PhD Program Requirements

 

The main steps in obtaining a Ph.D. are passing the qualifying examinations, writing a thesis, and passing a final oral examination on this thesis. The departmental regulations concerning each of these are given below. The regulations are interpreted by the Graduate Studies Committee which, on written petition from a student, may permit deviations from the rules, provided there are exceptional circumstances. In addition to the departmental regulations, there are university requirements which must also be satisfied.

Deficiency

A student is considered to have a deficiency if in his first semester as a graduate student at SUNYAB he officially enrolls in and completes Math 519 (introductory algebra) or Math 531 (introductory real variables).

The student should base his decision on whether to take these courses on advice from the Director of Graduate Studies and on evaluation of his knowledge in algebra and analysis by the relevant area committees.

Admission with Advanced Standing

At the time of admission to the Graduate School at SUNYAB, the Director of Graduate Studies may decide that certain students have advanced standing of one or two semesters of graduate work, depending on the Graduate School requirements. This will be done after examining the graduate records of the students and taking account of his previous courses, the institutions where he studied, his proficiency in English (TOEFL), etc. It will be clear from what follows that such students will have to fulfill various requirements more quickly than normally admitted students.

Definition of Total Semesters of Graduate Work

The sum of the semesters of graduate work as defined by (i) and (ii) below yields the total semesters of graduate work which will simply be called "semesters of graduate work".

(i) A student admitted with graduate coursework may credited with one or two semesters of graduate work, according to Graduate School requirements.

(ii) For every semester at SUNYAB that a student is registered for fewer than nine credit hours, the credit hours are to be totaled and divided by nine. The result, rounded down to the next integer, will also be counted as semesters of graduate work. In no event will a student be said to have completed more than two semesters of academic work in one calendar year.

First Qualifying Examination

This is a three-and-a-half-hour written examination based on a syllabus covering introductory real variables at the level of MTH 431-432, introductory abstract algebra at about the level of MTH 419, and linear algebra at about the level of MTH 420. The examination will be given twice a year, during the week prior to the beginning of each semester.

The purpose of the first examination is to assist the Director and the student in deciding soon after the student's entry into Graduate School, whether or not he should be in the Ph.D. program.

Normally, to remain in the Ph.D. program, a student is required to pass this examination within his first two years of graduate work. A student who entered with a deficiency is not required to pass this examination until the first opportunity after he has completed two semesters of graduate work.

Second Qualifying Exam

This consists of two three-hour area examinations, selected by each student from the following four choices: ALGEBRA, ANALYSIS, GEOMETRY/TOPOLOGY, and DIFFERENTIAL EQUATIONS. It is the purpose of the second qualifying examination to insure that each student has a rudimentary command of at least two "core" areas of mathematics.

To remain in the Ph.D. program a student is required to obtain a grade of A or B for one of the area examinations no later than the beginning of his fourth semester of graduate work and an average of at least B for both of the area exams no later than the beginning of his fifth semester. The Students may repeat the examinations, within the time limit, without penalty and are encouraged to take at least one of the examinations as early as possible.

Doctoral Committee

During the semester in which he completes the Second Qualifying Examination, each student will select a major professor, who is a member of the graduate faculty, in consultation with the Director of Graduate Studies. The latter and the major professor will then choose the student's doctoral committee, consisting of at least three members of the faculty with the major professor as chairman.

Admission to Candidacy

The student's doctoral committee will set the requirements for admission to candidacy. These are subject to the approval of the Director of Graduate Studies and may include, but are not restricted to, any of the following: an oral examination on "research level" material, a project, a series of lectures on "research level" mathematics, or a written qualifying examination in another department. These requirements must be satisfied by the end of the sixth semester of graduate work.

Language Requirements

None.

Additional Course Work

Before the final oral exam, each student should pass, with a grade of A, B , or S, two one-semester graduate course in subjects other than those of his or her second qualifying exam. These courses are to be approved by the Director of Graduate Studies.
Each Ph.D. student must complete 72-credit hours from: (a) selected 500 level Mathematics courses; (b) 600-800 level Mathematics courses, with the exception of thesis guidance, seminar courses, and other courses of this nature; (c) courses designated by his/her major professor.

Ph.D. Thesis and Final Oral Examination

The final departmental steps in attaining the degree of Doctor of Philosophy are:

1. completion of a thesis satisfactory to the major professor and the student's doctoral committee;

2. approval by the Graduate School that the student proceed to examination on his/her thesis at a final oral examination;

3. submission of the thesis to each member of the doctoral committee at least three weeks prior to the Final Oral Examination;

4. passing that examination.