The Ph.D.-program at the Department of Mathematics has a long tradition that goes back to the first Ph.D. degree awarded to Grace M. Bareis in 1909. The department started awarding Ph.D.'s on a regular basis in the late 1920's.

One hundered years later the department has awarded over 700 Ph.D.-degrees in mathematics. Lists of more recent dissertations can be viewed at our Department List (≥1996) or the ETD list (≥2002). An almost complete list of doctoral dissertations is available through Pro-Quest. Research topics of the theses represent all areas of mathematics.

There are currently over 110 students in our program pursuing a Ph.D.-degree. Nearly half of the graduate population consists of domestic students coming from both larger universities and smaller liberal arts colleges with a solid math major curriculum. International students come from all parts of the world and different educational backgrounds. About a quarter of our current graduate students are female.

The number of graduates per year has been around 20 in the past three years (up from an average of around 13 in the previous decade), indicating rather solid retention rates. In fact, our estimates are that among the current and recent cohorts aboout 60-70% of recruited students leave the program with the intended Ph.D.-degree. (The majority of those leaving before completing a doctoral degree do so for mostly non-academic reasons).

As detailed further below, times to degree vary significantly among our students, ranging from as little as four years for very well prepared students to more than seven years for students facing particular challenges. As a large program we recognize the diversity of academic demand of different types of students working in different research areas. While students are urged to complete degree requirements in as timely a manner as possible, we also seek to maximize the output of high quality doctoral theses.

Thus our program has no a-priori limit to the number of years of support (as it may be the case in other programs) but requires students to annually report on their academic progress and show sufficient promise to our committee towards the completion of the degree. Currently, the average time to degree is somewhat above 6 years.

Other numbers include various rankings of our programs, which, of course, heavily depend on methodology and which may not address details relevant to individual students. The annual, poll-based US New & World Report places our graduate program 15^th among public school and 30^th overall in the country (tied with other programs). Rankings compiled by the National Research Council (NRC, used also in PhD.org) are more difficult to discern and summarize. We point out that these mostly rely on data collected from students we admitted to our program in the early and mid 1990's. Therefore, as measured in numerous important indicators, the NRC data no longer accurately reflects the realities in our program, which has undergone significant reforms and improvements in the past decade.

The Doctor of Philosophy (Ph.D.) is the highest possible degree in mathematics. It implies the mathematical maturity and abilities required from a faculty at the college and university level who is expected to carry and advance the discipline of mathematics through research and teaching. Our Ph.D. program seeks to achieve this formation through a thorough training in the core areas in mathematics in the first years, research specialization in reading classes, seminars, and supervised thesis work, as well as teaching of undergraduate mathematics.

Most of our graduates continue their careers in academia. In fact in recent years a majority of our Ph.D. found employment in competitive post-doctoral research positions. In the last two years the list of institutions where our graduates were placed as post-docs include the following.

In addition, many of our graduates are awarded regular faculty teaching positions at established four year colleges all over the United States. In most years a smaller number of graduates also enters the government jobs, for example, with the National Security Agency but find employment also in the private sector working, such as the financial industry or in software development, and there often in leadership positions.

The department invites applications from qualified students all over the world who intent to pursue a Ph.D.-degree in mathematics at our department. Detailed application instructions can be found on our Admissions Page.

The academic prerequisites for being considered for admission are listed below. For the detailed types and forms of documents that need to be submitted in support of these qualifications please consult the Admissions Page

The department plans to recruit between 15 and 20 students with Ph.D.-degree intent every year. The number of admission is roughly three times the recruitment target (that is, up to about 60). We usually receive between 250 and 300 Ph.D. applications every year.

Screening of applications will begin shortly after the deadline in early January. The committee will consider applicants from all backgrounds and evaluate them entirely on academic merits and the criteria above. We expect to be able to make the bulk of our admission offers by mid March.

All admissions are for the autumn semester. Students are required to arrive 4 to 5 weeks prior to the beginning of the autumn semester (the exact date will be contained in the admission letter) in order to participate in the preparatory Headstart program. Exceptions can be made only for students who win university fellowships.

Admission and continued support go hand-in-hand. All students who are admitted into the Ph.D. program receive GA or fellowship support. Conversely, students without continued GA or fellowship support by the department of the university are not admitted to the program regardless of external funding.

All forms of support include full tuition support for the entire year. Regular GA appointments include nine month of stipend support. Stipend levels increase with academic progress and from year to year. For details see the Graduate Handbook. Fellowships include 12 month stipends which are adjusted to be at regular GA levels. GA and fellowship appointments include an 85% health insurance subsidy and other privileges. See this GA Benefits Overview.

