Mathematics

Students must complete 11 approved letter-graded courses (44 units); each must be passed with a B or better. At least eight (32 units) of the 11 courses must be graduate courses in Mathematics. Courses from outside the department that are predominantly mathematical in nature may be used with approval from the Graduate Vice Chair. One letter-graded 596 course may also be used with Graduate Vice Chair approval.

Course approval (separate from study plan approval, discussed under Advising): Any course applied toward the degree must have a sufficient amount of advanced mathematical content and an appropriate evaluation plan, and must be approved by the department to be applied toward the degree. For most mathematics graduate and upper division courses with 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 is made only in an exceptional circumstance.

Students cannot apply the following courses towards their M.A. degree:

If the following pairs of courses are taken during enrollment at the graduate level, only one course can apply towards the degree.

Teaching Experience

Not required.

Field Experience

Not required.

Capstone 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 twice a year and can be taken whenever offered, provided the student is matriculated in the graduate program. The possible outcomes of the basic examination are Pass or Fail. 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. Students must pass the basic examination by the end of their sixth quarter.

Thesis Plan

None.

Time-to-Degree

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 course work 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 course work within two years. Students who fail to make satisfactory progress are subject to a recommendation for academic disqualification 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 course work 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 accordance with the schedule for satisfactory progress in order to be accepted into the Ph.D. program.

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Advising

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

None.

Course Requirements

11 courses (44 units) are required as follows:

Core Courses. Students must take Mathematics 201A-201B-201C (12 units total) and 202A-202B (8 units total). Students also take one quarter of Mathematics 596 (4 units) while fulfilling the essay requirement described below.

Additional Courses. Besides the six core courses described above, an additional five upper division or graduate courses in mathematics are 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 applied toward the degree.

Students may not apply Mathematics 370A, or 370B toward the degree. In addition, students may not apply toward the degree more than two quarters (8 units) of Mathematics 596 or more than two 300-series courses (8 units).

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.

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.

Teaching Experience

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 Mathematics 495. Students are eligible for teaching assistantships.

Field Experience

Not required.

Capstone Plan

In the M.A.T. program, one examination in mathematical subject matter, the departmental basic examination, is required, as well as 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 up to four times, at the discretion of the Graduate Vice Chair. Students must pass the basic examination by the end of their sixth quarter.

Thesis Plan

None.

Time-to-Degree

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.

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Advising

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 Research at UCLA page of the department website that describes the specialties of the faculty and the active research areas in the department in some detail.

Foreign Language Requirement

None.

Course Requirements

Under the pure mathematics option, students must pass (with a letter 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 lecture for 90 minutes (normally two lectures) in at least two advanced seminars. Students may enroll in the advanced seminars only after passing the written qualifying examinations; 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 letter 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 the 285 series.

Teaching Experience

Not required.

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.

All committee nominations and reconstitutions adhere to the Minimum Standards for Doctoral Committee Constitution.

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 twice 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. The possible outcomes of the basic examination are Pass or Fail. 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. Students must pass the basic examination by the end of their sixth quarter.

Two 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. Students are permitted to take each area examination up to four times in order to pass. 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. Students are expected to pass the University Oral Qualifying Examination by the ninth quarter.

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.

Doctoral Dissertation

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.

Time-to-Degree

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 16 quarters of full-time study.

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Termination of Graduate Study and Appeal of Termination

University Policy

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

Master's
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 academic disqualification. The Graduate Vice Chair decides in each case whether a recommendation for academic disqualification is warranted. A student may appeal a recommendation for academic disqualification to the Graduate Studies Committee, which makes the final departmental decision on this matter.

Doctoral
A student who fails to meet a deadline for passing a written qualifying examination is subject to a recommendation for academic disqualification. 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 academic disqualification.

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