Mathematics, Ph.D.

The PhD degree in Mathematics is intended as a research degree and is awarded based on scholarly proficiency (as demonstrated by course work and the written Qualifying Exams or the Comprehensive Exam) and the ability to conduct independent, original research (demonstrated by the PhD dissertation).

Admissions

The Doctor of Philosophy degree in Mathematics is intended as a research degree and is awarded based on scholarly proficiency (as demonstrated by course work and the Qualifying Examination) and the ability to conduct independent, original research (demonstrated by the PhD dissertation).

In addition to the minimum Graduate School admission requirements, to be considered for regular admission an application must include:

A resume/CV
3 letters of recommendation.

Scores on the general test of the GRE are optional. We encourage applicants to submit GRE scores if they think doing so will boost their chance of getting admitted. However, applications with and without GRE scores will both get full consideration.

See the Admission Criteria section of this catalog for more information.

Curricular Requirements

Students must complete 48 credit hours of graduate level courses with a minimum of 39 hours in mathematics. The following courses do not count toward this degree: MATH 500 Teaching Workshop, MATH 503 Algebra: Secondary Teachers, MATH 504 Topics Mod Math Teachers, MATH 505 Geometry: Secondary Teachers, MATH 508 Topics In Algebra, MATH 509 Data Analysis: Sec Teachers, MATH 537 Data Science and Programming, MATH 551 Math Stats W/Applictn I, MATH 552 Math Stats W/Applictn II, MATH 570 Prin Modern Algebra I, MATH 572 Advanced Linear Algebra, MATH 585 Intro Complex Variables, MATH 586 Intro Real Analysis I, MATH 587 Intro Real Analysis II, and MATH 591 Teaching College Math (except Math Education students).

Most of the courses required for a master's degree, but not all, are part of the approved collection. In consultation with the student’s dissertation advisor, the Graduate Program Director must approve the student’s program of study. Sample study plans for students wishing to focus in Algebra, Analysis, Scientific Computing, PDE, Topology, Math Education, or Optimization can be found in the graduate student handbook.

Coursework Requirements		Hours
Two Course Sequences (Choose 3)		18
Algebra
MATH 571 & MATH 573	Prin Modern Algebra II and Abstract Algebra I
Boundary Value Problems and Partial Differential Equations
MATH 541 & MATH 642	Boundary Value Problems and Partial Differential Equations
Mathematical Statistics
MATH 554 & MATH 555	Advanced Math Statistics I and Advanced Math Statistics II
Numerical Analysis
MATH 511 & MATH 512	Numerical Analysis I and Numerical Analysis II
Optimization
MATH 520 & MATH 521	Linear Optimization Theory and Non-Linear Optimization Theory
Real Analysis
MATH 580 & MATH 681	Real Analysis I and Real Analysis II
Topology
MATH 565 & MATH 566	Intro General Topology and Intro Algebraic Topology
Additional Courses (choose 10)		30
Besides the sequences, additional courses are available to students that provide the foundation to do research at the PhD level.
MATH 510	Numerical Linear Algebra
MATH 538	Topics in Mathematics
MATH 557	Stochastic Processes I
MATH 559	Stochastic Processes II
MATH 560	Intro Differential Geom
MATH 583	Complex Analysis I
MATH 588	Theory Diff Equations I
MATH 593	Collegiate Math Education Rsrc
MATH 598	Non-Thesis Research
MATH 610	Iteratve Meth Linear Sys
MATH 611	Numerical PDEs
MATH 644	Singular Perturbations
MATH 648	Topics in PDE
MATH 661	Algebraic Topology I
MATH 674	Abstract Algebra II
MATH 677	Topics Algebra I
MATH 684	Complex Analysis II
MATH 686	Functional Analysis I
MATH 688	Topics in Analysis
MATH 698	Non-Dissertation Research
Dissertation		18
MATH 699	Dissertation Research

Total Hours		66

Transfer Credit

See the Graduate School policy.

Doctoral Plan of Study Requirement

See the Graduate School Policy on the Doctoral plan of study.

