# Graduate Programs

The Applied Mathematics and Statistics Department at UCSC offers master’s and doctoral programs in Statistics and Applied Mathematics, or Applied Mathematics and Statistics, depending on chosen emphasis, and a master’s program in Scientific Computing and Applied Mathematics (SciCAM). The goal of these programs is to help students develop into independent scholars who are prepared for productive careers in research, teaching, and industry. The department also offers a designated emphasis in statistics, a minor in statistics, and a minor in applied mathematics.

Applications for admission are handled by the School of Engineering. Academic questions can be addressed to the Graduate Director , 831-459-5536, while administrative questions can be addressed to the Graduate Advisor , 831-459-5737.

Statistics and Applied Mathematics MS/PhD Requirements

Applied Mathematics and Statistics MS/PhD Requirements

Scientific Computing and Applied Mathematics MS Requirements

Financial Support

Designated Emphasis in Statistics

Graduate Exam Committees

## Requirements for a Graduate Degree in Statistics and Applied Mathematics

This track is for students emphasizing Statistics. All students must complete the core courses described below.

M.S. Program and Ph.D. Program |
---|

AMS 200 |

AMS 203 |

AMS 205B |

AMS 206B |

AMS 207 |

AMS 211 |

AMS 256 |

AMS 280B |

In addition to these 35 units, M.S. students must complete two additional 5-unit courses from the approved list, for a total requirement of 45 units. Ph.D. students must complete four additional 5-unit courses from the approved list, for a total requirement of 55 units.

## Requirements for a Graduate Degree in Applied Mathematics and Statistics

This track is for students emphasizing Applied Mathematics. All students must complete the core courses described below.

M.S. Program and Ph.D. Program |
---|

AMS 200 |

AMS 203 |

AMS 211 |

AMS 212A |

AMS 212B |

AMS 213 |

AMS 214 |

AMS 280B |

In addition to these 35 units, M.S. students must complete two additional 5-unit courses from the approved list, for a total requirement of 45 units. Ph.D. students must complete four additional 5-unit courses from the approved list, for a total requirement of 55 units.

For both emphasis tracks, M.S. students will be allowed to substitute up to two courses with their required research project in which they conduct a research program in one or two of the quarters of their second year. The project will consist of solving a problem or problems from the selected area of application and will be presented to the sponsoring faculty member as a written document.

Ph.D. students will be required to serve as teaching assistants for at least two quarters during their graduate study.Certain exceptions may be permitted for those with extensive prior teaching experience or those who are not allowed to be employed due to visa regulations.

### Qualifying Examinations

At the end of the first year, all students will take a pre-qualifying examination covering the six (non-seminar) core courses. This examination will have two parts: an in-class written exam, followed by a take-home project involving data analysis. Students who do not pass this exam will be allowed to retake it before the start of the following fall quarter; if they fail the second examination they will be dismissed from the program.

Ph.D. students must complete the oral proposal defense, through which they advance to candidacy, by the end of the spring quarter of their third year. The proposal defense is a public seminar as part of an oral qualifying examination given by the qualifying committee.

### MS Capstone and/or Dissertation Requirements

A capstone project is required for the M.S. degree and a dissertation for the Ph.D. degree.

For the M.S. degree, students will conduct a capstone research project in their second year (up to three quarters). Students must submit a proposal to the potential faculty sponsor by the start of the fourth academic quarter. 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 individuals, consisting of the faculty adviser and one additional reader. Additional readers will be chosen appropriately from within the Applied Mathematics and Statistics Department or outside of it. Either the adviser or the additional reader must be from within the Applied Mathematics and Statistics Department.

A dissertation is required for the Ph.D. degree. Ph.D. students must select a faculty research adviser by the end of the second year. A written dissertation proposal will be submitted to the adviser, and filed with the graduate secretary. A qualifying examination committee will be formed, consisting of the adviser and three additional members, approved by the Chair of the Graduate Program and the Dean of the Graduate Division. The student will submit the written dissertation proposal to all members of the committee and the graduate secretary no less than one month in advance of the qualifying examination. The dissertation proposal will be formally presented in a public oral qualifying examination with the committee, followed by a private examination. Students will advance to candidacy after they have completed all course requirements (including removal of all incompletes), passed the qualifying examination, and paid the filing fee. Under normal progress, a student will advance to candidacy by the end of the spring quarter of her/his third year. A student who has not advanced to candidacy by the start of the fourth year will be subject to academic probation. Upon advancement to candidacy, a dissertation reading committee will be formed, consisting of the dissertation supervisor and at least two additional readers appointed by the Graduate Program chair upon recommendation of the dissertation supervisor. At least one of these additional readers must be in the Applied Mathematics and Statistics Department. The committee is subject to the approval of the Graduate Division. The dissertation will consist of a minimum of three chapters composed of material suitable for submission and publication in major professional journals in statistics and stochastic modeling. The completed dissertation will be submitted to the reading committee at least one month before the dissertation defense, which consists of a public presentation of the research followed by a private examination by the reading committee. Successful completion of the dissertation defense is the final requirement for the Ph.D. degree.

