Degree type
Ph.D.
Length
5-6 years
Years 1-3: Conference Courses, Elective Coursework & Preliminary Courses
Post-Candidacy: Dissertation (minimum 6 hours)
Students must enroll in 9 credit hours per semester, completing a minimum of 30 semester hours of advanced coursework, including at least 6 dissertation hours. The program requires students to pass preliminary examinations in at least seven distinct areas and involves conference courses to help establish research direction and academic advising.
Throughout their studies, students work closely with faculty mentors, leading to original research culminating in a dissertation. The program encourages collaboration and prepares graduates for a range of careers in academia, finance, technology, data science and engineering. Alumni have secured positions at prestigious institutions such as MIT and UC Davis, as well as companies like Google.
Key milestones in the program include passing oral candidacy exams, forming an advisory committee, and successfully completing a dissertation within three years of candidacy. Students are supported by faculty throughout the process, ensuring a thorough preparation for their future careers in mathematics.
Steps to obtaining a Ph.D.
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1
Demonstration of broad competence
This is accomplished through the passage of Preliminary (“prelim”) examinations and coursework. The department offers twelve prelim courses, which are usually presented as six two-semester sequences. The twelve courses are:
- Algebra (parts I and II);
- Analysis (Real and Complex);
- Methods of Applied Mathematics (parts I and II; these courses cover functional analysis, harmonic analysis, and other analytic methods);
- Numerical Analysis (part I, covering linear-algebraic topics, and part II, covering differential equations); Probability (parts I and II);
- Topology (Algebraic and Differential).
In addition to the courses, exams are offered twice yearly (in August and January) in the twelve prelim areas. Students can fulfill a part of their prelim requirement by passing a course with a grade of B or higher, or by passing the corresponding exam. Students are required to pass at least 7 prelims in distinct areas, at least 3 of them by exam. Details of the prelim policy will be explained in section VII.
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2
Identification of an academic advisor
You should identify an area of specialization and an academic advisor with one year of passing the third prelim exam. To do so, you should identify a potential advisor and take a Conference Course under the advisor’s supervision - and subsequent conference courses if both you and the instructor consider it likely that the faculty member will become your academic advisor. Taking conference courses need not be delayed till the completion of prelim requirements; often the second or third semester is an appropriate time for a first conference course. Once an academic advisor has been identified, and has agreed to serve in this role, you will work with the advisor to select an advisory committee of three faculty members to oversee the candidacy exam; and, after passing the candidacy exam, a committee of four to oversee the dissertation.
You are guided in this process by the Graduate Advisor, who ensures that all steps conform to Graduate School requirements.
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3
Oral candidacy exam
Having identified an area of specialization and an academic advisor, you must successfully complete an oral candidacy exam in the chosen area of specialization. The topics of this exam are set by the advisory committee in consultation with the student. In order to pass the exam, you must demonstrate to their advisory committee:
- acquired adequate content knowledge in the area of specialization,
- the ability to interpret existing research literature and devise a program of original research, and
- the ability to effectively communicate mathematics in English.
The candidacy exam takes the form of a lecture presentation by the student, followed by questions from the committee. While some candidacy lectures present original research by the students, this is not a requirement; presentation of existing material relevant to the area of specialization and the student’s planned research may also be appropriate, as determined by the academic advisor and candidacy committee.
Students become eligible for oral candidacy exams after passing 5 distinct prelims, at least 3 by exam. Students are expected to complete their candidacy exam by August of their third year.
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4
Formal admission to Ph.D. candidacy
To advance to doctoral candidacy, you must have:
- Passed the oral candidacy exam (as well as the prelim eligibility requirement as described above);
- Obtained the agreement of faculty members to serve on the dissertation committee (including one external member, meaning a qualified faculty member, either from another university, or from UT Austin but not a member of the Mathematics GSC); and
- Submitted a formal candidacy application to the Graduate School. The formal application includes a statement of proposed research which must be approved by the student’s academic advisor, chair of the GSC, Graduate Advisor, and Graduate School. Students must comply with any other applicable Graduate School requirements.
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5
Completion of Prelim requirements
If you have any remaining prelim requirements, these must be completed within a year of formal admission to Ph.D. candidacy. The requirements are 7 prelim courses and exams in distinct areas, passed via courses or exams, but at least 3 of them by exam.
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6
Completion of dissertation
The research written in the dissertation is the most important part of the Ph.D. program. This, fundamentally, is what a Ph.D. is about. It consists of original research in mathematics performed by the student with regular input from his or her academic advisor. You are expected to complete the dissertation within three years of passing the candidacy exam. While writing the dissertation, students must be continuously registered in the dissertation course during the Fall and Spring semesters.
Exceptions
A student wishing an exception to be made to any of the regulations above must first consult with the Graduate Advisor, and then, if circumstances warrant, make a formal appeal to the Administrative Subcommittee of the Graduate Studies Committee (ASGSC). The ASGSC is the final arbiter in all such matters.