# MATHPHD - Mathematics

### College

College of Science

### Career

Graduate

### Program Description

The department offers programs leading to the Master of Arts, Master of Science, and Doctor of Philosophy degrees with a major in mathematics. Concentrations are available in pure, applied, or computer mathematics, in mathematics education, or in probability and statistics. As there are no sharp boundaries between these concentrations, students are encouraged to pursue a broad range of mathematical topics. Programs are planned in consultation with faculty advisers.

To be admitted, applicants must have completed the equivalent of an undergraduate major in mathematics with at least 15 units of upper-division or higher level work including one semester each of advanced analysis at the level of Math 425A, abstract algebra at the level of Math 415A, and linear algebra at the level of Math 413. Applicants are asked to submit scores on the Graduate Record Examination, including the subject Examination in Mathematics.

For the Doctor of Philosophy degree, the requirements are: 36 units of graduate credit in the major and 12 units in a supporting minor, which may be declared in Mathematics, although outside minors are encouraged. Students will normally either take the first year graduate core courses in Algebra (Math 511A-B), Real Analysis (Math 523A-B), and Geometry-Topology (Math 534A-B), or otherwise learn this material by the end of their first year of Ph.D. studies for the Qualifying Examinations. Qualifying examinations are offered twice yearly, in August and in January, shortly before the beginning of Fall and Spring semesters. Students with prior preparation may attempt the examinations upon entrance to the program, or after one semester. Ideally a student will complete the qualifying examinations by the August following entrance to the Ph.D. program. Students must attempt at least three assessment options. Two of the assessments must be chosen from the traditional core exams (the first three options). Each written exam is offered in August and January. There is no limit to the number of attempts for the written exams. Students may attempt more than three assessment options. Students with prior preparation may attempt the examinations upon entrance to the program, or after one semester. Students who do not complete the three examinations within five semesters and with a cumulative passing grade will not be continued in the Ph.D. program unless the Graduate Committee, upon review of the case, finds extenuating reasons to justify such continuation. Two year-long Mathematics course sequences that are not co-convened and are not part of the required core of algebra, real analysis, and geometry-topology are required. These two sequences must be in two of the three general areas: algebra and number theory, analysis and geometry, mathematical physics and applied mathematics. For most students one of the sequences will be Complex Analysis (Math 520A-B). Students must also complete a series of Professional Development Requirements consisting of Professional Development, Community Development, Broader Impact Development and Equity Requirement. The principal component of the program is the completion of a dissertation involving original creative research.

Ph.D. candidates with other majors who wish to minor in Mathematics are required to take four approved graduate level courses in mathematics and a written examination which covers the content of those courses.

To be admitted, applicants must have completed the equivalent of an undergraduate major in mathematics with at least 15 units of upper-division or higher level work including one semester each of advanced analysis at the level of Math 425A, abstract algebra at the level of Math 415A, and linear algebra at the level of Math 413. Applicants are asked to submit scores on the Graduate Record Examination, including the subject Examination in Mathematics.

For the Doctor of Philosophy degree, the requirements are: 36 units of graduate credit in the major and 12 units in a supporting minor, which may be declared in Mathematics, although outside minors are encouraged. Students will normally either take the first year graduate core courses in Algebra (Math 511A-B), Real Analysis (Math 523A-B), and Geometry-Topology (Math 534A-B), or otherwise learn this material by the end of their first year of Ph.D. studies for the Qualifying Examinations. Qualifying examinations are offered twice yearly, in August and in January, shortly before the beginning of Fall and Spring semesters. Students with prior preparation may attempt the examinations upon entrance to the program, or after one semester. Ideally a student will complete the qualifying examinations by the August following entrance to the Ph.D. program. Students must attempt at least three assessment options. Two of the assessments must be chosen from the traditional core exams (the first three options). Each written exam is offered in August and January. There is no limit to the number of attempts for the written exams. Students may attempt more than three assessment options. Students with prior preparation may attempt the examinations upon entrance to the program, or after one semester. Students who do not complete the three examinations within five semesters and with a cumulative passing grade will not be continued in the Ph.D. program unless the Graduate Committee, upon review of the case, finds extenuating reasons to justify such continuation. Two year-long Mathematics course sequences that are not co-convened and are not part of the required core of algebra, real analysis, and geometry-topology are required. These two sequences must be in two of the three general areas: algebra and number theory, analysis and geometry, mathematical physics and applied mathematics. For most students one of the sequences will be Complex Analysis (Math 520A-B). Students must also complete a series of Professional Development Requirements consisting of Professional Development, Community Development, Broader Impact Development and Equity Requirement. The principal component of the program is the completion of a dissertation involving original creative research.

Ph.D. candidates with other majors who wish to minor in Mathematics are required to take four approved graduate level courses in mathematics and a written examination which covers the content of those courses.