Applied Mathematics and Statistics

Baskin School of Engineering
335 Baskin Engineering Building
(831) 459-2158
http://www.soe.ucsc.edu

Program Description

Applied mathematics and statistics are disciplines devoted to the use of mathematical methods and reasoning to solve real-world problems of a scientific or decision-making nature in a wide variety of subjects, principally (but not exclusively) in engineering, medicine, the physical and biological sciences, and the social sciences. Applied mathematical modeling often involves the use of systems of (partial) differential equations to describe and predict the behavior of complex real-world systems that unfold dynamically in time. Statistics, construed broadly, is the study of uncertainty: how to measure it (using ideas and methods in probability theory), and what to do about it (using concepts from statistical inference and decision theory).

The Applied Mathematics and Statistics Department at UCSC offers both a master’s program and a doctoral program in Statistics and Stochastic Modeling. 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 minor in Statistics.

Additional information on these programs can be found on the department’s web pages at www.soe.ucsc.edu.

Undergraduate Programs

Requirements for an Undergraduate Minor in Statistics

The statistics minor is available for students who wish to gain a quantitative  understanding of how to (a) measure uncertainty, and (b) make good decisions on the basis of incomplete or imperfect information, and to apply these skills to their interests in another field. This minor could also be combined with a major in mathematics as a preparation for a graduate degree in statistics or biostatistics.

Students are required to take a two-quarter basic calculus sequence:

Basic Calculus Sequence:

• Applied Mathematics and Statistics 11A-B or Economics 11A-B or Mathematics 11A-B or Mathematics 19A-B or Mathematics 20A-B

Plus one course from each of the following nine categories:

• Statistical Concepts: Applied Mathematics and Statistics 5 or 7/L
• Computer Programming: Bioinformatics 60 or Computer Science 12A/L  or 60G or 60N
• Engineering Mathematics or Linear Algebra: Applied Mathematics and Statistics 27/L or Mathematics 21
• Multivariate Calculus: Mathematics 22 or 23A
• Probability: Applied Mathematics and Statistics 131 or Computer Engineering 107
• Statistical Inference: Applied Mathematics and Statistics 132 or Applied Mathematics and Statistics 162
• Computational Methods: Applied Mathematics and Statistics 147
• Bayesian Statistics: Applied Mathematics and Statistics 206
• Statistical Elective: Applied Mathematics and Statistics 198, or Applied Mathematics and Statistics 205, or Biomolecular Engineering 205, or Computer Engineering 108, or Economics 114, or Electrical Engineering 151, or Mathematics 114,  or Psychology 181, or Sociology 103A

At most two upper-level courses may be used to satisfy the requirements of another major or minor degree. With the permission of the AMS Department, students may substitute any graduate-level AMS course for an upper-level requirement. Students planning graduate work in statistics are recommended to choose Mathematics 21, Mathematics 23A, and Applied Mathematics and Statistics 205, and also to take Mathematics 23B and Mathematics 105A-B.

Graduate Programs (M.S., Ph.D.)

Requirements for a Graduate Degree in Statistics and Stochastic Modeling

All students must complete the first six core courses described below (30 units) and a 3-unit course on research and teaching, together with participation in a 2-unit research seminar (Applied Mathematics and Statistics 280B) for one quarter per year.  M.S. students must complete two additional 5-unit courses from the approved list, bringing the total requirement to 43 units. Ph.D. students must complete an additional four 5-unit courses from the approved list, for a total requirement of 53 units.

The core courses for the Ph.D. in Statistics and Stochastic Modeling are:

Applied Mathematics and Statistics 205 Mathematical Statistics
Applied Mathematics and Statistics 206 Bayesian Statistics
Applied Mathematics and Statistics 207 Intermediate Bayesian Modeling
Applied Mathematics and Statistics 211 Applied Mathematical Methods I
Applied Mathematics and Statistics 256 Linear Statistical Models
Applied Mathematics and Statistics 261 Probability Theory and Markov Chains
Applied Mathematics and Statistics 280B Seminar in Statistics and Stochastic Modeling

For students seeking a parenthetical degree notation in Applied Mathematics and Statistics, the core courses for the Ph.D. in Statistics and Stochastic Modeling are:

Applied Mathematics and Statistics 205 Mathematical Statistics
Applied Mathematics and Statistics 211 Foundations of Applied Mathematics for Science and Engineering
Applied Mathematics and Statistics 212A Applied Mathematical Methods I
Applied Mathematics and Statistics 212B Applied Mathematical Methods II
Applied Mathematics and Statistics 213 Numerical Solutions Differential Equations
Applied Mathematics and Statistics 214 Applied Dynamical Systems
Applied Mathematics and Statistics 280B Seminar in Statistics and Stochastic Modeling

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.

Thesis 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 AMS or outside of it. Either the adviser or the additional reader must be from within AMS.

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 AMS. 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 will 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 Stochastic Modeling 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 (see Graduate Handbook for policy on satisfactory academic progress) are subject to dismissal from the program. For specific guidelines on the annual student reviews, please refer to http://www.soe.ucsc.edu/programs/ssm/graduate/index.html.