2012-2013 Program Requirements for UCLA Graduate Degrees
Applicable only to students admitted during the 2012-2013 academic year.
College of Letters and Science
The Department of Mathematics offers the Masters of Arts in Teaching (M.A.T.) degree and the Master of Arts (M.A.) and Doctor of Philosophy (Ph.D.) degrees in Mathematics.
6356 Math Sciences
Los Angeles, CA 90095-1555
Leading to the degree of
M.A.T., M.A., Ph.D.
Admission Limited to
Deadline to apply
GRE (General and/or Subject)
GRE: General and subject in Mathematics
Letters of Recommendation
3, from mathematicians or professionals in related fields who know the applicant's recent work.
In addition to the University's minimum requirements and those listed above, all applicants are expected to submit the departmental application and a statement of purpose.
Although prospective graduate students in mathematics need not have an undergraduate mathematics major, they must have completed at least 12 quarter courses (or eight semester courses) in substantial upper division mathematics, particularly advanced calculus, algebra, differential equations, and differential or projective geometry.
M.A.: Applicants must have earned a cumulative grade-point average of at least 3.2 in the above-mentioned upper division mathematics courses.
M.A.T.: The Master of Arts in Teaching (M.A.T.) program serves the needs of present and prospective mathematics teachers in high school and junior college. Applicants should consult the department for specific admission requirements.
Ph.D.: Applicants must present a grade-point average of at least 3.5 in upper division mathematics courses. Applicants who have already obtained a master's degree must have maintained an average of better than 3.5 in graduate study. International applicants should have at least a comparable record in their mathematical education.
Exceptions to these requirements are granted only in cases where exceptional ability in quantitative science has been demonstrated.
Students typically spend two years in the master's degree program. Therefore, upon matriculation each master's degree student is assigned a faculty adviser to assist with the careful planning needed for an optimal educational experience. In consultation with the adviser, students are asked to formulate a tentative study plan for the first year. This plan is subject to change over the year as is appropriate or necessary. After matriculation the faculty adviser can be changed, with consent of the Graduate Vice Chair, to another member of the permanent departmental faculty who is willing to advise the student.
Study plan approval: At the beginning of each quarter, the study plan of courses the student is to take that quarter must be approved and signed by the faculty adviser. The approved study plan must then be submitted to the Graduate Office for the review and approval of the Graduate Vice Chair.
If at any point the Graduate Vice Chair determines that it is likely the student will need more than six quarters in residence following matriculation to complete the master's degree requirements, from then on the student is required to meet with the Graduate Vice Chair at the beginning of each quarter for the review and approval of the study plan and for an evaluation of the student's overall progress.
Areas of Study
All areas of study in which the department offers coursework at the beginning to middle graduate level are open to M.A. students. Although the primary focus of the M.A. program is mathematics, students may pursue a well-planned program with a substantial interdisciplinary component. For qualified students, a thesis plan provides an opportunity for supervised specialized study and research at a high level.
Foreign Language Requirement
Eleven approved letter-graded courses are required; each must be passed with a grade of B- or better. At least eight of the 11 courses must be graduate courses in mathematics.
Course approval (separate from study plan approval, discussed under Advising): Any course used for degree credit must have a sufficient amount of advanced mathematical content and an appropriate evaluation plan, and must be approved by the department for degree credit. For most mathematics graduate and upper division courses having standard syllabi and evaluation plans, course approval is routine. For other courses, in particular those offered by other departments, course approval is given on a course-by-course basis after review of the syllabus and evaluation plan. In these cases, course approval must be obtained in writing from the Graduate Vice Chair at the start of the quarter in which the course is to be taken. Retroactive consideration of such a course by the Graduate Vice Chair would be made only in an exceptional circumstance.
There are many upper division and graduate courses in mathematics that students can take but for which degree credit is normally not approved. These courses include Mathematics 100 through 109, and Mathematics 285, 290A through 290M, and 296A through 290M. A maximum of four units of Mathematics 596 taken for a letter grade can be applied toward the M.A. degree requirements. Students who pursue the thesis plan may apply 16 units of Mathematics 596 taken for a letter grade toward the M.A. degree, eight units of which may be applied toward the graduate course requirement.
Comprehensive Examination Plan
Students must pass the departmental basic examination. The syllabus for this examination, available in the departmental graduate office and website, consists of a selection of advanced topics that are essential prerequisites for the field of graduate mathematics study at the University. The examination is offered several times a year and can be taken whenever offered provided the student is matriculated in the graduate program. Students who fail to take or fail to pass this examination upon matriculation are advised to devise a study plan that leaves time to prepare for it.
Every master's degree thesis plan requires the completion of an approved thesis that demonstrates the student's ability to perform original, independent research.
