# Applied Mathematics and Statistics

- Program Overview
Applied Mathematics and Statistics Department

The Department of Applied Mathematics and Statistics, within the College of Engineering and Applied Sciences, offers programs in computational applied mathematics, operations research, quantitative finance, statistics, and computational biology leading to the M.S. and Ph.D. degrees. The department offers an integrated series of courses and seminars, supervised reading, and facilities for research. Emphasis is on the study of real-world problems, computational modeling, and the development of necessary analytical concepts and theoretical tools. A state-of-the-art, computational laboratory is operated for student education and research, with access available to university-based high-performance computing facilities. It also features a network of advanced Unix workstations and modern printing facilities. The laboratory’s full-time staff is available to help students become familiar with the laboratory facilities.

Students participate in joint research with 5 national laboratories, several industrial groups and various sciences, biomedical, and engineering programs. Students, who receive a broad training, find themselves excellently prepared for careers in government and industry in which mathematics is used as a computational or conceptual tool.

Faculty research programs receive significant external funding and provide students with an opportunity for active participation in a variety of projects in all areas of the department. Faculty interests include applied graph theory, biostatistics and computational biology, structure-based drug design, computational fluid dynamics, combinatorial optimizations, computational statistics, data analysis, flow through porous media, fracture mechanics, inverse problems, mixed-boundary value problems, nonlinear conservation laws, quantitative finance, reliability theory, risk management, robust estimation, nonparametric statistics, stochastic modeling and sequential decision making and structure-basedvdrug design. Most doctoral students are supported through either a research or teaching assistantship.

The Ph.D. program normally takes about four to five years for students with a strong analytical and computing background. The M.S. programs, when pursued on a full-time basis, may be completed in three or four semesters. Students who have taken graduate courses before enrolling at Stony Brook may request transfer of up to twelve credits. If such a request is approved, it may be possible to complete the M.S. degree in two semesters. It is strongly urged that all applicants develop some facility in computer programming.

A more detailed description of the graduate program is available from the departmental office. This includes specific distribution requirements, fields of specialization, and information on the preliminary and qualifying examinations. Interested students should request information and application forms as early as possible, especially if they plan to apply for financial aid.

**Advanced Graduate Certificate Program in Operations Research**

This advanced certificate program of 18 credits, consisting of six three-credit courses, trains students in the fundamental mathematical tools for working in the operations research profession. Operations research is the field of applied mathematics related to efficient management of the activities of private companies, government agencies and nonprofit organizations. The following courses are required for certificate: AMS 507 Introduction to Probability, AMS 540 Linear Programming, AMS 550 Stochastic Models, AMS 553 Simulation and Modeling, AMS 572 Data Analysis I, plus one (3 credit) elective chosen by student in consultation with an advisor.**Advanced Graduate Certificate Program in Quantitative Finance**This advanced certificate program of 15 credits, consisting of five three-credit courses, trains students in the fundamentals required for the application of quantitative methods in the financial world. The certificate is open to students in related graduate programs at Stony Brook, as well as to non-matriculated students registered through the School of Professional Development. The following courses are required for certificate: AMS 511 Foundations of Quantitative Finance, AMS 512 Capital Markets & Portfolio Theory, AMS 513 Financial Derivatives & Stochastic Calculus, one elective chosen from AMS 514523, plus one additional (3-credit) elective chosen by the student with the approval of an advisor.

**Combined B.S./M.S. Degree**Undergraduate applied mathematics majors, with strong academic credentials may apply for admission to the special Bachelor of Science-Master of Science program in Applied Mathematics and Statistics at the end of the junior year. The combined B.S./M.S. program in applied mathematics and statistics allows students with superior academic records to use up to six graduate credits toward the B.S. and M.S. requirements. In essence, those six credits count toward two goals simultaneously. Normally, it would take six years to complete two separate degrees, but with the combined B.S./M.S. program, there is only a 5 year commitment (10 semesters). The advantage of the combined program is that the M.S. degree can be earned in less time, thus costing less money than that required by the traditional course of study. A minimum cumulative GPA of 3.3 in all courses, as well as a GPA of 3.5 in required courses for the AMS major, is typically required to apply for the combined degree program; exceptions may be made for students with significantly improved

Students apply to the program during their junior year. In the first semester of the senior year, students in the B.S./M.S. program are granted permission to take up to six graduate credits which will be applied towards the Masters degree requirements. In the second semester of the senior year, they become enrolled as graduate students. Because students in this program only need to earn 114 undergraduate credits, they are usually finished with undergraduate coursework by the first semester of their senior year. If needed, however, they may enroll in up to twelve credits of undergraduate coursework during the second semester of senior year. The undergraduate degree is issued at the end of the senior year, and the student continues in the graduate program through the fifth year. The requirements stated in the Graduate Bulletin must be earned to qualify the student for the master’s degree; this includes a total of at least 30 graduate level credits (including the six taken as an undergraduate). Further information about the combined program may be obtained from either the graduate program director or the undergraduate program director.

