scientific, technological and industrial problems. The program has three tracks to meet studentsâ€™ specific professional aspirations: Applied Mathematics Track, Applied Probability and Statistics Track, and Pure Mathematics Track.

Through coursework and independent study, students will gain the vital knowledge in mathematics and statistics needed to teach at college-level, conduct strong independent research in their areas of expertise or succeed in a range of diverse careers within government and private sector environments.

Students of the Ph.D. program will display:

*Professionalism*: Motivated students will sharpen leadership, collaboration and communication skills to successfully communicate their work to a wide audience (including non-specialists).*Academic Excellence*: Students can work alongside department faculty with research accomplishments in their field to successfully pass the qualifying Ph.D. exams, conduct advanced independent research and complete their dissertation work.- C
*ommitment to Career Development*: Through activities, such as a regular colloquium series and seminars, students will continuously explore the latest innovations in the mathematical sciences.

Graduates of the Mathematical Sciences Ph.D. program are trained to a very high level of mathematical expertise and will have acquired essential skills in mathematical and/or statistical modeling, computational techniques and research methods, in addition to in-depth expert knowledge of their own thesis research field. At graduation, students have demonstrated the capacity for independent and in-depth research (evidenced by their doctoral dissertation and its defense) and should be prepared to move on to a professional career as a mathematician in an academic, business or industrial context.

The learning outcomes expected of graduates include:

- Ability to apply knowledge of mathematics, and mathematical/statistical methods.
- Ability to identify well-defined features of quantifiable systems.
- Ability to formulate a mathematical or statistical model of a quantifiable system, and to interpret and criticize existing models of such systems.
- Ability to use mathematics effectively and efficiently to solve a mathematical model or problem. In particular, an ability to extract quantitative data and information from a mathematical model.
- Ability to carry out independent research on a chosen topic, of a depth and quality sufficient to produce results worthy of publication in peer-reviewed journals in the field.
- Ability to communicate effectively. In particular, an ability to communicate concepts and results of the studentâ€™s own, and related, research in mathematics, and the relation to problems in other science and engineering disciplines.
- Ability to work effectively, both independently and as part of an interdisciplinary group.
- Performance criteria: Core course grades.
- A recognition of the need for and an ability to engage in lifelong learning