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DOCTOR OF PHILOSOPHY IN MATHEMATICS - EMPHASIS IN APPLIED MATHEMATICS


The Ph.D. in Mathematics with emphasis in Applied Mathematics is designed to train students to become researchers and educators at the forefront of interdisciplinary science. The official degree requirements for the Doctor of Philosophy degree in Mathematics are detailed here. This page is a very important guide through the graduate experience.

Our graduate experience is broken up into "Phases". For the Ph.D degree, there are three phases. The expected duration of time for each phase is:

Phase I: Between 1 year and 2.5 years
Phase II: Between 1 and 1.5 years
Phase III: Between 2 and 3 years
The Ph.D. is designed to take between 4 and 6 years. Very few finish in 4 or less, and most finish within 6. Students admitted to the Ph.D. program who remain in good standing receive financial support (T.A. or R.A.) for 5 years; additional years are supported on an individual basis.


PHASE I: Comprehensive Courses and Examination
During this phase, students develop their mathematical knowledge and skill by taking 3 or 4 courses from among the 5 core comprehensive courses offered. It is strongly recommended that students take the core Scientific Computation courses, Math 191 and 192, and the core Methods of Applied Mathematics courses, math 198 and 199.

Separate from the core requirements, there is also an emphasis on breadth outside of Mathematics during Phase I. Students are encouraged to take classes each semester in another discipline (or disciplines) of science. Possible departments include Environmental Sciences, Marine Sciences, Computer Science, Physics, Biology, and Chemistry.

--- Completion of Phase I: passing Comprehensive Examination(s)
To complete Phase I, students must pass, at the Ph.D. level, either the 2 exams in applied mathematics (Scientific Computation and Methods of Applied Mathematics) or any 3 exams from the available 5 exams in the Department.


PHASE II: Preliminary Research and Oral Examination
Upon completion of Phase I, students begin choosing an area in which to begin research. The first priority is to select a research advisor. It is recommended that students approach a number of faculty members and figure out what sort of research they do. Only by understanding what sort of research possibilities are out there can students decide which area they find most appealing.

Once an area of mathematical and scientific emphasis, and an advisor have been determined, the student then works closely with the advisor to begin a research program. This includes:

  • Organizing and carrying out a plan of study designed to deepen the student?s knowledge of the area of mathematical and scientific emphasis.
  • Selecting an oral exam committee, consisting of at least 3 faculty members.
  • The determination of an area of research, and possible topics for doctoral thesis research.
Additionally, it is expected that students will take at least two semesters of core courses in other disciplines of science. Suggested departments for this purpose include Environmental Sciences, Marine Science, Computer Science, Biology, Physics, and Chemistry.

--- Completion of Phase II
Phase II is completed when the student passes the oral examination. This is a closed exam, with the student and Exam Committee as well as any faculty the student and committee choose to invite. This is anticipated to take place between 1 and 1.5 years after passage of the Comprehensive Exams, for approximately 2 hours. The purpose of this exam is for each student to choose an area of applied mathematical and applications emphasis, and to develop a solid foundation for original research. The student has two chances to pass the Oral Examination.


PHASE III: Ph.D. Candidacy
The primary goal of students during Phase III is to carry out research, leading to a Ph.D. dissertation. As all graduate students know, the length of time required to finish a Ph.D. dissertation depends on many factors both predictable and unpredictable. Therefore Phase III may last one year or many years. Achieving a Ph.D. from start to finish in five years is a realistic goal, but six or seven years is not uncommon (even for several of the UNC faculty).


Email: info@amath.unc.edu *
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