Applied Mathematics M.S.


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, high-performance computing, mathematical biology, dynamical systems, stochastic processes, control, and optimization. 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 is designed to prepare the students for professional careers in applied domains requiring mathematical skillsets.


Course Requirements

Core Courses

All AM M.S. students must complete the following core courses. All non-seminar 5-credit core courses (AM 212A, AM 213A, AM 213B, and AM 214) must be taken for letter grades.

AM 212AApplied Partial Differential Equations


AM 213ANumerical Linear Algebra


AM 213BNumerical Methods for the Solution of Differential Equations


AM 214Applied Dynamical Systems


AM 280BSeminar in Applied Mathematical Modeling


Elective Courses

In addition to the 22 core course 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. These electives must be taken during the first year, and must be selected from the following list, with approval from the student's official advisor or the graduate director:

AM 215Stochastic Modeling in Biology


AM 216Stochastic Differential Equations


AM 217Introduction to Fluid Dynamics


AM 227Waves, Instabilities, and Turbulence in Fluids


AM 229Convex Optimization


AM 230Numerical Optimization


AM 231Nonlinear Control Theory


AM 232Applied Optimal Control


AM 238Fundamentals of Uncertainty Quantification in Computational Science and Engineering


AM 250An Introduction to High Performance Computing


AM 260Computational Fluid Dynamics


AM 275
/EART 275


STAT 203Introduction to Probability Theory


M.S. students will be allowed to substitute one elective course for an independent study course with their required research project (see the M.S. Project Requirements section below).

The remaining elective courses can be chosen from any non-core 5-credit AM graduate courses (200 or above) with approval from the student's official advisor or the graduate director. Elective courses outside of AM will be considered if approved by the student's official advisor or 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

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 both the student and the student’s potential faculty sponsor agree on the proposal topic, 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, 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 pass the Ph.D. pre-qualifying examination, also known as the Ph.D. First-Year Exam), 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