Introduction
Graduate studies in applied mathematics (AM) at UC Santa Cruz focus on developing skill sets in mathematical modeling, analysis, and scientific computation applied to a broad range of science and engineering disciplines, including fluid mechanics, high-performance computing, mathematical biology, dynamical systems, stochastic processes, control, optimization, and scientific machine learning. The overarching goal of the AM graduate programs at UC Santa Cruz is to underscore the application of mathematics in solving real-life problems. In particular, the master of science (M.S.) program in applied mathematics prepares the students with the foundational analytical and numerical tools of applied mathematics, enabling them to perform research that transcends the disciplinary boundaries in science and engineering.
Requirements
Course Requirements
Students in the AM M.S. program must demonstrate mastery in the foundations of scientific computing and applied mathematics, either by submitting evidence of undergraduate transcripts to the AM graduate director for approval or by taking all of the following foundational courses upon entry to the M.S. program, or a combination of the two, by the end of their first year. These foundational courses can be taken for letter grade, or the Satisfactory/Unsatisfactory (S/U) grade scale option.
All of the following five courses:
| AM 100 | Mathematical Methods for Engineers | 5 |
| AM 112 | Introduction to Partial Differential Equations | 5 |
| AM 114 | Introduction to Dynamical Systems | 5 |
| AM 129 | Foundations of Scientific Computing for Scientists and Engineers | 5 |
| AM 147 | Computational Methods and Applications | 5 |
Core Courses
All AM M.S. students must complete the following core courses: four regular courses (AM 212, AM 213A, AM 213B, AM 224), as well as one quarter of seminar course AM 280B, and one quarter of AM 296, during which they work on their M.S. project. All four non-seminar courses must be taken for letter grades.
| AM 212 | Advanced Methods of Applied Mathematics | 5 |
| AM 213A | Numerical Linear Algebra | 5 |
| AM 213B | Numerical Methods for the Solution of Differential Equations | 5 |
| AM 224 | Applied Dynamical Systems | 5 |
| AM 280B | Seminar in Applied Mathematical Modeling | 2 |
| AM 296 | Masters Project | 5 |
Elective Courses
In addition to the 27 core course credits, M.S. students must complete three additional regular 5-credit elective courses for a total requirement of 42 credits. As part of the three elective courses, students are required to take (at least) one elective course during their first year (called first-year elective). First-year electives are designed to prepare students for their ultimate research emphasis within applied mathematics, and must be selected from the following list, with approval from the student's official advisor or the graduate director:
| AM 160 | Introduction to Scientific Machine Learning | 5 |
| AM 170A | Mathematical Modeling 1 | 5 |
| AM 170B | Mathematical Modeling 2 | 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 |
The remaining elective courses can be chosen from any non-core 5-credit AM graduate courses (between course numbers 201 and 279) with approval from the graduate director. Elective courses outside of AM will be considered if approved by the graduate director.
Note that some upper-division electives may be allowed, bearing in mind that no more than a total of 15 credits of upper-division courses may be used to satisfy the degree requirements.
M.S. Project Requirements
Students must also conduct a capstone research master's project (AM 296) to satisfy the Master's Plan II university requirement. Students in the AM M.S. program should identify a project advisor and research topic. The project will involve the solution of a problem or problems from the selected area of application. When the project is completed, students must submit an M.S. project report to their project reading committee for the committee's approval. The M.S. report must consist of at least 30 pages and no more than 60 pages of printed written work and accompanying pertinent figures, consisting of a coherent introduction and presentation of the current state of the field, a clear presentation of the questions raised, of the methodology used to solve them, and a discussion of the results obtained. The report will be read by the M.S. project reading committee to assess the quality of both written work for awarding the M.S. degree to the student.
The M.S. project reading committee must include two ladder-rank faculty members, consisting of the faculty advisor 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 advisor 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 program. Students completing the M.S. program may request to transfer into the Ph.D. program (provided they also pass the Ph.D. pre-candidacy 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 of Credit
Up to three UC Santa Cruz 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. However, students will still need to take courses totaling 35 credits as graduate students to satisfy the university 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 UC Santa Cruz 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 SR 686 and the UC Santa Cruz Graduate Division.
Review of Academic 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 the Graduate Division's specific guidelines on annual student reviews. In addition, students will work with their faculty sponsors to fill out an AM advising form at least once a year to discuss the overall academic progress, research relationship, and students’ welfare.
Applying for Graduation
All candidates for a degree must submit an application for the M.S. degree to the Baskin Engineering 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 or on Filing Fee Status during the quarter in which the degree is conferred. For more information about applying for graduation, visit the Baskin Engineering Graduate Studies website.