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Graduate Catalog | 2025-2026
Applied Mathematics, Ph.D.
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 Return to: Academic Programs (Doctoral)
The Ph.D. degree program in Applied Mathematics is designed to enable its students to master a significant body of mathematics; to relate this knowledge to a coherent area of science or engineering; and to carry on fundamental research in mathematics at a nationally competitive level. The Statistics Concentration of the Ph.D. in Applied Mathematics addresses the growing demand for expertise in statistical theory, data science, and quantitative analysis. It emphasizes both theoretical foundations and data-driven methodologies, preparing graduates for leadership roles in research, decision-making, and innovation across academia, industry, and government sectors.
Recipients of the Ph.D. degree will, depending on their abilities and choice of sub-specialty, be able to work effectively in research and development environments involving mathematical and statistical analysis and modeling in business, government or industry, to teach mathematics and/or statistics at the college or university level, or to carry out fundamental research in their area of expertise.
For further information, please see the Department of Mathematics and Statistics.
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Admission Requirements
Applicants will be evaluated in a holistic manner to identify those who have the greatest potential to complete the program. In addition to the general requirements for admission to the Graduate School, to begin study toward the Ph.D. in Mathematics, students admitted to the program should have: - A B.S. or B.A. degree in mathematics or statistics or a closely related field from a college or university accredited by an accepted accrediting body.
- An overall grade point average of at least 3.0 out of 4.0.
- A minimum of 27 credit hours in mathematics and/or statistics at the undergraduate level, as approved by the department Graduate Committee, with grades of a C or above. These typically include 12 credit hours of calculus at the level of MATH 1241, MATH 1242, MATH 2241, and MATH 2242; 3 credit hours of linear algebra at the level of MATH 2164; and 3 credit hours of differential equations at the level of MATH 2171. For admission to the Ph.D. in Applied Mathematics program, these also include 6 credit hours of proof-based analysis courses at the level of MATH 3141 and MATH 3142 and 3 credit hours of modern abstract algebra at the level of MATH 3163, while for admission to the Ph.D. in Applied Mathematics with a Concentration in Statistics program, these also include 6 credit hours of probability and statistics at the level of STAT 3122 and STAT 3123 and 3 credit hours of analysis at the level of MATH 3141. In addition, admission requires that the candidate be able to take MATH 8143 or be able to take MATH 5143 and have other factors in their record that indicate strong potential to complete the program.
- A score of at least 83 on the Internet-based Test of English as a Foreign Language (TOEFL), or an overall band score of at least 6.5 on the International English Language Testing System (IELTS), or a score of at least 115 on the Duolingo English Test, for applicants whose native language is not English. To be considered official, the score must be sent directly from the testing agency to UNC Charlotte.
- Three letters of reference, at least two of which must be from faculty members.
- A score on the GRE General Test or the GMAT with a quantitative score of at least 70th percentile. To be considered official, the score must be sent directly from the testing agency to UNC Charlotte. However, there are two exceptions:
- A student who has already earned a Ph.D., M.D., or J.D. from a U.S. institution will not be required to submit a GRE General Test or GMAT score.
- A student who has already earned a Master’s degree from a U.S. institution will not be required to submit a GRE General Test or GMAT score IF the student can demonstrate that they have completed the test in the past. In such cases, the program will accept the official student’s copy of the official test scores.
For prospective students who have completed work in mathematics and/or statistics beyond the bachelor’s degree, performance on that work will be considered in admission decisions. Candidates with relevant research experience and professional publications will be given priority consideration. Students are admitted to the program by the Graduate School, based on the recommendation of the department Graduate Committee or its designate, the Graduate Program Director. Recommendations are based on the Committee’s judgment of the candidate’s ability to complete the program, as supported by the application materials. The department may waive certain admission requirements if it judges the candidate to be nonetheless capable of completing the program. Degree Requirements
Students in the Ph.D. in Applied Mathematics program must maintain satisfactory academic progress towards completion of the degree. Student satisfactory academic progress is primarily assessed by: (a) satisfactory coursework performance, (b) the qualifying examination, and (c) a dissertation. The students must complete an approved program of study of 54 credit hours, including the following: Research and Ethics Courses
Students should complete the following courses in the first year of their program. Required Courses and Dissertation (24 credit hours)
Students must complete 18 hours of Doctoral Research and Reading credit. Breadth Elective Courses (9 credit hours)
Students must complete either (a) 1 course from Group I and 2 courses from Group II, or (b) 2 courses from Group I and 1 course from Group II: Elective Courses
Students must complete at least 3 credit hours from the following MATH courses. Students are encouraged to include interdisciplinary elective courses in their program of study. These courses are generally expected to be in STEM disciplines, see examples below; however, courses in the social sciences may also be included if they are directly relevant to a student’s dissertation work. While students may take more than three interdisciplinary electives, a maximum of 9 credit hours from such courses will count toward the 54 credit hours required for the degree. Degree Total = 54 Credit Hours
Degree Requirements, Statistics Concentration
Students in the Ph.D. in Applied Mathematics with a Concentration in Statistics program must complete an approved program of study of 54 credit hours, including the following: Research and Ethics Courses
Students should complete the following courses in the first year of their program. Required Courses and Dissertation (42 credit hours)
Students must complete 18 hours of Doctoral Research and Reading credit. Restricted Elective Courses (6 credit hours)
Students must complete two courses from the following MATH/STAT courses: Elective Courses (6 credit hours)
Students are encouraged to include interdisciplinary elective courses in their program of study. These courses are generally expected to be in STEM disciplines; however, courses in the social sciences may also be included if they are directly relevant to a student’s dissertation work. While students may take more than two interdisciplinary electives, a maximum of 6 credit hours from such courses will count toward the 54 credit hours required for the degree. Examples of elective courses allowed for several fields include: Mathematics and Statistics
Degree Total = 54 Credit Hours
Qualifying Examination
After being admitted to the Ph.D. program, students are expected to take the qualifying examination within three semesters. This time limit may be extended for up to two additional semesters in certain cases, depending on the background of the student and with program approval. The qualifying examination for the Ph.D. in Applied Mathematics consists of the following two parts. The qualifying examination for the Ph.D. in Applied Mathematics with a Concentration in Statistics consists of the following two parts. - Part I: A written examination based on Theory of Statistics I and II (STAT 8116 and STAT 8117 ).
