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 student’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