# Graduate 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.

The Department of Mathematics offers programs leading to the Master of Science and Doctor of Philosophy degrees in both pure and applied areas of mathematics.

### Contacts

### Program Details

**Degree Classification:**Graduate**Related Degrees:**M.S., Ph.D.**Program Frequency:**Full-Time**Format:**In Person

### Admission Requirements

Students admitted into the graduate mathematics program must have at least a bachelor's degree and a GPA of 3.2 in their major undergraduate mathematics courses.

**Note:** In response to COVID-19, the Graduate School has made temporary changes to the GRE requirement. For the 2021-22 academic year, the GRE requirement has been **waived** for all programs in the Graduate School. Applicants will be evaluated holistically: GPA, letters of recommendation, statement of academic interests and professional goals, and an autobiographical statement that foregrounds your research interests. For more information, contact the Department of Mathematics' Director of Graduate Studies, Dr. Dennis Davenport.

#### Degree Requirements

**The Master of Science Degree Program**

To obtain a Master of Science degree in mathematics, a student must earn a minimum of thirty credit hours or thirty-six credit hours depending upon whether or not the student elects to write a thesis.

**M.S. Degree (Thesis Option) Requirements**

A student

- must take a year sequence in graduate algebra, or graduate analysis; (Six (6) credit hours)
- will take at least six additional courses of which two may be approved courses given outside the mathematics department; [Advanced approval must be obtained for courses taken outside the department. No more than two courses with course numbers less than 200 will count in this category] (Eighteen (18) credit hours)
- will write a thesis. (Six (6) credit hours)

**M.S. Degree (No Thesis Option) Requirements**

A student

- must take a year sequence in graduate algebra, or graduate analysis; (Six (6) credit hours)
- will take at least ten additional courses of which three may be approved courses given outside the mathematics department. [Advanced approval must be obtained for courses taken outside the department. No more than two courses with course numbers less than 200 will count in this category.] (Thirty (30) credit hours)

**Examinations**

**Oral Examination**

A student writing a thesis must defend it successfully during an oral examination.

**No Thesis Option Examination**

A student in the M.S. program not writing a thesis must pass at least one of the three Ph.D. qualifying examinations.

**The Expository Writing Requirement**

Howard University mandates that all entering graduate students pass an expository writing requirement administered by their department of study, unless the student has earned a score of 5.0 or better on the GRE Analytical Writing test. The expository writing requirement must be met within the student's first year of enrollment.

There are several options mathematics majors can use to satisfy the Department of Mathematics writing requirement:

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 B or better.

i. In this course, students are required to write a paper in LaTeX on a mathematical history topic. The paper must include both historical and mathematical content.

ii. Using a rubric developed by a subcommittee of the Department of Mathematics Graduate Committee, the paper will be evaluated according to analysis, language control, grammar, clarity, and logic.

**Residence Requirements**

At least two semesters of full-time study or the equivalent, shall be undertaken in the Department of Mathematics within the Graduate School of Arts and Science.

**Other Requirements**

Graduate students shall regularly attend seminars, lecture series, and colloquia sponsored by the Department of Mathematics.

**The Ph.D. Degree Program**

This degree program 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 course work. In addition 12 graduate credits are required for the Ph.D. dissertation.

**Course Requirements**

The courses for the Ph.D. degree presented by a candidate must include at most one course from Group 1, all courses from Group 2, at least two courses from Group 3 and a course on topics in History of Mathematics. Additional courses to cover the areas of qualifying examinations as well as topics courses will be on subjects corresponding to the research interests of the faculty.

**Core Course Groups**

##### Group 1

- 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-199)

##### Group 2

- Algebra I (MATH-210)
- Algebra II (MATH-211)
- Real Analysis I (MATH-222)
- Real Analysis II (MATH-223)
- Topology I (MATH-250)
- Complex Analysis I (MATH-229)

##### Group 3

- NumberTheory I (MATH-214)
- Applications of Analysis (MATH-224)
- Complex Analysis II (MATH-230)
- Functional Analysis I (MATH-231)
- Algebraic Topology I (MATH-252)
- Algebraic Topology II (MATH-253)
- Differential Geometry I (MATH-259)
- Differential Geometry II (MATH-260)
- Partial Differential Equations II (MATH-237)

**Ph.D. Degree: Admission and Examination Requirements**

To obtain a Ph.D. degree, a student admitted to the program must:

- pass two qualifying examinations on subjects, not closely related to each other, chosen from two of the following six groups:
- Real Analysis or Complex Analysis or Functional Analysis or Harmonic Analysis
- Algebra or Number Theory
- Combinatorics
- Geometry or Topology
- Dynamical Systems or Ordinary Differential Equations or Partial Differential Equations
- Probability or Mathematical Statistics.

- take a third qualifying examination in an area of the student's choice, that may include one from the above six groups, and
- write a Ph.D. dissertation and defend it satisfactorily.

**Financial Support**

Financial support from the university is contingent upon the student making satisfactory progress. Students in the Ph.D. degree program are expected to have successfully completed six graduate courses in the first year in the Ph.D. program and to have passed at least two of the qualifying examinations by the end of their second year in the Ph.D. program in order to obtain continuing university support.

**Language Requirement**

Students must exhibit proficiency in one of the following languages: Arabic, Chinese, French, German, Russian. In exceptional cases, other languages may be accepted by the Department. In lieu of a language from the above list and upon approval of the Chairman of the Department, students may take suitable graduate level courses from one of the following departments or schools: Computer Science, Sociology, Economics, Biology or Education.

**Requirements for Admission to Candidacy for the Ph.D. degree:**

- Candidates must have passed two of the Qualifying Examinations.
- Candidates must satisfy the language requirement and the writing skills requirement.

**Other Requirements**

- A minimum of 18 credits of work toward the Ph.D. degree shall be pursued after admission to candidacy.
- Doctoral candidates shall participate actively in at least two seminars during their candidacy.
- 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.

#### Admission to Candidacy

A student should file for admission to candidacy after 12 hours of work has been completed and this student has satisfied the GSAS writing proficiency requirement. Forms provided by the dean should be filed a semester before graduation and approved by the student's thesis committee and the Executive Committee of the Graduate School of Arts and Sciences.

#### Residence Requirements

At least four semesters of residence and full-time study or the equivalent, shall be in the Department of Mathematics of Howard University.

### Faculty

### Dennis Davenport

#### Associate Chair, Director of Graduate Studies

##### Mathematics

dennis.davenport@howard.edu### Program Resources

## Core graduate courses

## Core course groups

##### Group 1:

- 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-199)

##### Group 2:

- Algebra I (MATH-210)
- Algebra II (MATH-211)
- Real Analysis I (MATH-222)
- Real Analysis II (MATH-223)
- Topology I (MATH-250)
- Complex Analysis I (MATH-229)

##### Group 3:

- NumberTheory I (MATH-214)
- Applications of Analysis (MATH-224)
- Complex Analysis II (MATH-230)
- Functional Analysis I (MATH-231)
- Algebraic Topology I (MATH-252)
- Algebraic Topology II (MATH-253)
- Differential Geometry I (MATH-259)
- Differential Geometry II (MATH-260)
- Partial Differential Equations II (MATH-237)