Applied Mathematics M.S.



Course Requirements

All applied mathematics M.S. students must complete the core courses listed below.

Core Courses

All applied mathematics M.S. students must complete the following core courses:

AM211Foundations of Applied Mathematics


AM212AApplied Mathematical Methods I


AM213ANumerical Linear Algebra


AM213BNumerical Methods for the Solution of Differential Equations


AM214Applied Dynamical Systems


AM280BSeminar in Applied Mathematical Modeling



In addition to these 27 credits, master of science (M.S.) students must complete three additional 5-credit courses, including a first-year elective (see below), for a total requirement of 42 credits. All elective courses must be approved by the student’s official adviser.

First-year electives are designed to prepare students for their ultimate research emphasis within applied mathematics. They must be taken during the first year, and must be selected from the following list:

AM129Foundations of Scientific Computing for Scientists and Engineers


AM209Foundations of Scientific Computing


AM216Stochastic Differential Equations


AM217Introduction to Fluid Dynamics


AM227Waves and Instabilities in Fluids


AM229Convex Optimization


AM230Numerical Optimization


AM231Nonlinear Control Theory


AM232Applied Optimal Control


AM238Fundamentals of Uncertainty Quantification in Computational Science and Engineering


AM250An Introduction to High Performance Computing


AM260Computational Fluid Dynamics


/EART 275


STAT203Introduction to Probability Theory


Students cannot receive credit for both AM 129 and AM 209.

M.S. students will be allowed to substitute one elective course for an independent study course with their required research project (see capstone requirement).


M.S. Project Requirements

A capstone project is required for the M.S. degree.

For the M.S. degree, students will conduct a capstone research project. Students must submit a proposal to the potential faculty sponsor. If the proposal is accepted, the faculty member will become the sponsor and will supervise the research and writing of the project. The project will involve the solution of a problem or problems from the selected area of application. When the project is completed and written, it will be submitted to and must be accepted by a committee of two individuals, consisting of the faculty adviser and one additional reader. Additional readers will be chosen appropriately from within the Applied Mathematics Department or outside of it. Either the adviser or the additional reader must be from within the Applied Mathematics Department.

Relationship of Master's and Doctoral Programs

The M.S. and Ph.D. programs are freestanding and independent, so that students can be admitted to either. Students completing the M.S. program may proceed into the Ph.D. program (provided they pass the pre-qualifying examination), and students in the Ph.D. program can receive a non-terminal M.S. degree upon completion of M.S. requirements, including the capstone research project. 

Transfer Credit

Up to three School of Engineering courses fulfilling the degree requirements of the M.S. degree may be taken before beginning the graduate program through the concurrent enrollment program. Courses from other institutions may not be applied to the M.S. degree course requirements.

Petitions should be submitted along with the transcript from the UC Santa Cruz Extension. Such petitions are not considered until the completion of at least one quarter at UCSC. At most, a total of three courses may be transferred from concurrent enrollment.

Students who complete an M.S. degree in applied mathematics at UCSC and continue on to a Ph.D. program in applied mathematics at UCSC can transfer all applicable courses taken during the M.S. to the Ph.D. program, provided that such students meet the minimum residency requirement for Ph.D. programs, as specified by the UCSC Graduate Division.

Foreign Language Requirements

Applicants whose native language is not English must take the TOEFL or IELTS exam and submit an official score report with the admission application. For admission purposes, the minimum passing score for the TOEFL exam must be 570 on the paper-based, 230 on the computer-based, or 89 on the internet-based test. The minimum passing score for the IELTS exam is 7. If you have received a degree from an English-speaking institution or have lived in the United States for more than four years, you are eligible for a TOEFL exemption.

To be considered for teaching assistant support you must have scored a minimum of 26 on the spoken portion of the Internet-based TOEFL or an overall 8 on the IELTS. International students may also participate in the Graduate Preparation Program (GPP) prior to starting the graduate program. Successful completion of the GPP satisfies the English-language requirement for teaching assistants.

Applying for Graduation

All candidates for a degree must submit an Application for Master's Degree to the Graduate Student Affairs Office by the date stated in the Academic and Administrative Calendar for the quarter they wish to receive the degree. The deadline for degree applications is typically in the second week of the quarter. A student is required to be registered during the quarter in which the degree is conferred.  For more information about applying for graduation, visit the Baskin School of Engineering Graduate Studies website

Review of Progress

Each year, the faculty reviews the progress of every student in all programs and tracks. Students not making adequate progress toward completion of degree requirements are subject to dismissal from the program (see the Graduate Handbook for the policy on satisfactory academic progress). Also, please refer to specific guidelines on the annual student reviews.