Scientific Computing and Applied Mathematics M.S.

Introduction

The Department of Applied Mathematics (AM) offers an M.S. program in Scientific Computing and Applied Mathematics (SciCAM). SciCAM students learn a combination of applied mathematical modeling and cutting-edge computational methods for modern high-performance computing and scientific machine learning. The SciCAM M.S. degree is ideal for meeting the increasing need for graduates in the rapidly growing markets of machine learning 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 submitting evidence through undergraduate transcripts to the AM graduate director for approval or by taking some or 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:

All of the following five courses:

These foundational courses can be taken for letter grades or the Satisfactory/Unsatisfactory (S/U) option.

Core Courses

All SciCAM M.S. students are required to take the four core courses listed below. These courses must be taken for letter grades.

Elective Courses

Any regular 5-credit AM graduate courses (between course numbers 201 and 279) not already listed as a core course can be counted as electives with approval from the graduate director. Elective courses outside of AM must be approved by the graduate director. Elective courses can be taken for the Satisfactory/Unsatisfactory grading option or the letter grade option.

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. The three foundational courses (AM 100, AM 112, AM 114, AM 129, and AM 147) cannot be used toward the elective degree requirements, but do not count toward the 15 credits limit either.

Other Requirements

The SciCAM program offers two capstone options: Plan I thesis track and Plan II capstone exam track. Students in the SciCAM program pursue either a Plan I thesis or Plan II capstone (comprehensive examination) curriculum.

• Candidates for a Plan I thesis must complete one graduate-level five-credit elective course (between course numbers 200 and 279) and take a minimum of 10 credits of independent study to write a thesis (i.e., at least two five-credit independent studies over two quarters or one 10-credit independent study over one quarter). The thesis requirements are as follows. Students should identify a thesis advisor and a research topic as soon as possible upon joining the M.S. (before completing all core courses), ideally during the first or second quarter, and begin working on their research. They must ultimately write a thesis, which 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 quality and novelty of the thesis must be appropriate for potential publication in an international journal. 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 (between 30 minutes and 45 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 regular 5-credit elective courses from an approved list, at least one of which should be a graduate-level course, and pass the SciCAM comprehensive examination. The exam takes place in the spring quarter each year, and is a take-home exam covering the core and foundational courses. Passing the comprehensive examination fulfills the capstone requirement. A student has two attempts to pass the exam. If a student does not pass the exam in spring, they are allowed to retake it 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:

1. having completed at least three calculus courses, including multivariate differential and integral calculus,
2. having completed a course on ordinary differential equations, a course on linear algebra, and a course on programming, and
3. having completed at least four of the five foundational requirement 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 of 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 15-credit limit does not apply to the requirements of the foundational courses (AM 100, AM 112, AM 114, AM 129, and AM 147), which may all be taken prior to the start of the SciCAM program without penalty. However, students still need to take courses totaling 35 credits as graduate students to satisfy the 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 upon completion of their SciCAM M.S. degree. 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. 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 (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.