The program of studies for a Math Department PhD student is divided into two main parts: Pre- and Post-Candidacy. Before taking the Candidacy Exam, students need to fulfill numerous requirements which ensure solid preparation in core mathematical areas as well in their chosen specialization. These include passing the Qualifying Requirements as well as fulfilling the Breadth and Foreign Language requirements. The Candidacy Exam is usually taken sometime during the third year, marking the end of the preparatory period and the beginning of research leading ultimately to the PhD Dissertation. Time from admission to graduation usually averages around 6 years but may vary greatly depending on many factors such as initial preparation level, individual academic progress, complexity of chosen specializations, and strategic thesis and job decisions. The OSU Graduate School has requirements as well, which can be found in the Graduate School Handbook.
Newly admitted graduate students are required to arrive 4 weeks prior to the beginning of the Autumn semester in order to participate in our Headstart Training teaching preparation program. This is prerequisite for holding a GTA appointment. Further academic preparation activities are scheduled during this time as well. Exceptions can be made only for students who are offered university fellowships and typically involve a one-year deferment of the teaching portion only. Monetary compensation is provided to all Headstart participants.
There are four Qualifying Requirements, corresponding to the content of the four courses Math 6111, Math 6112, Math 6211, and Math 6212 in Abstract Algebra and Real Analysis. Each requirement can be passed by either receiving a grade of A or A- in the respective course, or by receiving a passing grade on a respective (separate) qualifying examination. The Math 6111 and 6211 courses are offered every Autumn Semester and the Math 6112 and 6212 courses are offered every Spring Semester. The four examinations, one for each course, are offered each August (typically in the week before the start of classes) and are open to both incoming and continuing students. Each exam is two hours in length and covers roughly the material of the respective courses.
All four requirements need to be fulfilled by the end of the third semester of study (not including summer). Thus a student has four attempts to fulfill, for example, the 6111-requirement (twice by taking the course, and twice by exam) and three attempts to fulfill the 6112-requirement (once by taking the course, and twice by exam). The 6211 and 6212 requirements are analogous.
Interested students may substitute one of these four requirements with an approved 6000-level year-long course sequence with A or A- grades. This includes all regular full-year 6000-level sequences, namely, Math 6221-6222, 6251-6252, 6411-6451, 6501-6502, 6601-6602, 6701-6702, and 6801-6802. (For example, the 6112 requirement can be substituted by taking the Math 6411-6451 Differential Equations sequence with A or A- grades in each course). Students should consult the GSC Chair about the use of the 6001-6004 Logic courses.
Passing the Qualifying Requirements also entails an increase in stipend, assuming otherwise satisfactory academic progress (see Financial Support). The outcome of initial exams and coursework will also inform future advising.
Syllabi and exam materials can be viewed at https://math.osu.edu/grad/current/phd/quals.
Upon attaining Regular PhD status, students are matched with faculty members who guide them to potential dissertation research ideas. The primary task of this Dissertation Advisor is to facilitate their advisee's development as a mathematician.
Course sequences used for the qualifying requirement (such as, for example, 6111-6112) may also be used for the breadth requirement. However, a passed qualifying exam does not count towards a breadth requirement.
Nearly all PhD students complete their Breadth Requirements within their first two years from admission. General expectation is that students fulfill two breadth sequences within one year from passing their Quals and the third one in the following year. Timely completion of breadth requirements may influence stipend level and summer support.
All Breadth Requirements must be completed by the time of the Candidacy Exam.
Exam: Alternatively, a student may pass a translation exam in one of the languages above.
An important candidacy requirement is the choice of a dissertation specialization and a Dissertation Advisor. The diligent, timely, and careful pursuit of a future research direction is likely the most important responsibility of a prospective PhD candidate. The student should be fully invested in the choice of specialization, which will impact his/her future academic trajectory more than anything else. There are currently 65+ regular mathematics faculty on the Columbus campus, plus over 20 additional faculty on the branch campuses, who can supervise doctoral dissertations. Consult our current Graduate Faculty List for names, contacts and specializations. Under special circumstances, students can also be advised by faculty outside of the department. The advisor pool in our department is thus as large as that of any department in the country.
There are numerous opportunities for students to get to know potential advisors. This includes having them as teachers in introductory classes, attending the Invitations to Mathematics lecture series, regular research seminars, and colloquia (see Events), or self-development through academic advisors, peers, and publicly available research information. After narrowing down possible specializations, students typically sample faculty and topics by taking numerous reading courses (MATH 6193) on special topics with a few prospective advisors. These provide introductions to future research areas that are too specialized to be covered in regular courses. The one-on-one teaching of a reading course may also serve as a preview of the advisor / advisee interaction in future thesis work.
The choice of thesis advisor usually evolves out of this process. After student and faculty agree on the thesis advising, the student reports the change from the Preliminary Academic Advisor to the chosen Dissertation Advisor to the Math Graduate Office using the form located outside the Grad Office.
