Program requirements are based upon the premise that Ph.D. students should have a broad exposure to graduate level mathematics, as well as experience doing mathematical research in an area of specialization. To achieve this goal, we offer a wide spectrum of courses each semester. Each semester's course offerings can be found here. (graduate courses start at the 600's). Typically each course in our catalogue is taught at least once every two years.

The student's advisory committee for a Ph.D. degree should consist of no fewer than four members of the graduate faculty representative of the student's fields of study and research. The Chair (main advisor) must be from the student's major department and at least one of the other members must be from a department other than the student's major department. It's usually easiest to start off by choosing the Chair-- then the Chair can assist the student in choosing the remaining members of the committee. The duties of the committee include responsibility for the proposed degree plan, the research proposal, the preliminary examination, the dissertation and the final exam/defense.

The goals of "breadth of training and depth of knowledge in an area of specialization" are fostered through the Qualifying Examination Requirement, the Subject Area Breadth Requirement, the Foreign Language Requirement, and the Dissertation Requirement. Each is described in detail as follows:

Qualifying Examinations and Course Sequences

To be considered in good academic standing in the Ph.D. program, a student must pass two departmental Ph.D. qualifying examinations by the end of their second year in the Ph.D. program as prescribed in the following sections. For purposes of the qualifying exam timetable, students will be considered to have begun their Ph.D. program with the Fall semester occurring in the calendar year in which they first enroll in the program. In addition to the guidelines below, students should also see Special Notes on Qualifying Examinations

Except for students being admitted to the Ph.D. program upon completion of a M.S. degree in mathematics at Texas A&M University, the following guidelines apply:

• Students are expected to have passed at least one qualifying exam by the end of their first year in the Ph.D. program.
  
• Students are expected to have passed at least two qualifying exams by the end of their second year in the Ph.D. program.
  

Since students being admitted to the Ph.D. program upon completion of a M.S. degree in Mathematics at Texas A&M University must have already passed at least one Ph.D. qualifying exam prior to admission to the Ph.D. program, the following amended guidelines will apply:

• Students are expected to have passed their second qualifying exam by the end of their first year in the Ph.D. program.
  

All new students beginning from Fall 2008 must follow the New Qualifying Exam System. Current students who began prior to Fall 2008 can continue to follow the Old Qualifying Exam System until it ends August 2009 OR they can elect to follow the New Qualifying Exam System immediately. However, once they switch to the New Qualifying Exam System, they can not switch back to the Old System.

Old Qualifying Exam System (will no longer run after August 2009)
A total of eight qualifying exams are offered twice a year, August and January. The subject areas for the exams are Algebra, Applied Analysis, Combinatorics/Number and Graph Theory, Complex Analysis, Differential Geometry, Numerical Analysis, Real Analysis and Topology. Copies of syllabi and previous exams can be viewed here.

New Qualifying Exam System (beginning August 2008 and will be only exam system after August 2009)
A total of five qualifying exams are offered twice a year, August and January. The subject areas for the exams are Algebra, Applied/Numerical Analysis, Complex Analysis, Real Analysis and Topology/Geometry. Copies of syllabi and previous exams can be viewed here.

Regardless of which system is being followed, in addition to passing two qualifying exams, students must also take two additional full qualifying exam course sequences and pass them with at least a grade of B. The combination of qualifying exams and additional courses must cover three out the following four groups:

• Geometry, Topology
  
• Complex Analysis, Real Analysis
  
• Applied Analysis, Numerical Analysis
  
• Algebra, Combinatorics/Graph and Number Theory
  

Students have the option of passing a third qualifying exam in place of taking the additional two full qualifying exam course sequences but all the exams must cover three out of the above four subject groups.

Subject Area Breadth Requirements

With the goal of encouraging students to be exposed to a broad spectrum of mathematics during their graduate studies, students in the Ph.D. program must demonstrate experience in all eight of the following areas: algebra, applied analysis, complex analysis, geometry, combinatorics/graph and number theory, computational mathematics, real analysis, and topology. Experience may be demonstrated in any of the following ways:

• Passing a qualifying exam in the area
• Achieving a grade of B or better in a one semester graduate course in the area
• Credit from prior experience for either 1 or 2 above

Satisfaction of either 2 or 3 will be determined by the Graduate Programs Committee and interpreted within a broad perspective. It is expected that most permanent and special topic courses offered by the Department would apply to more than one subject area. However, a given course cannot be used by a student to satisfy the area requirement in more than one area, even though different students might use the same course to satisfy different area requirements. The course must have a substantial content from an area in order to satisfy the area requirement for that area.