Assuming satisfactory academic progress all students are expected to be supported until graduation. GA and fellowship support end once a student leaves the program. The academic standing of each student is reviewed each spring by the Graduate Studies Committee and, if deemed satisfactory, grants the renewal.

Most common are teaching assistantship (GTA's) held by usually over 80% of all students in a given semester. They usually involve teaching two recitation classes (each two hours a week, often the same class back-to-back) under the supervision of a lecturer. GTA experience not only serves support but is also part of the formation of graduate students as future teachers in faculty positions.

Graduate Research Assistantships (GRA's) during the regular (Au,Sp) semesters do not involve teaching and stipend may be slightly different. Some GRAs come from grants of advisors. Other GRAs are awarded each year by the department in an annual competition. There are typically around 16 semesters of departmental GRA's available but this number may vary. Employment as Graduate Administrative Assistantships (GAA's) either through the department or the university are rare but occur in special situations.

Fellowships are awarded through the Graduate School of the university. Several fellowships are given each year to applicants and incoming students with excellent academic records which may vary between one and three years. Similar fellowships are given to applicants from underrepresented groups with strong academics.

In addition, advanced students can compete for the highly prestigious university Presidential Fellowships for their dissertation years. Each year about 30 of these fellowships are given to the most outstanding students in the about 90 doctoral program across campus. In recent years at least one or two of them went to Ph.D. students in the mathematics department.

Full support during the summer term is included in university fellowships but is not automatic for regular GA's. Tuition is granted to all students who have been supported continuously on a GA in the previous two regular semesters. Stipend support for the summer is arranged for the majority of Ph.D. students through a combination of numerous resources though at lower level than in regular semesters.

Normally 80-95% of all Ph.D. students requesting summer support are granted a GA for the summer term. There are three types of GA's, each of which covers roughly one third of the students. GTA's are available to students with at least one semester of teaching experience and satisfactory teaching ratings. Departmental GRA's are awarded to students with strong academic records. In addition, many advanced students receive external GRA's through advisor grants.

The department has special funds reserved for graduate student travel which allow us to grant almost all travel support requests for trips that significantly contribute to the research development of job opportunities of a Ph.D. student.

All supported graduate students also have shared offices with their own desk and shared computer access. For beginning students these may be larger office, while typically two advanced students share one office.

Outlined below are the various steps in the academic progression of students who are pursuing a Ph.D.-degree in our program. The detailed departmental and university expectations can be found in our Graduate Handbook.

The typical graduate career is divided into two main parts divided by the Candidacy Exam. The latter is usually taken sometime during the third year, marks the end of a preparatory period and the begin of the research leading to the Ph.D. thesis.

Before taking the Candidacy Exam students need to fulfill numerous requirements which assure a solid training in the core areas of mathematics that is commonly expected from a mathematics Ph.D. as well as a sufficiently a deeper familiarity with their chosen specialization.

After passing candidacy students will mainly focus on their thesis. Times from admission to graduation usually average around 6 years but may vary greatly depending on many factors such as initial preparation level, individual academic progress regarding departmental expectations, complexity of chosen specializations, as well as strategic thesis and job decisions.

There are two qualifying exams, one in Real Analysis and one in Abstract Algebra. Both exams have to be passed in order to be admitted to candidacy. They are given at the beginning of each autumn and spring semester. Old exams and general information can be found on our Qualifying Exam Page.

As preparation for these exams the department offers each summer special problem solving courses, which are taken also by all incoming students. Nearly all incoming Ph.D. students will have their first attempt at the start of the autumn semester.

Based on the outcome of the first qualifying exams, prior preparations, and the summer courses are placed either as Regular Ph.D. or Ph.D.-Track students with the begin of the autumn semester. Regular Ph.D. students will have to pass these exams within their first year so that mostly only those who have already passed or very nearly passed them on their first attempt will be placed this way.

Students who would like more time at passing their qualifying exams may be placed as Ph.D.-Track students which will given them two years at passing them. Aside from the additional time this placement differs from the regular placement by the stipend amount. Up on passing the exams they are moved automatically to Regular Ph.D. status.

All subsequent time expectations are measured from the time of entering regular Ph.D. status which is for most students the same as the time of passing the qualifying exams.

