Program Requirements

Program Requirements

Course and milestone requirements should be viewed on the UCSC Academic Catalog. See the links below for your programs specific requirements. Also on this page, you will find example schedules and things to think about during different stages of your program. 

Ph.D. Program

The objectives of the Mathematics Ph.D. program are to prepare students for a career in academia, industry, or teaching. At the end of their studies, students will possess the ability to solve problems and communicate solutions in rigorous mathematical language, to communicate mathematical concepts effectively, and to conduct independent research. Ph.D. students are expected to obtain their Ph.D. degree within six years. Students admitted to the Ph.D. program may receive a master's degree en route to the Ph.D.

The following is an example academic plan for a Ph.D. student. Depending on progress and with faculty approval, a student may begin the work of year three in year two. Some faculty require you receive a 1st pass in the prelim of their topic before beginning work together. Others will do readings before prelims are passed. If you would like advising on ways to approach and discuss working together with a faculty member, you may reach out to the Graduate Vice Chair. 

Below is an example timeline for a student in the Ph.D. Program.

Masters Program: Preliminary Exam Track

Students are required to obtain a second-level pass on one of three written preliminary examinations: algebra, analysis, or geometry. A second-level pass signifies that the student has a very good understanding of the basic concepts, but not necessarily enough to conduct independent research.

Below is an example timeline for a Masters student pursing the Preliminary Exam Requirements

Masters Program: Thesis Track

A master’s thesis does not have to consist of original research results. At the minimum, it should show mastery of a specific subject area that goes beyond the knowledge taught in the core sequences in algebra, analysis, or geometry. This track is recommended for students that want to transfer to a Ph.D. program.

The student, in consultation with the Graduate Vice Chair or their thesis advisor, is responsible for selecting a master’s thesis reading committee. The majority of the membership of a thesis reading committee shall be members of the Santa Cruz Division of the Academic Senate. The Graduate Division must approve the committee.

The Nominations for Master’s Thesis Reading Committee Form must be completed and submitted by the end of the second week of the quarter in which the degree will be granted. The form can be found on the Graduate Division website or can be provided by the Mathematics Department. The form should be turned in to the graduate advisor for review and submission to the Graduate Division.

Below is an example timeline for a Masters student pursing a Masters Thesis

Masters to Ph.D. Program Transfer Timeline

If you are interested in transferring to the Ph.D. program, consider scheduling an advising appointment with the graduate advisor. Transferring to the Ph.D. program requires the Ph.D. program requirements to be completed according to the Ph.D. timeline plus a letter of recommendation from a faculty member who will agree to be your research advisor.

You may be reviewed for admission without the preliminary examination requirements being complete, but approval to transfer to the Ph.D. program may be contingent on the preliminary examination requirements being complete by the spring exam of the second year. 

Below is an example timeline for a Masters student attempting to transfer to the Ph.D. program.