The specific requirements for the Master of Arts in Mathematics and the Master of Arts in Applied Mathematics are listed below. In consultation with a departmental academic advisor, all students are required to create an individual academic plan to satisfy the degree requirements.

An M.A. degree candidate must complete 42 units, 24 of which must be graduate courses in the 200 series offered by the Department of Mathematics. The remaining 18 units may be selected from upper division or graduate courses in mathematics, or in appropriate related fields with the approval of the Mathematics Graduate Committee. A maximum of 8 units of Math 596 and/or Math 598 may be counted toward the degree. All graduate level courses (200 series) must be taken for a letter grade, with a minimum grade point average of B. Other courses may be taken S/U. Approval of the student's advisor is required to utilize Math 260 as part of the 24 graduate level units. Normally a student will complete the M.A. degree in four to six quarters.

At the earliest reasonable time, students enrolled in the Thesis Option should choose a faculty member familiar with their work to serve as their Thesis Advisor. Normally this faculty member would be one of the student's instructors. The thesis may be either an exposition of an area of mathematics needing organization and synthesis or a presentation of original research on a relatively small (but interesting) problem.

Graduate students who expect to complete the requirements for the Master's degree by the end of a given quarter must notify the Staff Graduate Advisor at the beginning of that quarter. Students interested in continuing on to the Ph.D. may be admitted to the Ph.D. program only by formal petition to the Graduate Committee. Approval is not automatic and will depend upon the student's academic record. These students will normally follow the Examination Option for the Master's degree. To be considered for admission to the Ph.D. program, students are expected to complete their coursework and comprehensive examinations at a higher level than is expected of terminal Master's degree candidates, and should follow the schedule described in the Ph.D. program section of this booklet under the heading, “Normal Progress for Ph.D. Students.”

**Master of Arts - Mathematics**

**Degree Requirements**

Students who have had some but not all of the requisite material in upper division undergraduate coursework in linear algebra, algebra, real analysis, and complex analysis should complete their work in these areas during their first year by taking the appropriate courses chosen from Math 108 AB, 111 ABC, 118 ABC, and 122 AB.

The department offers two options for completing the degree: thesis or examination. In consultation with a departmental academic advisor, all students are required to create an individual academic plan to satisfy the degree requirements.

**Thesis Option**

This option requires demonstration of adequate knowledge in linear algebra, modern algebra, real and complex analysis, as well as preparation of an acceptable thesis and oral defense of the thesis before a faculty committee. The 24 graduate units in mathematics must include at least one basic full-year graduate course sequence in either Algebra or Analysis.

Before embarking upon a thesis, students should be certain that they have the approval of the faculty member they wish to be their Thesis Advisor. The student and Thesis Advisor must present to the Graduate Committee for its approval a coherent coursework and thesis program no later than the start of their second year. The Thesis Committee will be appointed in accordance with general University policies. All Thesis Committees must have a mini¬mum of three regular (not visiting) faculty. One member, at most, may be from outside the Mathematics department.

The final copies of the thesis are to be prepared in accordance with the requirements given in the document entitled, “Guide to Filing Theses and Dissertations” which can be obtained via the Graduate Division website, http://www.graddiv.ucsb.edu.

**Examination Option**

Students must satisfy the area requirements for Algebra and Analysis. A student who wishes to substitute a different area requirement for one of the above areas may, with the support of a faculty advisor, petition the Graduate Committee for approval.

**Master of Arts - Applied Mathematics**

**Degree Requirements**

Students who have had some but not all of the requisite material in upper division undergraduate coursework in linear algebra, differential equations, real and complex analysis, and numerical analysis should complete their work in these areas during their first year by taking the appropriate courses chosen from Math 108AB, 124AB, 118ABC, 122AB, and 104ABC.

An M.A. Applied Mathematics student has the option to take up to 9 units of coursework outside the Mathematics Department. These outside units may be applied toward the 42 unit requirement with the approval of the Mathematics Graduate Committee.

The department offers two options for completing the degree: thesis or examination. In consultation with a departmental academic advisor, all students are required to create an individual academic plan to satisfy the degree requirements.

**Thesis Option**

This option requires demonstration of adequate knowledge in linear algebra, real and complex analysis, numerical analysis, and differential equations, as well as preparation of an acceptable thesis and oral defense of the thesis before a faculty committee. The 24 graduate units in mathematics must include at least one basic full-year graduate course sequence in Applied Math.

Before embarking upon a thesis, students should be certain that they have the approval of the faculty member they wish to be their Thesis Advisor. The student and Thesis Advisor must present to the Graduate Committee for its approval a coherent coursework and thesis program no later than the start of their second year. The Thesis Committee will be appointed in accordance with general University policies. All Thesis Committees must have a minimum of three regular (not visiting) faculty. One member, at most, may be from outside the Mathematics department.

The final copies of the thesis are to be prepared in accordance with the requirements given in the document entitled, “Guide to Filing Theses and Dissertations” which can be obtained via the Graduate Division website, http://www.graddiv.ucsb.edu.

**Examination Option**

Students must satisfy the area requirements in Applied Mathematics and Analysis. A student who wishes to substitute a different area requirement for Analysis areas may, with the support of a faculty advisor, petition the Graduate Committee for approval.

**NORMAL PROGRESS FOR M.A. STUDENTS**

The ideal course load for the well-prepared first-year M.A. student should consist of three courses per quarter, at least two of which are graduate courses satisfying the course component of two area requirements. It is expected that a student will make sufficient progress to finish the Master's degree in no more than six quarters of full-time study.