Master Degrees

Students who initially intend to study for a Master degree but subsequently decide on a Ph.D. program are subject retroactively to the requirements for the Ph.D. degree. In particular they must pass the Ph.D. Preliminary Examination by no later than the end of their second year of full time graduate study. Consequently, students are advised to consider the available degree options and requirements carefully before beginning a graduate program.

MASTER OF ARTS DEGREE

General Requirements
In addition to University regulations, the requirements for the M.A. are:

1. Completion of at least eight mathematics courses (24 credit hours). A minimum of five courses must be taken at the 2000 or 3000 level and completed with an average grade of B or better. The remaining ones may be Departmental courses at the 1000 level. Courses given in closely related disciplines such as computer science or statistics may be substituted for these remaining courses if approved by the Graduate Committee.
   
   
2. Achievement of an overall course average of B or better.
   
   
3. The passing of a Comprehensive Examination.

There are no specific required courses. Thus a program can be arranged to suit the student's interests and goals. The well-prepared student studying full time can complete the degree in one year. Most, however, will take two. Pursuit of the M.A. degree beyond two years by full-time students will be allowed only with permission of the Graduate Committee. Part-time candidates may take up to the University-allowed maximum (four calendar years) to complete all requirements.

Comprehensive Examination
The Comprehensive Examination for the M.A. degree is based on the content of three 2000 level mathematics courses. These are chosen by the student in consultation with his or her advisor, and these topics, along with the names of three examiners, must be submitted in writing to the Graduate Committee for approval. After approval has been obtained, the examination committee, chaired by the student's advisor, will give the student a list of basic questions in the chosen areas. At an agreed-upon time the committee will conduct an oral examination of the student. Examination questions will be drawn from the list of basic questions. The committee will also be free to ask additional questions in the areas encompassed by the chosen subjects. If the student is judged to have passed the oral part of the exam, the committee at its option will request the student to prepare a short paper on a subject in one of the examination areas. This must be submitted within two weeks, and the committee will then re-convene to determine if the student has passed or failed.

A student who fails the examination is allowed a re-examination. The student is not bound by the subjects declared for the first exam, but any changes must be submitted in writing to the Graduate Committee. He or she may also petition for a new group of examiners.

A third examination will be allowed only in extraordinary circumstances and must be approved by the Graduate Committee.

The oral examination is open to interested faculty. However, they cannot act as examiners.

MASTER OF SCIENCE DEGREE

General Requirements
In addition to the University regulations the requirements for the Master of Science are the following:

1. The completion of at least eight courses (24 credit hours). A minimum of five courses must be taken at the 2000 or 3000 level and completed with an average grade of B or better. These eight courses must be selected in consultation with a faculty advisor with a view to the writing of a dissertation.
   
   
2. Achievement of an overall course grade average of B or better.
   
   
3. In addition to the 24 credits in item 1, completion and defense of a dissertation in mathematics (six credit hours).

As in the M.A. degree there are no specified required courses. Each student plans a program in conjunction with a faculty advisor. The significant difference between the M.A. and the M.S. is the thesis requirement. Although it does not have to be as extensive or as original as a doctoral dissertation, it should clearly demonstrate the student's mastery of the chosen topic.

A well prepared student carrying a full schedule should be capable of completing the degree within two years. Full-time students appointed by the Department as teaching assistants may require an additional term. During this term, the student will be expected to register in at least one course. The remaining credits needed to maintain full-time status can be obtained through research. Pursuit of the M.S. degree by full-time students for longer than two years will be permitted only with the approval of the Graduate Committee. Part-time students are allowed up to four calendar years from date of entry to complete all requirements.

Thesis Defense
The thesis defense for the M.S. degree is an oral examination based on the content of the student's thesis. The examination is conducted by a committee consisting of three faculty members, one of whom is the student's advisor. Subject to the approval of the Graduate Committee, the committee is chosen according to the recommendations of the advisor, who then serves as chairperson. It is preferable that the committee be formed early in the student's career in order that its members can guide the student in his or her work.

Thesis Format
The proper format for a master's thesis at the University of Pittsburgh is described in detail in the Style and Form Manual.

MASTER OF ARTS AND MASTER OF SCIENCE DEGREES IN APPLIED MATHEMATICS

The Department of Mathematics offers programs leading to the Master of Arts and the Master of Science (thesis) degrees with a major in applied mathematics. Successful completion of the program will enhance the student's potential for a position in industry or government or for additional study. The program is flexible in order to meet the needs of students whose specializations may vary widely.

In addition to the University requirements for admission to graduate school, a student should have completed courses in linear algebra, differential equations, and advanced calculus. Some computer experience is also helpful. However, an undergraduate major in mathematics or applied mathematics is not necessary, and students with majors in other disciplines and who have sufficient background are a central part of this program. Moreover, well-motivated students lacking the prerequisites mentioned above may be admitted with the provision that deficiencies be removed by course work in appropriate areas.

Since various program emphases are possible, students must consult their advisors concerning the alternatives. In addition to the requirements of the University, the following also apply:

1. For the M.A. degree, 30 credits of course work are required. A minimum of seven departmental courses must be taken, and at least five of these seven must be at the 2000 level or above.
   
   
2. The M.S. degree requires the completion of 24 credits of course work and the completion of a thesis in mathematics (six credits). A minimum of five courses must be departmental, at least four of which must be at the 2000 level or above.
   
   
3. For either degree, courses must be distributed over the areas of numerical analysis, differential equations and analysis. In addition, a minimum of two courses at the 2000 level or a minimum of three courses, of which one is at the 2000 level, must be taken outside the Department and approved by the Graduate Committee.
   
   
4. For either degree, a final oral examination must be passed. The examination committee must contain one member from outside the Department who was an instructor in one of the outside courses described in item 3. The form of the examination is as described above for the respective degrees.

DUAL MASTER DEGREE PROGRAMS

Some dual degree programs leading to a dual Master's degree in Mathematics and an allied field (e.g., Computer Science and Engineering) exist in the department and can be arranged upon request.