First Year Coursework and Preliminary Examination

All first year PhD students are required to attend a weekly seminar about first year experience of graduate school, led by a full or associate graduate faculty member. In addition, they are required to take two master’s core sequences:

(1) MATH 586 Intro Real Analysis I, MATH 587 Intro Real Analysis II, and either

(2a) MATH 572 Advanced Linear Algebra and MATH 570 Prin Modern Algebra I, or

(2b) MATH 572 Advanced Linear Algebra and MATH 537 Data Science and Programming.

For MATH 572 and MATH 586, in addition to regular lectures there are also weekly discussion sessions led by TA. Students must attend the discussion sessions as well as the lectures. Students are required to obtain at least a grade of B and at least 75% in the final exams of all master’s core courses. Those who do not will be required to take the corresponding preliminary exams in the August after the first year. Students may also test out of these two core sequences by taking and passing the corresponding preliminary exams.

The final exams for MATH 586, MATH 587, MATH 572, MATH 570, and MATH 537 will be prepared and graded by exam committees appointed by the Graduate Program Committee, in consultation with the department chair. Each course will have an exam committee consisting of three members: the instructor of the course and two additional faculty members. All three members must be full or associate members of the graduate faculty.

In the first fall semester, all students who are supported as GTA must take MATH 500 Teaching Workshop and two regular graduate courses, MATH 586 and MATH 572. Students who are supported as GRA are not required to take MATH 500, but are required to take at least two regular courses ( MATH 586, MATH 572), and are recommended to take one more regular course. Students who are supported by fellowships are not required to take MATH 500 but are required to take at least three regular courses ( MATH 586, MATH 572, and one more regular course).

The math department offers three preliminary exams (PEs):

Analysis Exam that is based on MATH 586 and MATH 587.
Linear Algebra and Mathematical Foundations of Data Science Exam that is based on MATH 572 and MATH 537.
Linear Algebra and Principles of Modern Algebra Exam that is based on MATH 572 and MATH 570.

The PEs are offered once a year in August and are prepared and graded by the exam committees for MATH 586, MATH 587, MATH 572, MATH 570, MATH 537, respectively. Students must receive 75% or above to pass the preliminary exams. First year students can choose to test out of one or both master’s core sequences by taking and passing one or both PEs on arrival. If they pass one or both PEs, then they are exempted from taking the corresponding courses. Otherwise, they must take the courses.

PhD Students must either test out of the master’s core sequences, or get at least a B and receive at least 75% in the final exams of all of the corresponding courses, or pass the corresponding PEs by the August after their first full academic year of PhD studies in the Department of Mathematics at The University of Alabama; those who do not will not be able to continue in the PhD program and will have to transfer to the master’s program.

The PhD Qualifying or Comprehensive Exams

PhD students must fulfill one of the following two options no later than the August after their third year of PhD studies in the Department of Mathematics at The University of Alabama; those who do not will not be able to continue in the PhD program. They may choose to move to the master’s program.

Option 1: Pass two written qualifying exams from five subjects: Algebra, Topology, Real Analysis, Numerical Analysis, and Partial Differential Equations.

Written qualifying exams are given twice a year, in January and August respectively, lasting four hours each. Students may take no more than two qualifying exams at a time, and they have at most three attempts in each qualifying exam. Although not recommended, it is allowed for students to take different subjects in different testing periods. However, doing so will not extend the deadline of passing two exams beyond the August after their third year. If a dispute arises, the final interpretation of the exam rules and scores will be made by the Graduate Program Committee.

Each exam is written and graded by a committee appointed by the Graduate Program Committee, in consultation with the department chair. To guarantee independence and avoid conflict of interests, each committee will, if possible, consist of two faculty members who are not instructors of the corresponding courses in that year. The committees must seek input from the instructors on the preparation of the exams. After the qualifying exams are graded, the exam committees make a recommendation of a grade of Fail or Pass to the GPC and the Graduate Program Director. The GPC will have the final authority to assign the grade, which is then conveyed to each student by the Graduate Program Director, who will also inform the graduate school. The full grade will also be available to potential advisors.

Option 2: Pass a comprehensive exam that is based on the plan of study.

Instead of taking two written qualifying exams, students may choose to take a comprehensive exam led by their dissertation advisors. Students who want to choose this option must satisfy the following conditions:

(a) They must have a dissertation advisor by the end of their third semester.

