University at Albany

Programs Leading to the Master of Arts Degree

This program is appropriate for students who want a flexible general education in mathematics, including students pursuing the Ph.D. degree.

Requirements for Admission
In addition to the general University requirements for admission to graduate studies, an applicant's undergraduate major preferably should have been in mathematics. Students who are deficient in their mathematical preparation must make up such deficiencies before being formally admitted into the program.

Program Requirements for the Master’s in Mathematics:

  1. A minimum of 30 graduate credits with an average of B or better. A minimum of 18 credits must be in mathematics. With the advisor’s approval, up to 12 of the remaining credits can be taken in other departments.
  2. Completion of the Master’s Seminar (680,681, 682 or 683).
  3. Successful completion of a special field examination within one year of the end of  coursework.

There is no foreign language requirement.

Description of Master’s in Mathematics Programs: most students work in one of the following three programs.
General Sequence: This program allows for the greatest flexibility, allowing students to design programs that better suit their interests. Individual programs range from a concentration in one area of mathematics to a broad spectrum of courses

  1. Mathematics (18 credits, minimum): Courses as advised, including Mat 680.
  2. Supporting courses (0-12 credits): Courses in other areas as approved by the advisor.
  3. Satisfactory completion of a special field examination in mathematics.
  4. Recommended courses: At least three of the following courses: Mat 510A, 513A, 520A, 540A.

Secondary School Teaching Sequence:

  1. Mathematics (18 credits, minimum): Courses as advised, including Mat 681.
  2. Education (6 credits): Courses in education as approved by the advisor.
  3. Supporting courses (0-6 credits): Courses as approved by the advisor.
  4. Satisfactory completion of a special field examination in mathematics.
  5. Recommended courses: Mat 511, 521, 526, 531, 552, 681, E Phl 601, and E Psy 560.

Statistics Sequence:

  1. Mathematics (18 credits, minimum): Courses in statistics as advised, including Mat 682.
  2. Supporting courses (0-12 credits, minimum): Courses as approved by the advisor.
  3. Satisfactory completion of a special field examination in statistics.
  4. Recommended courses: Mat 554-555, Mat 558-559, and at least one of Mat 556, 562, 564, or 566.

Special Field Examination:
Graduate students who expect to complete the requirements for the Master's degree by the end of a given semester, must notify the Director of Graduate Studies at the beginning of the semester. The special field examination is given near the end of coursework. Ordinarily, students satisfy this requirement by successful completion of a comprehensive examination as detailed in option 1 below. With permission of the Department of Mathematics and Statistics’ Chair or the Chair’s designee, students may satisfy this requirement by successful completion of either option 2 or 3.
Option 1: With approval of the Director of Graduate Studies, the student selects three graduate courses from the student’s program, for comprehensive examination. The Special Field Examination Committee consists of three different faculty members knowledgeable on the corresponding approved courses. One of the faculty members should be selected as chair of the special field examination and is responsible for directing the examination. The examination consists of a comprehensive oral examination on the selected and approved courses. The exam is not open to the general public.
Option 2: Students who took the Master’s Seminar and wrote a master’s thesis must obtain formal permission from the advisor and department Chair to submit a thesis and give an oral presentation on its results in fulfillment of the special field examination. With approval of the master’s thesis advisor, a committee consisting of three faculty members shall be formed. The chair of the committee is the master’s thesis advisor. The other two faculty members are selected in areas close to the master’s thesis topic.  The thesis should follow the University’s Master Thesis guidelines. A copy of the thesis should be presented to the members of the special field examination committee at least one week prior to the examination.  The special field examination consists of an oral presentation of the thesis and an examination of the thesis. The exam is not open to the general public.
Option 3: Students may fulfill the special field examination by passing two of the PhD preliminary examinations.
The special field examination must be taken by the end of the final examination period of the semester in which the degree is to be conferred.
A student who fails the special field examination may retake the examination one more time. The second examination may not be taken until the subsequent semester, and must be taken within a calendar year of the first attempt. Only two tries are permitted.  The special field examination must be first attempted within one year of completion of course work. 
Master’s Seminar
This requirement of the program is designed to provide an independent learning experience either outside the context of a formal course or in a seminar, and at its best approximates a research experience.  The format followed by the faculty member directing the seminar varies widely. The Master’s Seminar should ordinarily be taken during the last semester or year of the student’s program. The results are either written up as a term paper or are presented in a seminar.
Master’s Thesis
A student wishing to write a Master’s thesis should sign up for MAT 699, which is repeatable for credit, or one of the 680, 681, 682, 683 courses. Students are encouraged to write a thesis as it represents a complete and permanent work of recognized quality. Option 2 of the special field examination gives the student a chance to show off his or her accomplishments.
Completing a thesis involves some extra effort. It must be prepared in a manner conforming to university standards, accepted, and submitted on or before the first day of the month in which the degree is to be conferred to the Graduate Office, together with prepayment for binding charges. Students allowed to use option 2 in fulfillment of the special field examination must give a copy of their thesis to the exam committee members one week prior to its presentation.