The department does not admit students whose intended degree is a generic Master's outside of the MMS specializations program. However, students admitted for the PhD can obtain a general MS degree in Mathematics during their academic progression towards the PhD degree.
There are three ways for a PhD student to earn an MS degree (listed below).
Thesis Option: After completing 30 credit hours of approved work, a student may select the option of writing a thesis which has to be defended and approved by a two-faculty member exam committee, one of whom has to be the student's Master's Faculty (Thesis) Advisor.* Students utilizing this option should be signed up for MATH 6999 with the supervising Master's Faculty (Thesis) Advisor during the semester they write and defend their thesis.
The Master's Thesis needs to follow university formatting guidelines, be approved by the exam committee, and be submitted to the OSU Graduate School and OhioLink. For further details see Section VI of the Graduate School Handbook.
* The Master's Faculty (Thesis and/ or Non-Thesis) Advisor needs to be a Math Department faculty member of category M level or higher. They are selected separately from your Dissertation Advisor. When the student has established with a faculty member that they will advise the student's Master's Thesis, the student reports the chosen Master's Faculty (Thesis and/ or Non-Thesis) Advisor to the Math Graduate Office.
Committee: The committee consists of four regular faculty with graduate P-status, including the advisor of the candidate who serves as the chair. Other committee members can be from other Ohio State departments but have to have graduate P-status in their programs. Additional members, beyond these four, can be added by petition and according to Graduate School rules.
Written Portion: The written portion consists of a 10-15 page dissertation proposal in which goals, scope, methods, and background of the planned research is outlined. The document has to contain mathematically rigorous statements, needs to be type-set along the usual publishing standards in the field (e.g., LaTeX), and should contain a substantial bibliography that includes all pertinent publications the intended research will be based on. The proposal of the written portion should be submitted to the committee at least ten days before the presentation and oral portion.
Presentation: The candidate is required to describe his/her proposal in a short presentation of approximately 30 minutes to the committee immediately before the start of the oral portion of the examination. The details of the format are determined by the advisor, including whether the presentation should be public and questioning during the presentation.
Oral Portion: Following the presentation there is a two-hour oral examination by the committee. This time has to be completely dedicated to the questioning by the committee and is not allowed to contain further presentations. The questions can focus on the proposal itself and the validity and relevance of the research questions, but can also include skill and knowledge examination of the needed mathematical background, as well as test familiarity with prior research.
Timeline: An application for candidacy must be submitted via gradforms.osu.edu at least three weeks before the oral examination. The candidacy examination can be taken at any time during business hours when the university is open -- including summer terms and breaks. The final date on which a candidacy exam can be counted as being within any given semester is the day before the first day of the following semester (for example, a "Spring" exam can be scheduled up until the day before Summer Term begins). All committee members' approval signatures must also be submitted in GradForms prior to the first day of the following term.
Other Requirements: All pre-candidacy requirements of the Mathematics Department, as well as all credit and residency requirements of the Graduate School, have to be fulfilled by the end of the term prior to taking the exam. Candidates also need to be enrolled for at least 3 hours at the graduate level during the term of the exam (note: if you schedule your exam in summer, you will need to enroll in 4 credit hours in order for your summer tuition waiver to apply).
Following the exam, the Report on Candidacy form must be approved on GradForms by all committee members.
After the Candidacy Exam, PhD students spend most of their time on research related to their dissertation, under the close supervision of their Dissertation Advisor.
Time Limits: The university allows a maximum of five years from passing the candidacy examination until submission of the final copy of the dissertation. The Math Department however, has the expectation that you can accomplish this in three years or less. Continuation in the program is contingent on timely and satisfactory progress towards completing a dissertation as determined by the Graduate Studies Committee.
Once the Dissertation Advisor deems the Dissertation Doctoral Draft complete, the candidate needs to assemble a Final Oral Exam Committee. The committee consists of the Dissertation Advisor and two additional regular category P level faculty members, who will review the draft. The doctoral candidate must submit the Application for Final Exam form via GradForms no later than two weeks prior to the proposed final oral examination date. The approval of the draft is followed by the two-hour Final Oral Examination (dissertation defense) conducted before the dissertation committee members listed, plus a non-Math representative assigned by the Graduate School. See the PhD Dissertations link on the Department website for samples of past approved Dissertations.
The department supports the search for academic jobs in several ways. Before graduation, the department provides travel support for students, helps with letters, and circulates job opportunities. After graduation, many former students with can find employment as lecturers with the department while they are looking for permanent jobs, if interim employment is needed.
The qualifying requirements should be fulfilled by the middle of the second year. The graduate studies committee may decide on conditional continuation at either regular or probationary level in close cases.
International students should be classroom teaching certified by ESL's Spoken English Program by the beginning of the second year.
Students are expected to pass the candidacy examination before the Autumn Semester of their fourth year.
Students are expected to graduate by the end of their sixth year. In cases where this is not possible, the graduate studies committee can be petitioned for a seventh year of financial support at a reduced stipend level.