### Relationship of Masters and Doctoral Programs

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 proceed into the Ph.D. program, and students in the Ph.D. program can receive a M.S. degree upon completion of M.S. requirements, including the capstone research project. Each Ph.D. student will be required to have knowledge of statistics and applied mathematics equivalent to that required for the M.S. degree. In addition, Ph.D. candidates will be required to complete coursework beyond the M.S. level.

### Transfer Credit

Up to three School of Engineering courses fulfilling the degree requirements of either the M.S. or Ph.D. degrees may be taken before beginning the graduate program through the concurrent enrollment program. Ph.D. students who have previously earned a master's degree in a related field at another institution may substitute courses from their previous university with approval of the adviser and the graduate committee. Courses from other institutions may not be applied to the M.S. degree course requirements. Petitions should be submitted along with the transcript from the other institution or UCSC 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 UCSC. At most, a total of three courses may be transferred from concurrent enrollment and other institutions.

### Review of Progress

Each year, the faculty reviews the progress of every student. Students not making adequate progress toward completion of degree requirements are subject to dismissal from the program (see the Graduate Handbook for the policy on satisfactory academic progress).

### Program Learning Outcomes

**PhD PLOs (Program Learning Outcomes):**

1. Mastery of the fundamental knowledge in applied mathematics or statistics.

2. Ability to use analytical and computational methods to solve a problem.

3. Ability to develop and apply mathematical or statistical methods to model a

real-world problem in an application area, and understand its relevance within

the research context.

4. Ability to communicate concepts and results to both other experts in the

field and to people outside the field.

5. Ability to conduct independent research.

**Assessment:**

Each student must take the first-year exam, which tests for mastery of the fundamental knowledge, and the ability to use analytical and computational methods (PLOs 1 and 2). The QE provides a formative assessment of PLOs 3, 4, and 5. The thesis document and defense provide a summative assessment of PLOs 3, 4, and 5.

**MS PLOs (Program Learning Outcomes):**

1. Proficiency with the fundamental knowledge in applied mathematics or statistics.

2. Ability to use analytical and computational methods to solve a problem.

3. Ability to apply mathematical or statistical methods to model a real-world

problem in an application area.

4. Ability to communicate concepts and results to those with or without subject

matter knowledge.

**Assessment:**

Each student must take the first-year exam, which tests for mastery of the fundamental knowledge, and the ability to use analytical and computational methods (PLOs 1 and 2). The MS project provides an assessment of PLOs 3 and 4.

**Requirements for a Graduate Degree in Scientific Computing and Applied Mathematics**

All students must complete the Core and Foundational courses described below.

Core & Foundational Requirements |
---|

AMS 212A |

AMS 213A |

AMS 213B |

AMS 214 |

AMS 250 |

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: AMS 147 (Computational Methods and Applications), AMS 210 (Foundations of Scientific Computing) and AMS 211 (Foundations of Applied Mathematics).

**Electives and capstone requirements. **

*Approved elective courses*: Any regular graduate AMS course not already in the core except AMS 200 and supervised research courses; a list of current allowable electives in other departments is maintained by the graduate director, and updated on a yearly basis. Students may also petition the program to add one or more courses to the elective list. Note that some upper division electives are allowed, bearing in mind that no more than a total of 15 units of upper division courses may be used to satisfy the degree requirements.

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

Candidates for a Plan I capstone must, in addition to the 25 units required from core courses, (1) complete one additional 5-unit course from the approved elective list, (2) complete10 units of supervised research (in the form of AMS 297 or AMS 298 with one of the program faculty), and (3) write a thesis.

The thesis requirements are as follows. Students must submit a thesis proposal to the potential faculty sponsor after completion of all core courses. 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 at least 2 faculty from the AMS department, one of which must be the student’s adviser. The student will then be required to give a short (20 minute) public oral presentation of their thesis, 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 M.S. degree to the student.

Candidates for a Plan II capstone must, in addition to the 25 units required from core courses, (1) complete three additional 5-unit courses from the approved elective list, and (2) successfully pass the SciCAM comprehensive examination. The latter 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 project covering all core and foundational courses.

**Accelerated 1-year program plan**

The expected time to completion of the SciCAM degree program is two years. However, AMS also offers a one year accelerated track for interested students who can demonstrate sufficient proficiency in the foundational subjects. Information on the minimum requirements to join the accelerated track can be found on the program website. Requests to join the accelerated track must be made to the graduate director by email no later than August 31^{st} of each year.

**Relationship of SciCAM Masters program and AMS Doctoral Program**

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

**Transfer Credit**

Up to three UCSC courses fulfilling the degree requirements of the SciCAM degree may be taken before beginning the graduate program.

Up to one course from other institutions may be applied to the M.S. degree course requirements. Petitions should be submitted along with the transcript from the other institution or UCSC 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 UCSC.

**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 Graduate Handbook for the policy on satisfactory academic progress). For specific guidelines on the annual student reviews, please refer to http://www.soe.ucsc.edu/programs/ssm/graduate/index.html.

