# Scientific Computing and Applied Mathematics M.S.

## Introduction

The Department of Applied Mathematics offers an M.S. program in Scientific Computing and Applied Mathematics (SciCAM). SciCAM students learn a combination of cutting-edge computational methods for modern high-performance computing architectures and applied mathematical modeling. The SciCAM M.S. degree is ideal for meeting the increasing need for graduates in the rapidly growing markets of computational mathematics and modeling and high-performance computing. Such computationally knowledgeable and experienced modelers are highly sought after in industry and government agencies.

## Requirements

### Course Requirements

#### Foundational Courses

Students in the SciCAM program must also demonstrate mastery in the foundations of scientific computing and applied mathematics, either by producing evidence through undergraduate transcripts or by taking some or all of the following foundational courses upon entry to the M.S. program:

##### All of the following three courses:

AM 100 | Mathematical Methods for Engineers | 5 |

AM 129 | Foundations of Scientific Computing for Scientists and Engineers | 5 |

AM 147 | Computational Methods and Applications | 5 |

#### Core Courses

All SciCAM M.S. students are required to take the core courses listed below.

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 250 | An Introduction to High Performance Computing | 5 |

All non-seminar core courses must be taken for letter grades.

#### Electives

Any 5-credit AM graduate courses (200 or above) not already listed as a core course can be counted as electives 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.

Note that some upper-division electives are 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.

### Other Requirements

Students in the SciCAM program may pursue either a **Plan I thesis** or **Plan II capstone (comprehensive examination)** curriculum.

**Candidates for a Plan I thesis**must complete one elective and take a minimum of two-quarters of independent study to write a thesis. The thesis requirements are as follows. Students in the regular SciCAM M.S. must submit a thesis proposal to the potential faculty sponsor after completion of all core courses. Students in the SciCAM 4+1 M.S. should identify and submit a thesis proposal as soon as possible upon joining the MS (before completing all core courses) due to the accelerated timeline. If the proposal is accepted, the faculty member will become the sponsor and will supervise the research and writing of the thesis project. The project will involve the solution of a problem or problems from the selected area of application. The thesis 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 thesis will be read by a committee of three ladder-rank faculty members, consisting of the faculty advisor and two additional readers. Additional readers will be chosen appropriately from within the Applied Mathematics Department or outside of it. At least two members of the reading committee must be from within the Applied Mathematics Department. The student will then be required to give a public oral presentation of their thesis (no less than 20 minutes), which will be evaluated by the reading committee. The reading committee will assess the quality of both written work and oral presentation in making their recommendation for awarding the SciCAM M.S. degree to the student.**Candidates for a Plan II capstone (comprehensive examination)**must complete three electives and pass the SciCAM comprehensive examination. The exam takes place in June at the end of the academic year. Students may only take this exam following completion of the last core course. The exam will take the form of a take-home exam covering all core and foundational courses. Passing the comprehensive examination fulfills the capstone requirement. A student will have two attempts to pass the exam. If a student does not pass the exam in June, they will be allowed to retake the exam in late summer (late September before the fall quarter starts).

### Accelerated One-Year Program Plan

The expected time to completion of the SciCAM M.S. degree program is two years. However, AM offers a one-year accelerated track for interested students who can demonstrate sufficient proficiency in the foundational subjects. The minimum requirements to join the accelerated track are:

- having completed at least three calculus courses, including multivariate differential and integral calculus,
- having completed a course on ordinary differential equations, a course on linear algebra, and a course on programming, and
- having completed at least two of the threefoundationalrequirement courses of the SciCAM program or their equivalents.

Note that this is a separate accelerated track from that of the SciCAM 4+1 Contiguous Bachelor's/Master's Pathway.

Requests to join the accelerated track must be made to the graduate director via email no later than Aug. 31 of each year, prior to the student's first quarter in the program.

### Transfer Credit

Up to three UC Santa Cruz courses (15 credits) fulfilling the degree requirements of the SciCAM M.S. degree may be taken during students' undergraduate study at UC Santa Cruz. Note that this limit does not apply to the foundational requirements, which may all be taken prior to the start of the SciCAM program without penalty. However, students will still need to take courses totaling 35 credits as graduate students to satisfy university requirements.

Up to one course from other institutions may be applied to the SciCAM M.S. degree course requirements. Petitions should be submitted along with the transcript from the other institution or UC Santa Cruz Extension. For courses taken at other institutions, copies of the syllabi, exams, and other course work should accompany the petition. Such petitions are not considered until the completion of at least one quarter at UC Santa Cruz.

### Relationship of SciCAM Master's Program and AM Doctoral Program

Students in the SciCAM M.S. program interested in an academic career will be strongly encouraged to apply to the AM Ph.D. program. Applications are reviewed in the standard academic cycle. Students interested in applying to the AM Ph.D. program are encouraged to discuss this option with the graduate director in the fall of each year.

### Review of Academic Progress

Each year, the faculty reviews the progress of every student in the graduate programs. 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.

### 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 (thesis track only) during the quarter in which the degree is conferred. For more information about applying for graduation, visit the Baskin Engineering Graduate Studies website.