The main course work required for admission to candidacy is currently encoded in our so called Breadth Requirements. They require choosing course sequences from three different areas of mathematics and doing sufficient work in each of them. In total there are currently 23 course sequences with 63 courses to choose from. Individual course abstracts are also linked on the Breadth Requirements page.

Several revisions to these course offerings and requirements are expected in the near future. The most immediate is a reorganization of the topology & geometry curriculum planned to be implemented in 2010 (to include 700-level courses in cohomology theory, differential manifolds, and introductory differential geometry). In addition the change to semesters in 2012 is likely to entail numerous modifications to our current course offerings.

Nearly all Ph.D. 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 qualifiers and the third one in the following year. Timely completion of breadth requirements may influence stipend level and summer support.

Further course work required for candidacy is the language requirements. Students need to pass a course in either French, Russian, or German specially designed or graduate language requirements with a B or better. Alternatively, a student may pass a translation exam in one of these languages.

More detailed information about which courses are offered and additional courses in our graduate curriculum can be found at our Graduate Course List, the University Bulletin, as well as the Proposed Course Lists of annually offered courses.

An important candidacy requirement is the choice of a thesis specialization and a thesis advisor. The diligent, timely, and careful pursuit of a future research direction is likely the most important responsibility of a prospective Ph.D. 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 and over 20 more faculty on the branch campuses who can supervise doctoral theses. 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, visiting the Invitation to Mathematics colloquium for graduate students, regular research seminars and colloquia (see calendar), or informing themselves independently 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 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 naturally 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 thesis advisor to the department. Typically students should have chosen a thesis advisor about two years after passing their qualifiers.

In order for a graduate student to become an official Ph.D. Candidate as recognized by the university he/she has to pass the Candidacy Exam. This exam is regulated by the university's Graduate School and admission to the exam by the department is subject to the requirements listed above.

Students will need to find a committee of four regular faculty among which the thesis advisor is the chair. The student will negotiate the scope of the examination with each committee member with the constraint that at least two areas must be represented in the exam.

The exam includes a written portion taken usually over two to three weeks. Usually each committee member contributes one of four problem sets to this written portion. In addition the exam has a two hour oral portion which is held after the completion of the written portion.

After candidacy Ph.D. students spend most of their time on research related to the thesis under the close supervision of their advisors. Regular courses are visited only rarely during the thesis phase, usually only to patch up unexpected gaps in the pre-candidacy training.

Nevertheless post-candidacy students still continue to learn new mathematics while they are conducting research. Mostly this happens in regular discussions with the advisor, either one-to-one or in the form of advisor supervised students seminars for candidates working on similar topics. If sufficient interest exists the department also offers topics courses (900-level) at the beginning research level.

In addition, students often discuss mathematics among themselves. In fact in a few areas such as number theory, algebraic geometry, and ergodic theory students organize themselves regular seminars.

The individual thesis research is, of course, mainly the responsibility of the Ph.D. candidate. There is a wide range resources available at the department and Ohio State supporting Ph.D. research.

Ph.D. candidates can choose thesis advisors among 65 faculty on the Columbus campus as well as 26 faculty on branch campuses. In addition, students can consult with one of the dozen or so post-doctoral researchers as well as numerous visitors coming for seminars or through the MRI. For details of computer, library, and other support see the Faculty & Facilities section on the main page.

Time from graduation to graduation may vary depending on initial preparation, formation required in the chosen field, difficulty and scope of the research problem, talent and diligence of the candidate, results required to be competitive in the chosen area and job market, and other factors.

Once the advisor deems the thesis as completed the candidate needs to assemble a dissertation committee. The committee consists of the advisor and two additional regular faculty members who will review the thesis draft.

The approval of the draft is followed by a final oral examination (dissertation defense) conducted by the oral examination committee. The latter consists of the dissertation committee plus a non-math representative of the Graduate School. The examination is two hours and typically focuses on the content of the thesis but may also include general questions. Since 2002 all theses are posted to the Department List as well as the ETD list .

The department supports the search for academic jobs in several ways. Before graduation provides travel support for deserving students, help with letters, and circulation of job opportunities. After graduation many former students with sufficient teaching credentials can find employment as lecturers at the department for about a year while they are looking for jobs.

Normally the department does not admit students whose intended degree is a generic Masters outside of the M.M.S. -program with its designated specializations. However, students admitted with Ph.D.-intent can obtain a general M.S. degree in mathematics during their academic progression towards the Ph.D. degree.

There are three ways for a Ph.D. students to earn an M.S.-degree listed below. Details can be found in our Graduate Handbook.