**Program learning outcomes (PLOs)**

**SciCAM MS PLOs: **

- The ability to take a real-life science or engineering problem, and create a mathematical model of it, under supervision or with the help of discussions with colleagues.
- Proficiency in analytical methods for the solution of linear algebra problems, ordinary and partial differential equations.
- Proficiency in the construction of numerical algorithms for the solution of linear algebra problems, as well as ordinary and partial differential equations.
- Proficiency in at least 2 scientific computing languages such as: Fortran, C, Python, R, Matlab, etc. Familiarity with Unix-type operating systems, the use of compilers, professional scientific computing libraries, efficient IO algorithms, data visualization tools, etc.
- Proficiency in the two main parallel computing paradigms (shared vs. distributed memory) and in the use of OpenMP and MPI. Familiarity with parallel architectures and with supercomputing environments such as batch submission scripts, data transfer protocols, scripting, etc.
- The ability to identify and implement, among all of the methods and languages known, the most appropriate and efficient approach for the original problem posed.
- The ability to analyze critically the results from the model obtained, and to present them clearly and coherently to peers (orally and/or in writing).

**Assessment:**

The progress of each student towards the PLOs will be monitored by the program faculty through

- regular formative and summative assessments in the classroom context (participation, homework, quizzes, midterms),
- final examinations or final projects in each of the individual core courses

the comprehensive capstone requirement (whether Thesis or Comprehensive exam).

## Financial Support

The department of Applied Mathematics and Statistics attempts to provide financial support, in the form of Fellowships, Teaching and Research Assistantships, to all students admitted into its graduate programs, with priority typically given to Ph. D. students. Thanks to the generous support of the National Science Foundation the department is also able to offer scholarships through the S-STATSMODEL program. For more information check out the program's webpage here.

## Requirements for a Designated Emphasis in Statistics

Students from another degree program who meet the following requirements can have the designated emphasis of "statistics" annotated to their degree title. For example, a Ph.D. student in Electrical Engineering who meets the requirements would get a certification that read "Ph.D. Electrical Engineering with an Emphasis in Statistics". The course requirements are:

Designated Emphasis in Statistics |
---|

AMS 203 |

AMS 206 (or AMS 206B) |

AMS 207 |

AMS 256 |

and one other statistics course from a list of approved courses in AMS (currently 202, 205B, 221, 223, 225, 241, 245, 261, 263, 274 and 291 although others will be added in the future).

## Graduate Exam Committees

The Master's Capstone Reading Committee, Qualifying Exam Committee and Dissertation Reading Committee require Applied Mathematics & Statistics (AMS) Department approval. These are the current AMS policies on the committee membership. These policies are in addition to the Graduate Council requirements described in the Graduate Handbook.**MASTER'S CAPSTONE READING COMMITTEE**

The members of the Master's Project Reading Committee must include the following:

- A ladder rank AMS faculty member
- A ladder rank UCSC faculty member or a recognized expert in the student's research area as judged by the Graduate Director.

Additional members may be added to the committee. Students should consult their faculty advisors about the membership of their committee.

**QUALIFYING EXAM COMMITTEE**

The qualifying exam committee must consist of at least four examiners, one of whom is not a member of the student's department. The members of the committee must meet the following conditions:

- The
**chair**of the committee must be a tenured ladder rank SOE faculty member who is not the student's advisor. - A ladder rank AMS faculty member (may be the advisor).
- A ladder rank UCSC faculty member or a recognized expert in the student's research area as judged by the Graduate Committee.
- The
**outside member**must be a tenured ladder rank faculty member from a department other than AMS at UCSC or a recognized expert in the student's research area from outside UCSC. The outside member may not be the student's advisor. In the event that the outside member is not from UCSC she/he must have credentials equivalent to a tenured faculty member as judged by the Graduate Committee and the Graduate Dean. The outside member's CV must be submitted along with the exam committee nomination form.

Additional members may be added to the committee. Students should consult their faculty advisors about the membership of their committee.

**DISSERTATION READING COMMITTEE**

The members of the Dissertation Reading Committee must include the following:

- The advisor or supervisor of the student. This is the
**chair**of the committee. - A ladder rank SOE faculty member who is not the student's advisor. This member must be from AMS at UCSC if the advisor is not from AMS at UCSC.
- A ladder rank UCSC faculty or a recognized expert in the student's research area with credentials equivalent to a ladder rank UCSC faculty member as judged by the Graduate Committee.

If you have two advisors you should list both as co-chairs. Additional members may be added to the committee. Students should consult their faculty advisors about the membership of their committee. The Dissertation Reading Committee must be appointed in order to advance to candidacy.

## Tips

If you are inviting someone from outside to serve on your committee and it is not clear whether their credentials will satisfy the requirements for the outside member, then it is advisable to list them either as the third member or an additional fifth member of the committee to avoid embarrassing them and delaying the appointment of the committee.

A ladder rank faculty (Academic Senate member) holds the title of Assistant Professor, Associate Professor, or Professor. Associate Professors and Professors have tenure.