完成数学领域的博士学位后，学生将能够：应用代数，分析和拓扑的抽象结构来分析和解决具体问题和概念性问题。在常规课程结构之外独立学习基础数学。向数学家的读者以令人信服的方式展示数学结果和推理。使用数学文献和数据库查找定理，构造或反例。为自己的原始数学结果写清楚且令人信服的证明。在数学领域攻读博士学位的学生必须：达到B级或更高的学位，并获得本系认可的学习课程（学生只有在获得本系和大学研究生理事会的批准后才能从另一所大学转移学分）在合格的考试中表现令人满意（见下文）在以一种认可的外语（法语，德语或俄语）进行的考试
Upon completing the PhD Degree in the field of Mathematics, students will be able to: Apply abstract structures from algebra, analysis, and topology to analyze and solve both concrete problems and conceptual questions. Learn fundamental mathematics independently, outside the structure of a regular course. Present mathematical results and reasoning in a compelling way to an audience of mathematicians. Use the mathematical literature and databases to find theorems, constructions, or counterexamples. Write clear and convincing proofs of one's own original mathematical results. Students pursuing the PhD degree in the field of Mathematics must: Complete with a grade of B or better a course of study approved by the department (students may transfer credits from another university only with the approval of both the department and the University Graduate Council) Perform satisfactorily on qualifying examinations (see below) Perform satisfactorily on examinations in one approved foreign language (French, German, or Russian) Write an original thesis acceptable to the department Perform satisfactorily on a final oral examination on the thesis. Normally, students take one or two years after the BA degree to obtain an MA degree, and they take four or five years to obtain a PhD.