Students who demonstrate strong mathematical ability in coursework and who pass the basic examination by September of the second year, may petition the Graduate Vice Chair to do a master's thesis. The thesis must be an in-depth scholarly study of a mathematical topic of current research, and ideally should include sufficient original work, done under the guidance of the thesis adviser, to form a significant contribution to a published paper. The petition must include a letter of commitment from a proposed thesis adviser, selected from permanent members of the departmental faculty, that outlines a program of classroom study for the remainder of the degree program and a description of the proposed research. Approval of the petition is not guaranteed, and this option may not be available in all specialties in which doctoral program supervision is offered in the department. The M.A. thesis plan represents a significant opportunity for intellectual development, and for demonstration of solid achievement and research potential to other universities and prospective employers.
Students ordinarily are required to complete the requirements for the master's degree within two years following matriculation. Students who wish to remain in the program longer than two years must obtain approval in advance each quarter. Permission to remain in the program longer than two years is not automatically approved and no student is permitted to continue coursework for longer than three years.
Satisfactory progress toward the master's degree is defined as full-time enrollment (minimum of 12 units) with a minimum grade-point average of 3.00 or higher each quarter and completion of all coursework within two years. Students who fail to make satisfactory progress are subject to a recommendation for termination of graduate study to the Graduate Division.
Master's degree students who have passed the basic examination at the Ph.D. level by September of the second year may petition during the second year to transfer to the Ph.D. program. Students must demonstrate the ability to do Ph.D. level preparatory coursework to be accepted into the Ph.D. program. Acceptance into the Ph.D. program is neither automatic nor guaranteed. Students normally are required to pass the Ph.D. area examinations in accord with the schedule for satisfactory progress in order to be accepted into the Ph.D. program.
Master of Arts in Teaching
The vice chair for graduate studies is the chief graduate adviser and heads a committee of faculty advisers whose fields of expertise span most of the major areas of mathematics. Students are required to meet with a faculty adviser who helps them plan a reasonable course of study.
The graduate vice chair is responsible for monitoring students' progress toward their degree objective and approves student enrollment plans each quarter. Continuing students are normally asked to meet with the vice chair (or some other adviser) at least once each quarter and a record of this interview is placed in the student files. There are ample opportunities to meet with an adviser of the student's choice throughout the academic year.
Areas of Study
Consult the department.
Foreign Language Requirement
Eleven courses are required as follows:
Core Courses. Students must take Mathematics 201A-201B-201C and 202A-202B. Normally students also take one quarter of Mathematics 596 while fulfilling the essay requirement described below.
Credential Requirements. Students planning to teach in secondary schools who do not already have valid credentials for such teaching should enroll in the single subject instructional credential program in the Department of Education (Graduate School of Education and Information Studies). Of the courses required by this program, students receive M.A.T. credit only for the following courses: Education 312, 330A-330B, 406, 407. Actual receipt of the credential is not a degree requirement. Interested students should check with the Department of Education for a full and up-to-date description of credential requirements and should submit a Department of Education application for admission to the credential program.
Additional Courses. Besides the six core courses described above, a seventh upper division or graduate course in mathematics is required. Particularly recommended are Mathematics 106, 110B, 110C, 111, 131B, 134, and Statistics 100B. Candidates on the junior college track normally take five 100- or 200-level courses in mathematics in addition to the six core courses. However, with prior approval of the graduate vice chair, one course of a predominantly mathematical nature taken in another department may be presented for degree credit.
Students may not receive degree credit for Mathematics 370A, or 370B. In addition, students may not receive degree credit for more than two quarters of Mathematics 596 or for more than two quarters of any 300-series courses.
Essay Requirement. A master's essay on some subject in mathematics related to the student's prospective teaching is required. This essay is written by the student, under the direction of a faculty member, while enrolled in Mathematics 596.
Teaching experience is not a formal requirement for the M.A.T. degree; however, students who are working for a secondary credential must take the supervised teaching course. Students are eligible for teaching assistantships.
Comprehensive Examination Plan
In the M.A.T. program, one examination in mathematical subject matter, the departmental basic examination, is required, as is one examination in content and philosophy of secondary school mathematics. Ordinarily, these examinations are administered in conjunction with Mathematics 201A-201B-201C and 202A-202B. Reexamination after failure is allowed.
Students who are well-prepared should be able to complete the requirements for the M.A.T. degree in six quarters of full-time study.
Careful planning is needed for each stage of a doctoral student's training. Therefore, upon matriculation each student is assigned a faculty adviser to assist with this planning. In consultation with the adviser, students are asked to formulate a tentative study plan for the first year. This plan is subject to change over the year as is appropriate or necessary. After matriculation the faculty adviser can be changed, with consent of the Graduate Vice Chair, to another member of the permanent departmental faculty who is willing to advise the student.
Study plan approval: Entering and continuing doctoral students who are not advanced to candidacy are required to meet with their adviser and obtain approval of their study plan at the beginning of each quarter. The approved study plan must then be submitted to the Graduate Office for the review and approval of the Graduate Vice Chair. The Graduate Vice Chair, who has final approval over study plans, is responsible for monitoring student progress toward completion of the doctoral degree requirements, and for ensuring that study plans are directed toward that goal.
If at any point the Graduate Vice Chair determines that the student is not making satisfactory progress, from then on the student is required to meet with the Graduate Vice Chair at the beginning of each quarter for the review and approval of the study plan and for an evaluation of the student's overall progress. This requirement continues until the student is advanced to candidacy.
