Computational Mathematics, PhD

The PhD in Computational Mathematics requires a minimum of 60 semester hours, including 39-42 hours of course work in mathematics or related area and 18-21 hours of dissertation.

Application and Admission

For information regarding deadlines and requirements for admission, please see the Guide to Graduate Admissions.

In addition to the application materials required by The Graduate School, applicants must submit a 500-700 word Personal Statement to be considered for Fall admission.

Students with a master’s degree in mathematics, computer science or statistics may apply directly to the PhD program. In exceptional cases well-qualified applicants will be considered for admission directly after completing an undergraduate degree in mathematics, computer science or statistics.

Degree Requirements

Course Work (39-42 hours)

The student selects 39-42 hours of course work in mathematics and related areas with the approval of the Director of Graduate Study. With the approval of the Director of Graduate Study, up to 18 of the 39-42 hours may be accepted from UNCG’s MA in mathematics program or from a comparable master’s program.

Qualifying Examinations

Qualifying examinations, covering a student’s chosen field of research and related advanced course work, must be taken after the student has removed any provisions or special conditions attached to admission; three exams should be passed prior to the beginning of the fifth semester. These examinations each cover the material of two courses. Each student must pass at least one exam from Group I.

GROUP I

Algebra
MAT 591Advanced Abstract Algebra

3

MAT 592Advanced Abstract Algebra

3

Analysis
MAT 595Mathematical Analysis

3

MAT 596Mathematical Analysis

3

Linear Algebra
MAT 647Linear Algebra and Matrix Theory

3

MAT 648Linear Algebra and Matrix Theory

3

GROUP II

Combinatorics
MAT 631Combinatorics

3

MAT 632Graph Theory

3

Differential Equations
MAT 545Differential Equations and Orthogonal Systems

3

MAT 546Partial Differential Equations with Applications

3

Mathematical Statistics
STA 651Mathematical Statistics

STA 652Mathematical Statistics

Numerical Mathematics
MAT 623Numerical Mathematics

3

MAT 624Numerical Mathematics

3

Topology
MAT 697General Topology

3

MAT 698General Topology

3

Programming Project

The student must complete a programming project of such quality that it can become part of a computer algebra system, could be distributed as a package for a computer algebra system, or yields new mathematical data.

Dissertation (18-21 hours)

MAT 799Dissertation

1–12

Other Reviews and Examinations

After the student has passed three qualifying examinations, the student chooses a dissertation advisor and forms a dissertation committee. With the help of the advisor, the student proposes a dissertation topic in a public oral presentation. In this presentation, the student explains his or her dissertation topic in sufficient detail to demonstrate capability to begin research.

At the conclusion of the presentation, the dissertation committee will administer an oral exam to determine the student’s competence to begin work on the dissertation. A part of the exam is the computational/programming project. This project should clearly demonstrate that the student is fully capable of handling computational aspects of the intended dissertation topic. After passing this examination, the student may then make a formal application to the Graduate School for admission to candidacy. The dissertation proposal and oral exam can be attempted at most twice.

Schedule for Examinations and Projects

Semester

Examination or Project

1-4

3 written comprehensive examinations

4-7

Dissertation proposal, computational/programming project, (oral examination)

6-14

Dissertation work and defense (oral examination)


 

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