Introduction
Graduate studies in applied mathematics (AM) at UC Santa Cruz focus on developing skillsets in mathematical modeling, analysis, and scientific computation applied to a broad range of science and engineering disciplines, including fluid mechanics, mathematical biology, dynamical systems, stochastic processes, control, and optimization. The overarching goal of the AM graduate programs at UCSC is to underscore the application of mathematics in solving real-life problems. In particular, the master of science (M.S.) program is designed to prepare the students for professional careers in applied domains requiring mathematical skillsets.
This is a Plan II capstone M.S. program.
Requirements
Course Requirements
Core Courses
All AM M.S. students must complete the following core courses. All non-seminar core courses must be taken for letter grades.
| AM 212A | Applied Partial Differential Equations | 5 |
| AM 213A | Numerical Linear Algebra | 5 |
| AM 213B | Numerical Methods for the Solution of Differential Equations | 5 |
| AM 214 | Applied Dynamical Systems | 5 |
| AM 280B | Seminar in Applied Mathematical Modeling | 2 |
Elective Courses
In addition to these 22 credits, M.S. students must complete four additional 5-credit courses for a total requirement of 42 credits. As part of the four additional courses, students are required to take (at least) one elective course (first-year elective) during their first year. 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, with approval from the student's official advisor:
| AM 129 | Foundations of Scientific Computing for Scientists and Engineers | 5 |
| AM 215 | Stochastic Modeling in Biology | 5 |
| AM 216 | Stochastic Differential Equations | 5 |
| AM 217 | Introduction to Fluid Dynamics | 5 |
| AM 227 | Waves, Instabilities, and Turbulence in Fluids | 5 |
| AM 229 | Convex Optimization | 5 |
| AM 230 | Numerical Optimization | 5 |
| AM 231 | Nonlinear Control Theory | 5 |
| AM 232 | Applied Optimal Control | 5 |
| AM 238 | Fundamentals of Uncertainty Quantification in Computational Science and Engineering | 5 |
| AM 250 | An Introduction to High Performance Computing | 5 |
| AM 260 | Computational Fluid Dynamics | 5 |
| AM 275
/EART 275
| Magnetohydrodynamics | 5 |
| STAT 203 | Introduction to Probability Theory | 5 |
M.S. students will be allowed to substitute one elective course for an independent study course with their required research project (see capstone requirement).
The remaining elective courses can be chosen from any 5-credit AM graduate courses (200 or above) with approval from the student's official advisor or the graduate director. Also, elective courses outside of AM must be approved by the student's official advisor or the graduate director.
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 ladder-rank faculty members, consisting of the faculty adviser and one additional reader. At least one of these core two readers must be from within the Applied Mathematics Department. 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 AM Master's Program and AM Doctoral Program
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 request to transfer 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 (15 credits) fulfilling the degree requirements of the M.S. degree may be taken during students' undergraduate study at UC Santa Cruz. Courses from other institutions may not be applied to the M.S. degree course requirements.
Petitions should be submitted along with the transcript from their UC Santa Cruz undergraduate study. Such petitions are not considered until the completion of at least one quarter at UC Santa Cruz. At most, a total of three courses may be transferred.
Students who complete the M.S. degree in AM at UC Santa Cruz and continue on to the Ph.D. program in AM 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.
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 UC Santa Cruz Graduate Handbook and the AM Graduate Handbook for the policy on satisfactory academic progress). Also, please refer to specific guidelines on the annual student reviews.
Applying for Graduation
All candidates for a degree must submit an application for the M.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.