Major Fields or Subdisciplines
The Ph.D. degree in Mathematics may be earned under the pure or applied programs. Many possible choices of fields exist within these programs, and students are urged to read the booklet, Graduate Studies in Mathematics at UCLA, that describes the specialties of the faculty and the active research areas in the department in some detail.
Foreign Language Requirement
Prior to taking the oral qualifying examination for advancement to candidacy, students in the pure program must fulfill the foreign language requirement. Students must pass one written departmental language examination in either French, German, or Russian. These foreign language examinations, offered Fall and Spring quarters, require the translation of material in some basic field of mathematics. The examinations may be taken any number of times until passed.
Students in the applied program are not required to fulfill the foreign language requirement.
Under the pure mathematics option, students must pass (with a grade of B or better) at least 12 courses from Mathematics 205A through 285N, but excluding the basic courses 210A-210B, 245A-245B, and 246A-246B. At most, three of these courses may be in the 285 series. Each student must actively participate (and lecture 90 minutes, normally two lectures) in at least two advanced seminars. Credit for one of the seminars must be obtained within three registered quarters after passing the written qualifying examinations, the other within five quarters after passing the written qualifying examinations.
Under the applied mathematics option, students must pass (with a grade of B or better) at least 18 approved graduate courses, including at least 12 courses from Mathematics 205A through 285N. At most, three of these courses may be in Mathematics 285A through 285 L.
Written and Oral Qualifying Examinations
Academic Senate regulations require all doctoral students to complete and pass University written and oral qualifying examinations prior to doctoral advancement to candidacy. Also, under Senate regulations the University oral qualifying examination is open only to the student and appointed members of the doctoral committee. In addition to University requirements, some graduate programs have other pre-candidacy examination requirements. What follows in this section is how students are required to fulfill all of these requirements for this doctoral program.
Students must pass three written qualifying examinations:
The departmental basic examination. The syllabus for this examination, available in the departmental graduate office and website, consists of a selection of advanced topics that are essential prerequisites for the field of graduate mathematics study at the University. The examination is offered several times a year and can be taken whenever offered provided the student is matriculated in the graduate program. Doctoral students normally take the basic examination upon matriculation into the program. Students who fail to take or fail to pass this examination upon matriculation are advised to devise a study plan that leaves time to prepare for it.
The area examinations. Students are required to pass two area examinations chosen from the following six options: algebra, applied differential equations, computational mathematics, geometry/topology, logic, and real and complex analysis. One area examination must be passed by the sixth quarter of graduate study, and the second area examination must be passed by the seventh quarter of graduate study. Because preparation for an area examination can take a year or more, students should choose, as early as possible and in consultation with their adviser, the area examinations they plan to take.
The University Oral Qualifying Examination. After passing the basic examination and the two area examinations, the student may set up the doctoral committee which administers the University Oral Qualifying Examination for advancement to candidacy.
Advancement to Candidacy
Students are advanced to candidacy and awarded the Candidate in Philosophy (C.Phil.) degree upon successful completion of the written and oral qualifying examinations.
Every doctoral degree program requires the completion of an approved dissertation that demonstrates the student's ability to perform original, independent research and constitutes a distinct contribution to knowledge in the principal field of study.
Final Oral Examination (Defense of the Dissertation)
Not required for all students in the program. The decision as to whether a defense is required is made by the doctoral committee.
Students are required to pass the written qualifying examinations for the Ph.D. degree within the deadlines indicated under Written and Oral Qualifying Examinations. Completion of all degree requirements (including the dissertation) normally takes 15 quarters of full-time study.
Termination of Graduate Study and Appeal of Termination
A student who fails to meet the above requirements may be recommended for termination of graduate study. A graduate student may be disqualified from continuing in the graduate program for a variety of reasons. The most common is failure to maintain the minimum cumulative grade point average (3.00) required by the Academic Senate to remain in good standing (some programs require a higher grade point average). Other examples include failure of examinations, lack of timely progress toward the degree and poor performance in core courses. Probationary students (those with cumulative grade point averages below 3.00) are subject to immediate dismissal upon the recommendation of their department. University guidelines governing termination of graduate students, including the appeal procedure, are outlined in Standards and Procedures for Graduate Study at UCLA.
Special Departmental or Program Policy
A student who does not complete all the requirements for the M.A. degree within six quarters of full-time study is subject to a recommendation for termination. The Graduate Vice Chair decides in each case whether a recommendation for termination is warranted. A student may appeal a recommendation for termination to the Graduate Studies Committee, which makes the final departmental decision on this matter.
A student who fails to meet a deadline for passing a written qualifying examination is subject to a recommendation for termination. The Graduate Vice Chair informs a student of such a recommendation and the student is provided the opportunity to submit a written appeal that may include letters of support from members of the faculty. The appeal is considered by the Graduate Studies Committee, which make the final departmental decision as to whether the student is allowed to remain in the program or is recommended for termination.