- Part II: A written examination based on Applied Statistics I and II (STAT 5123 and STAT 5124 ).
Students may be allowed to retake a part of the qualifying examination a second time if they do not pass that part on the first attempt within the guidelines of the Graduate School regulations pertaining to the qualifying examination and as overseen by the department Graduate Committee. Students must pass the qualifying examination by the end of the 5th semester of study. Students who do not complete the qualifying examination as per the regulations of the Graduate School are terminated from the Ph.D. program. Dissertation
Students must complete and defend a dissertation based on a research program approved by their dissertation committee which results in a high quality, original and substantial piece of research. Dissertation Committee
Each student has a dissertation committee appointed by the department Graduate Committee in consultation with the student and approved by the Dean of the Graduate School. A dissertation committee must consist of at least four graduate faculty members, including the Graduate Faculty Representative appointed by the Graduate School. The committee is typically chaired by the student’s dissertation advisor. If the dissertation advisor is a graduate faculty member from an outside department or institution, a graduate faculty member from the Department of Mathematics and Statistics must be a co-chair of the committee. The dissertation committee should be appointed as soon as is feasible, usually within a year after passing the qualifying examination. Prior to the appointment of the dissertation committee the student is advised by a graduate faculty member appointed by the department Graduate Committee. Topic Approval Defense and Admission to Candidacy
After a student completes the qualifying examination and advanced coursework, the student, in consultation with the student’s dissertation advisor, may propose a dissertation topic. The dissertation topic proposal must be articulated and defended at a meeting of the student’s dissertation committee. A written dissertation proposal must be submitted to the dissertation committee at least two weeks prior to the scheduled defense. The student is expected during the course of the topic defense to outline and demonstrate sufficient proficiency with the advanced knowledge and techniques to be used in the conduct of the research. The topic approval defense and the committee’s deliberations in this regard are to be conducted according to the pertinent regulations of the Graduate School. A doctoral student advances to candidacy after the student’s dissertation committee and the Dean of the Graduate School have approved the dissertation topic proposal. A student may retake the dissertation topic approval defense if they fail the first time. The second failed attempt will result in the termination of the student’s enrollment in the Ph.D. program. Final Defense
A student must orally present and successfully defend the dissertation before the student’s doctoral dissertation committee in a defense that is open to the public. A working copy of the dissertation must be made available to each member of the student’s dissertation committee at least three weeks prior to the public defense, and along with the dissertation, the student must share their iThenticate similarity report with the committee. A copy of the dissertation must be made available to the graduate faculty of the department at least two weeks prior to the public defense. The final defense and the committee’s deliberations in this regard are to be conducted according to the pertinent regulations of the Graduate School: All members of the committee, including the Graduate Faculty Representative, must attend the defense; the decision of the committee is final; in the rare event of a split decision, typically the committee members come to an agreement as to whether the student defense is acceptable; it is the responsibility of the committee chair to work within their ability to resolve any impasse among committee members; if no resolution is feasible, then the chair should consult with the Graduate School; and no student is permitted to take the final dissertation defense more than twice. Grade Requirements
Students are expected to achieve As or Bs in all courses included in the program of study and must maintain a minimum 3.0 GPA to graduate. An accumulation of more than two marginal (C) grades will result in suspension of the student’s enrollment in the program. If students make a grade of U on any course, enrollment will be suspended and students cannot take further graduate work without being readmitted to the program. Readmission to the program requires approval of the Dean of the Graduate School upon the recommendation of the department Graduate Committee. Residency Requirement
Full-time Ph.D. students must enroll for one continuous full-time year (i.e., two consecutive semesters of at least nine graduate credit hours in each semester) following admission to the program. Time Limit for Degree Completion
Students must achieve admission to candidacy within six years after admission to the program and complete all requirements within six years after admission to candidacy for the Ph.D. degree. All requirements for the degree must be completed within nine years after first registration as a doctoral student. Transfer Credit and Credit by Exam
Only courses with grades of A or B may be accepted for transfer credit. Transfer credit must be recommended by the department Graduate Committee and approved by the Dean of the Graduate School. The amount of transfer credit cannot exceed the limit set by the Graduate School. Students who, because of their previous undergraduate and/or graduate work or other experience, can demonstrate sufficient knowledge of the material in one or more of the core, breadth, depth, or restrictive elective courses may be exempted from taking a course or courses by competence tests or credits by exam. Exemption from a course by a competence test carries no credit towards the degree. Dual Enrollment in Ph.D. and M.S. Degrees
Ph.D. students may choose to pursue a M.S. in Mathematics degree while continuing to work toward the doctoral degree. Doctoral students can apply for enrollment in the M.S. program after entering the Ph.D. program Teaching Assistant Training
Students receiving a teaching assistantship are required to complete the one-credit hour course MATH 6690 Graduate Teaching Assistant Training . This credit hour does not count toward the 54 credit hours required for the degree. Students with prior college teaching experience as an instructor of record may request a waiver of this requirement. |
Return to: Academic Programs (Doctoral)
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