Test Math Program
Mathematics | Graduate
The mathematics graduate program offers an opportunity to do research in both pure and applied areas of mathematics. Our program is designed for students who expect to pursue a career in academia as well as those preparing for careers as mathematicians in industry and government.
Contacts
Program Details
- Degree Classification: Graduate
- Related Degrees: Ph.D.
- Program Frequency: Full-Time
- Format: In Person
Admission Requirements
Students admitted to the graduate mathematics program must hold at least a bachelor’s degree and have both an overall undergraduate GPA of at least 3.2 and a GPA of at least 3.2 in their undergraduate mathematics major courses. Applicants who satisfy these minimum GPA requirements are evaluated in accordance with the admissions policies and requirements of the Graduate School and the Department of Mathematics.
Degree Requirements
The Ph.D. Degree Program
The Department of Mathematics offers a Doctor of Philosophy (Ph.D.) degree in Mathematics with two curricular tracks: Pure Mathematics and Applied Mathematics. The two tracks share the same general degree requirements and foundation courses, while each has a distinct set of core courses. This structure provides common preparation while preserving flexibility for advanced study and research.
The Ph.D. degree requires a minimum of 60 graduate credits beyond the B.S. degree or a minimum of 36 graduate credits beyond the M.S. degree in coursework. In addition, students must complete 12 graduate credits of Ph.D. dissertation research. Up to six credits of the required graduate coursework may be taken in non-MATH graduate-level courses, subject to approval of the Director of Graduate Studies and the Department Chairperson.
Course Requirements
The Ph.D. curriculum consists of a common set of foundation courses together with track-specific core requirements in Pure Mathematics or Applied Mathematics. A student may count no more than one foundation course toward the graduate coursework credits required for the Ph.D. Students must complete all core courses required for their selected track.
Foundation Courses
The following foundation courses are common to both the Pure Mathematics and Applied Mathematics tracks:
- Introduction to Analysis I (MATH 220 / MATH 195)
- Introduction to Analysis ll (MATH 221 / MATH 196)
- Introduction to Modern Algebra I (MATH 208 / MATH 197)
- Introduction to Modern Algebra ll (MATH 209 / MATH 198)
- Introduction to Complex Analysis (MATH 185)
- Introduction to Differential Geometry (MATH 186)
- Probability and Statistics (MATH 189)
- Introduction to Number Theory (MATH 184)
- Introduction to General Topology (MATH 249 / MATH 199)
Pure Mathematics Core Courses
Students in the Pure Mathematics track must complete the following core courses:
- Modern Algebra I (MATH 210)
- Modern Algebra II (MATH 211)
- Real Analysis I (MATH 222)
- Real Analysis II (MATH 223)
- Complex Analysis I (MATH 229)
- Topology I (MATH 250)
Applied Mathematics Core Courses
Students in the Applied Mathematics track must complete the following core courses:
- Real Analysis I (MATH 222)
- Complex Analysis I (MATH 229)
- Advanced Ordinary Differential Equations I (MATH 234)
- Partial Differential Equations I (MATH 236)
- Mathematical Statistics I (MATH 240)
- Dynamical Systems I (MATH 243)
- Numerical Analysis I (MATH 247)
Advanced Graduate Coursework
In addition to the required core courses for their track, students complete the remaining required graduate coursework credits with advanced graduate-level MATH courses. Courses should be selected, in consultation with the student’s academic adviser or the Director of Graduate Studies, to support qualifying-examination preparation, broader mathematical development, and the student’s research interests.
Qualifying Examinations
All Ph.D. students must pass three qualifying examinations. The first two examinations establish breadth and advanced preparation; the third may be taken in an area of the student’s choice, subject to departmental approval.
Pure Mathematics Track
A student must pass two qualifying examinations in subjects that are not closely related, each covering a year-long sequence, chosen from two of the following groups:
- Real Analysis, Complex Analysis, Functional Analysis, or Harmonic Analysis;
- Algebra or Number Theory;
- Combinatorics;
- Geometry or Topology;
- Dynamical Systems, Ordinary Differential Equations, or Partial Differential Equations;
- Probability or Mathematical Statistics.
The student must then pass a third qualifying examination in an area of the student’s choice; this area
may be one of the areas listed above.
Applied Mathematics Track
A student must pass two qualifying examinations, each covering a year-long sequence, chosen from two
of the following groups:
- Real Analysis (MATH 222, MATH 223) or Complex Analysis (MATH 229, MATH 230);
- Advanced Ordinary Differential Equations (MATH 234, MATH 235);
- Partial Differential Equations (MATH 236, MATH 237);
- Mathematical Statistics (MATH 240, MATH 241).
- Dynamical Systems (MATH 243, MATH 244);
- Numerical Analysis (MATH 247, MATH 248).
The student must then pass a third qualifying examination in an area of the student’s choice; this area may be one of the areas listed above.
The Expository Writing Requirement
All graduate students must satisfy the University’s expository writing requirement as administered by the Department of Mathematics. The requirement may be satisfied through an approved Graduate School alternative or by one of the following departmental options:
a. Score a 5.0 or better on the Analytical Writing portion of the GRE;
b. Publish an article in a professional mathematics or education journal;
c. Have written a master's thesis at an accredited institution;
d. Complete the McGraw-Hill Connect adaptive learning module for developing writers. A link to the course is given below:
http://connect.customer.mheducation.com/products/connect-mcgraw-hill-connect-writing-3-0-3e/
e. Complete the History of Mathematics course with a grade of B or better. In that course, students write a paper in LATEX on a topic in the history of mathematics that contains both historical and mathematical content. The paper is evaluated using a departmental rubric addressing analysis, language control, grammar, clarity, and logic.
Other Requirements
- A minimum of 18 credits of work toward the Ph.D. degree shall be pursued after admission to candidacy.
- Graduate students are expected to participate regularly in seminars, lecture series, and colloquia sponsored by the Department of Mathematics.
- Only courses in which students earn grades of "A" or "B" may be counted toward the Ph.D. degree.
- A student in the Ph.D. program who accumulates more than two courses of grades below "B" shall be dropped from the Mathematics Graduate Program.
- The mathematics Ph.D. program no longer has a foreign language requirement.
Academic Progress and Financial Support
- Only courses in which a student earns a grade of A or B may be counted toward the Ph.D. degree.
- A Ph.D. student who accumulates more than two course grades below B is subject to dismissal from the Mathematics Graduate Program.
- Financial support from the University is contingent upon satisfactory academic progress. Students entering the Ph.D. program with a bachelor’s degree are expected to pass at least one qualifying examination by the end of their second year. Students entering with a master’s degree are expected to pass at least two qualifying examinations by the end of their second year. Exceptions may be approved by the Graduate Committee based on a student’s prior preparation and academic progress.
Admission to Candidacy
To be admitted to candidacy for the Ph.D. degree, a student must:
- Pass at least two qualifying examinations;
- Satisfy the expository writing requirement; and
- Have an approved dissertation proposal.
Dissertation Requirement
Students must complete 12 graduate credits of MATH 550, Ph.D. Dissertation. Enrollment in dissertation credit is restricted to students who have reached candidacy status. Each student must write a Ph.D. dissertation and defend it satisfactorily.
Residence Requirements
At least four semesters of residence and full-time study, or the equivalent, must be completed in the Department of Mathematics at Howard University.