Doctor of Philosophy in Mathematics

Program Learning Outcomes for PhD in Mathematics Students graduating from this program will: Apply abstract structures from algebra, analysis, geometry, 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. Degree Requirements for PhD in Mathematics Admission to graduate study in mathematics is granted to a limited number of students who have indicated an ability for advanced and original work. 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. An MA is not a prerequisite for the PhD. For general university requirements, see Graduate Degrees. A number of graduate scholarships and fellowships are available, awarded on the basis of merit. As part of the graduate education in mathematics, students also engage in teaching or other instructional duties, generally for no more than six hours a week. For courses carrying dual undergraduate and graduate numbers, (e.g., MATH 463/563), the 500-level version is intended to prepare students for advanced work in mathematics. In particular, written assignments should be prepared to high professional standards, typically using LaTeX or other mathematical typesetting software. Mathematics graduate students should enroll in the 500-level version. PhD Program—Candidates for the PhD in 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