(b) The dissertation advisor must be willing to form a dissertation committee and lead the committee to design a comprehensive exam that covers topics in the student’s plan of study, emphasizing topics most relevant to their research.

The committee can decide whether the comprehensive exam is written or oral. It is up to the committee to choose a time to test the students. Under Option 2, each student has a maximum of three attempts in the comprehensive exam. As always, students have the freedom to change areas of research, dissertation advisors, or members of their dissertation committee. However, if changing advisors, at the discretion of the new advisor, the student may need to retake the comprehensive exam. In addition, changing areas, advisors, or committee members do not give students an extension of the deadline to pass the comprehensive exam by the August after their third year.

PhD Dissertation Committee Requirements

Students need to decide on a major area of specialization, and find an advisor in that area. This should happen no later than the beginning of the third year. Although the Graduate Program Director will assist students in choosing a dissertation advisor, students are in the end responsible for finding a dissertation advisor. Students must form a dissertation committee consisting of at least five members, with at least three from the Department of Mathematics of UA and at least one from outside the Department of Mathematics of UA, possibly outside of UA. Note that they all need to be graduate faculty. Contact the Graduate Program Director about requesting temporary graduate faculty membership for non UA faculty. The dissertation advisor must be a full member of graduate faculty of the Department of Mathematics of UA and serve as the committee chair.

Admission to Candidacy Requirements

Advancing to candidacy requires the passing of either two qualifying examination or one comprehensive exam, the completion of all the coursework as listed on the approved plan of study, and successfully presenting and defending a dissertation proposal. In a formal meeting, students present their dissertation research proposal to the dissertation committee in which students should demonstrate they have meaningful directions of research to pursue and a good foundation for research. The committee will assess the worthiness of the research proposal and approve or disapprove it. Students should fulfill all PhD candidacy requirements by the end of their fourth year.

Continuous Enrollment Policy

See the Graduate School policy.

Dissertation Requirements

See the Graduate School policy.

Time Limits for Degree Completion Requirements

See the Graduate School policy.

Student Progress Requirement

The following is an acceptable progress toward a PhD in Mathematics.

1st Year – Complete two master’s core sequences with a grade of B or better and at least 75% in the final exams in all master’s core courses, or pass the corresponding preliminary exams, and maintain a 3.00 GPA or higher.
2nd Year – Discuss with the initial advisor to create a PhD plan of study, complete at least two 2-course PhD sequences with a satisfactory GPA, and find a dissertation advisor.
3rd Year – Maintain a satisfactory GPA, pass either two written qualifying exams or one comprehensive exam no later than the August after their third year.
4th Year – Determine a potential dissertation topic, form a dissertation committee, prepare the dissertation proposal and defend it in front of the dissertation committee by the end of the fourth year. Obtain approval of the research proposal from the dissertation committee and begin dissertation research. Also, complete the 48 hours with a satisfactory GPA. Request the Plan of Study form and the Admission to Candidacy form by contacting the Graduate Program Assistant.
5th Year – Check the student deadlines from the graduate school’s website. At least one month before the deadline for submission of the dissertation to the graduate school, students must distribute a hardcopy of their dissertation to committee members, and the defense needs to be scheduled to give students at least one week to make corrections.
Provided satisfactory progress towards the PhD is being made, a student’s advisor may request an extension for a 6th year of support. This request must be made before the end of the semester before the last semester of funding.

Other Requirements

Every graduate student need not only to make satisfactory progress in their studies and research, but also to carry out the teaching and/or other duties assigned to them by the department and the university. Failing to carry out their duties will result in prorated stipend, the termination of their assistantships, or the suspension from the graduate program. Examples of failing to carry out duties include, but are not limited to

Failure to teach assigned classes or perform assigned duties in the MTLC.
Failure to consult with course coordinator or the Director of Lower Division Instruction about changes to their courses.
Failure to consult with the Supervisor of Tutors and Proctors or the MTLC Lab Coordinator about changes to MTLC schedules or duties.
Leaving before the end of the semester (defined as the date grades are due) or returning after the Monday before classes start without permission of the MTLC Lab Coordinator and the Graduate Program Director.