Preliminary Exam Requirement

All Ph.D. students are required to do a Preliminary Exam. It is through this exam the student's committee satisfies itself that the student has demonstrated a mastery of the subject matter of all fields in their program, obtained adequate knowledge of the literature in these fields and has the ability to carry out bibliographical research. The exam is to be given no earlier than a date at which the student is within approximately 6 credit hours of completion of the formal course work on the degree plan (i.e. all course work except 681, 684, 690, 691 and 692) or no later than the end of the semester following the completion of the formal course work on the degree plan. The Chair of the student's advisory committee must report the results of the exam promptly to the Office of Graduate Studies using the Report of the Doctoral Preliminary Examination Form and the Preliminary Examination Checklist. The Office of Graduate Studies must receive these results within 10 days after the exam was completed otherwise it will be recorded as a failure. After passing the Preliminary exam, students must complete all remaining requirements for the degree within four calendar years or else be required to repeat the Preliminary exam.

Research Proposal

As soon thereafter as the research project can be outlined in reasonable detail, the dissertation research proposal should be completed. The approved proposal and Proposal Title Page form with appropriate signatures must be submitted to the Office of Graduate Studies at least 15 working days prior to the submission of the Request for the Final Examination (dissertation defense).

Admission to Candidacy

To be admitted to candidacy for a doctoral degree, a student must have: (1) completed all formal course work on the degree plan with the exception of any remaining 681,684,690 and 691 hours, (2) a 3.0 Graduate GPR and a Degree plan GPR of at least 3.0 with no grade lower than C in any course on the degree plan, (3) passed the Preliminary Examination, (4) submitted an approved dissertation proposal, (5) met the residence requirements. The final oral examination will not be approved for any doctoral student who has not been admitted to candidacy.

Foreign Language Requirement

This departmental requirement may be satisfied by taking and passing a translation examination in Chinese, French, German, Russian or Spanish. The translation exam for a particular language is given by a faculty member appointed by the Associate Head for Graduate Programs-- Chinese: Dr. Chen, French: Dr. Borosh, German: Dr. Straube, Russian: Dr. Lazarov, Spanish: TBA. The examiners are provided with a list of books from which a passage for translation is selected. The student can chose the book for the translation but not the passage. The passage for translation is chosen by the faculty member administering the exam. Students and examiners will mutually decide on the time and location for the exam. Dictionaries are allowed but the exam can not be taken home. Transfer credit for the foreign language requirement will be allowed if it is course work comparable to courses here at A&M, or if it is passing the ETS exam with a suitable score. Translations administered at other universities will not be accepted. Students with demonstrated fluency in one of the designated languages may be exampted by the Graduate Programs Committee from the translation exam. Fluency may be demonstrated in the following ways:

• Native language
• Extensive university study of or in the language

Dissertation Requirement

Ph.D. students must demonstrate an ability to conduct independent research by completing an original dissertation. Acceptance of the dissertation is based primarily on its scholarly merit, however, it must also have creditable literary workmanship. The format of the dissertation must meet the guidelines of the Office of Graduate Studies and the Thesis Office as stated in the "Thesis Manual" which is available online at thesis.tamu.edu/thesismanual.php. After successful defense and approval by the student's advisory committee and the head of the student's major department, students must submit their dissertation to the Thesis Office in electronic format as a single PDF file. The PDF file must be uploaded to the Thesis Office website, thesis.tamu.edu. Additionally, a signed approval page (available online at the Thesis Office website) must be brought or mailed to the Thesis Office. Both the PDF file and the signed approval page are required by deadline day (see OGS calendar for deadlines).

Steps to Fulfill Doctoral Degree Requirements

Meet with departmental graduate advisor to plan course of study

When: before first semester registration

Establish advisory committee and submit a degree plan

When: prior to registration for a fifth semester excluding summer terms

Complete course work detailed on degree plan

When: before preliminary examination

Have preliminary examination

When: no earlier than a date at which the student is within 6 credit hours of completion of formal course work on the degree plan or no later than the end of the semester following completion of all formal course work on the degree plan. Also the student's degree plan must have been submitted to OGS and approved at least 90 days before the date of the preliminary exam. OGS must receive the preliminary exam results at least 14 weeks prior to the final exam date.

Submit proposal for dissertation

When: at least 15 working days prior to the submission of the Request for the Final Exam (dissertation defense)

Be admitted to candidacy

When: before submitting request to schedule the final oral examination

Apply for degree and pay graduation fee

When: during the first week of the final semester

Submit request to schedule final oral examination

When: at least 10 working days before requested exam date

Upload one approved final copy of dissertation as a single pdf file (thesis.tamu.edu) and submit a signed approval page to the Thesis Office

When: see Office of Graduate Studies semester calendar for deadlines

Graduation

When: see Office of Graduate Studies semester calendar for dates