Combined B.S./M.A. and B.A./M.A. Programs
Qualified undergraduates may apply for admission to the M.A. program and, if accepted, simultaneously work toward completion of the requirements for both undergraduate and graduate degrees. See Combined Baccalaureate- Master's Degree Programs for details, in the Undergraduate Programs web page.

Program Leading to the Doctor of Philosophy Degree
The general aim of the program leading to the Ph.D. in mathematics is to prepare students to become productive research scholars capable of communicating their knowledge to students and to the mathematical community. The program is planned to develop in the student a fundamental understanding of certain basic fields of mathematics, a deep understanding of the major field of interest, the ability to formulate and recognize significant research problems, and the ability to analyze problems and reach solutions and to transmit ideas to others.
The program of study and research requires at least three academic years of full-time study and research, or the equivalent over a longer period, beyond the baccalaureate and, typically, may involve four years or more.
Requirements for Admission
In addition to the general University requirements for admission to doctoral study, an applicant's undergraduate major preferably should have been in mathematics. Students who are deficient in their mathematical preparation must make up such deficiencies.
Program of Study
In the first two years of study the student acquires a general education in mathematical science through a program of coursework planned in conjunction with the Graduate Director. During this period the student completes preliminary examinations in four areas and at least two courses in areas not examined.
Following the preliminary examinations, the student completes the general education requirement and begins the process of specialization. As soon as possible, the student selects a dissertation advisor. A committee consisting of the advisor and three other faculty members is formed to guide the student's subsequent progress toward the degree. Readiness to begin the dissertation is marked by completion of the qualifying examination, which should take place in the third year of study.
Upon completion of the qualifying examination and satisfaction of the appropriate research tool and communication skills requirements, the student is advanced to candidacy and begins work on the dissertation.  
Program Requirements for the PhD in Mathematics:

  1. Credits: A minimum of 60 graduate credits in mathematics as approved by the advisor, with an average of B or better.
  2. Successful Completion of four Written Preliminary Examinations: The preliminary examinations are offered each year at the beginning of the Fall and Spring terms. A syllabus for each examination is available in the departmental office and in the departmental webpage. The student must successfully complete the examinations in four of the following seven areas: algebra, topology, complex analysis, real analysis, probability, applied statistics, and mathematical statistics. At least two examinations shall be attempted by the beginning of the second year of study and it is expected that all four examinations shall be attempted after no more than five semesters of study. A student who fails one of the preliminary examinations may retake the examination one more time. Only two tries are permitted in each subject. Any deviation from this policy requires approval of the Executive Committee and the Graduate Studies Committee.
  3. Successful Completion of the Oral Qualifying Examination: Within a month of completion of the preliminary examinations, the student shall select a faculty member as his/her dissertation advisor. At this time the student begins specializing in the areas on which the student will write his/hers PhD dissertation. Within two semesters of selecting the advisor, an oral qualifying examination shall be administered to test the student's preparation in the area of specialization and readiness to begin work on a dissertation. At this point, an Advisory Committee is formed to guide the student's subsequent progress toward the degree. It consists of four faculty members: the PhD advisor who chairs the committee together with three members selected by the PhD advisor, in consultation with the PhD candidate. The examination is not open to the general public.
  4. Completion of a Research Tool: The student must display a reading knowledge of French, German, Russian, or another foreign language appropriate to the area of specialization and approved by the department. This requirement is to be satisfied by departmental examination and shall be completed before the oral qualifying examination.
  5. Full Time Study in Residence: Each student in a doctoral program must engage in full-time study beyond the master's degree or equivalent at the University in at least two sessions after admission to the advanced program. This requirement is designed to insure for each doctoral student a sustained period of intensive intellectual growth. For this purpose a student must: be registered for 12 credits per semester, or hold a full assistantship and (i) complete one academic year in such a position, (ii) be registered for a minimum of 9 credits per term, and (iii) satisfactory completion of assigned duties.

