MATH-PHD - Mathematics (PhD)
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Program Overview
The Mathematics PhD program trains students in ambitious and independent mathematical research to set the stage for becoming leaders in their own research fields. Hence, the most important component is to tackle a cutting edge research program and to bring it to completion, including producing publication, as appropriate. Graduate students should aspire to expand human knowledge in one area of mathematics, broadly construed, and effectively sharing the new knowledge as appropriate in the culture of their field. The initial curriculum provides the broad foundations for this, which are then deepened in supervised advanced reading and research with faculty. In addition, the program strives to support students to become effective educators, with teaching being a key part of many mathematicians’ careers.
Admissions Information
Information on how to apply for graduate study at Stanford is available on the university’s Graduate Admissions website. Application information specific to the PhD program in Mathematics can be found on the Mathematics Graduate Admissions webpage.
Minimum Units in the Program
Minimum University Units
Course requirements:
27 units of Math graduate courses numbered between 200 and 297 for a Letter grade.
Completion of MATH 355: Graduate Teaching Seminar in the second year of the program.
Additional units should be Math department courses or approved courses from other departments. The course program should display substantial breadth in mathematics outside the student’s field of application.
Students are expected to enroll in all required courses for a letter grade unless that option is not available. The student must receive a grade point average (GPA) of 3.0 (B) or better in courses that satisfy the PhD requirement.
Qualifying Exams:
Departmental qualifying exams are held in the first week of Spring quarter of the first year of the PhD program to assess student knowledge of core subjects. Students are required to pass qualifying exams in two of four areas:
Algebra
Real analysis
Geometry and topology
Applied mathematics
Students who do not successfully pass qualifying examinations are provided a second attempt the week before Autumn quarter of the second year. Failure to pass qualifying exams on the second attempt results in dismissal from the PhD program.
Additional details on the Qualifying Exams can be found on the department website: https://mathematics.stanford.edu/academics/graduate-students/phd-program/phd-qualifying-exams
Area Exam:
The student must complete their Area Exam by the end of Winter quarter of the third year.
This exam assesses the student’s breadth of knowledge in their particular area of research. The Area Examination is also an opportunity for the student to present their committee with a summary of research conducted to date and a detailed plan for the remaining research.
Although teaching is not a requirement for the degree, students may teach as part of the financial support commitment and their professional training.
Admission to candidacy is a prospective judgement by the faculty of a student’s potential to successfully complete the requirements of the degree program. Students are expected to complete qualifying procedures and apply for candidacy by the end of Spring quarter of their second year in the program. Qualifying procedures in the Department of Mathematics include required coursework, identification of an advisor, and completion of the Qualifying Exam requirement.
In the Department of Mathematics, the oral exam is a defense of the dissertation presented upon the completion of a substantial portion of the dissertation or upon completion of a pre-final draft. Students consult with their dissertation advisor and reading committee members on the timing of the defense. Students are expected to complete this milestone by the end of their fifth year in the program.
Students are required to submit an approved dissertation that makes an original contribution to scientific knowledge in the field of mathematics. Students are expected to submit the dissertation by the end of their fifth year in the program.