Graduate students enrolled for less than 12 credits per semester who are participating in a program required full-time work may also be certifiable as in full-time status, subject to the approval of the Dean of Graduate Studies or the Graduate Academic Council, based upon the recommendation of the program faculty.

  1. Continuous Registration of Doctoral Students: All students enrolled in the doctoral program must maintain continuous registration for each fall and spring session, until they have completed all program requirements. Minimum registration consists of 3 credits of approved course work or registration for dissertation load (899 courses only).When this is not possible, a student should apply for a leave of absence for up to four semesters. The duration of a leave does not count against deadlines for the comprehensive exam or degree requirements. Being on leave means a student is not working with University personnel to complete his/hers degree. A student who simply "drops out" and tries to return may have difficulty obtaining retroactive leave and readmission. Note: Students with a full assistantship must be registered with full-time status for the duration of the assistantship. International students must be registered full-time for the duration of their studies.
  2. MAT 899: Students must be registered for Doctoral Dissertation, MAT 899, during the semester in which the degree is conferred. Credits for this course do not count toward the 60 credits mentioned in item 1.

Admission to Candidacy
A student is formally admitted to candidacy for the degree of Doctor of Philosophy upon the following:

  1. Satisfactory record in course and research study;
  2. Completion of the University residence requirements;
  3. Satisfactory completion of the research tool;
  4. Satisfactory completion of the preliminary and oral qualifying examinations.

The degree can not be conferred before the end of the semester following admission to candidacy.

The dissertation is based on independent research by the student and should constitute a significant original contribution to mathematics or statistics.  The dissertation must be approved by a majority of the student's Advisory Committee and the Chair of the Department. It must conform to university requirements for preparation and submission. More information is available at the Graduate Admissions office.  A copy of the dissertation should be given to each member Advisory Committee and displayed in the Department of Mathematics Lounge at least three weeks prior to its defense. The dissertation is defended publicly.

Assistantships and Fellowships
Graduate Assistantships or Fellowships are awarded to students in the Ph.D. program. Students with Assistantships and Fellowships can obtain tuition waivers by submitting the appropriate forms. United States citizens must become New York State residents to be eligible for waivers on a continuing basis.

Students with Teaching Assistantships must satisfactorily complete 9 credits per semester in order to be considered full-time. The tuition waiver associated with a teaching assistantship will not cover more credits than this and it will not cover undergraduate courses.
Presently University Regulations do not allow continuation of Teaching Assistantships beyond four years.  Renewal of Teaching Assistantships is contingent to satisfactory performance in the required teaching duties and satisfactory progress in the doctoral program.
A Teaching Assistantship is expected to require approximately 20 hours per week, on average, throughout the semester.

Conflict of Interest
Students with Teaching Assistantships are expected not to have other jobs, even part time jobs, sales for commissions, etc. Students with jobs are expected to resign their assistantships. Small amounts of tutoring in mathematics (for money) is generally allowed. More details on conflict of interest are available at the Office of Graduate Studies.


Rules described herein and in the Graduate Bulletin are Official University Policy which cannot be ignored. If you have a special problem, discuss it with your advisor, the Graduate Studies Committee, or the Department Chair. You can also contact an ombudsperson at the Office of Graduate Studies. Special cases are handled on a case by case basis.

Graduate Studies Committee

The Graduate Studies Committee oversees the graduate program. Its members are faculty and graduate students of the department of Mathematics and Statistics. The Department Chair is an ex-officio member of the Graduate Studies Committee.
The responsibilities of the Graduate Studies Committee include:

  1. Monitoring the graduate curriculum.
  2. Addressing graduate student problems and complaints.
  3. Granting transfer credits.
  4. Advising the Department of Mathematics and Statistics Chair on admissions, assistantships, fellowships, disputes, discipline, etc.

The Department Chair has final authority on the above items.