**Part-Time Graduate Studies**

In addition to the full-time graduate program leading to the M.S. and Ph.D. degrees, the department conducts a part-time program on campus. The part-time program is governed by regulations governing the resident full-time program with the exception that students in the part-time program have greater flexibility in choosing the time for the qualifying examination if they are contemplating pursuing the Ph.D.The purpose of the part-time program is to provide an opportunity for men and women who are employed full time to pursue graduate study leading to advanced degrees in applied mathematics, statistics, and operations research. Applicants who hold a bachelor’s degree in applied mathematics, mathematics, engineering, physical sciences, life sciences, or social sciences with a strong background in undergraduate mathematics will be considered for admission to this program. Qualified students may continue beyond the master’s degree for the Ph.D. degree.

Additional information, including the scheduling of courses for part-time students, may be obtained from the graduate program director.

- Admissions
Admission Requirements of Applied Mathematics and Statistics Department

For admission to graduate study, the minimum requirements are as follows:

A. A bachelor’s degree in engineering, mathematics, the physical sciences, or in the life or social sciences with a strong mathematics background.

B. A minimum overall grade point average of at least 3.00, as well as a minimum grade point average of 3.00 in all courses with a significant mathematical or quantitative component.

C. Results of the Graduate Record Examination (GRE) General Test.

D. Three letters of reference.

E. Official transcripts for all undergraduate study completed.

F. Acceptance by both the Department of Applied Mathematics and Statistics and the Graduate School.

G. In some circumstances, a student may be admitted provisionally although they are missing some of the above requirements. Students admitted provisionally must follow an approved course sequence and maintain a cumulative GPA of at least 3.0 during the first year of graduate study before being admitted to full degree candidacy.

- Degree Requirements
Requirements for the M.S. Degree in Applied Mathematics and Statistics

In addition to the minimum Graduate School requirements, the following are required:

**A. Course Requirements**

The M.S. degree in the Department of Applied Mathematics and Statistics requires the satisfactory completion of a minimum of 30 graduate credits in letter-graded (A,B,C,F) graduate courses, with some specializations requiring up to 36 credits.All credits in satisfaction of the degree must be at the graduate level. The department may impose additional requirements as described below. In addition, the cumulative grade point average for all courses taken must be B or higher, and at least 18 credits of all courses taken must carry a grade of B or above, and the grade point average over all core (nonelective) requirements must be 3.0 or higher.

The student pursues a program of study planned in consultation with an academic advisor. The program and any subsequent modifications require approval by the graduate program director.

*Core Requirements for the M.S. Degree*1. Computational Applied Mathematics

AMS 501 Differential Equations and Boundary Value Problems

AMS 503 Applications of Complex Analysis

AMS 510 Analytical Methods for Applied Mathematics and Statistics

AMS 526 Numerical Analysis I

AMS 527 Numerical Analysis II

AMS 528 Numerical Analysis III

AMS 595 Fundamentals of Computing (1 credit)

Four elective courses (12 credits total) chosen in consulation with advisor

2. Computational Biology

AMS 507 Introduction to Probability

AMS 510 Analytical Methods for Applied Mathematics and Statistics

MCB 520 Graduate Biochemistry OR

CHE 541 Biomolecular Structure and Analysis

AMS 531 Laboratory Rotations in Computational Biology (two semesters, 0 credit)

AMS 532 Journal Club in Computational Biology (two semesters, 0 credit)

AMS 533 Numerical Methods and Algorithms in Computational Biology

AMS 535 Intro to Computational Structural Biology & Drug Design

AMS 537 Biological Networks & Dynamics

AMS 539 Introduction to Physical & Quantitative Biology (0 credit)

CSE 549 Computational Biology

Three elective courses (9 credits total) chosen in consultation with advisor

3. Operations Research

AMS 510 Analytical Methods for Applied Mathematics and Statistics

AMS 507 Introduction to Probability

AMS 540 Linear Programming

AMS 550 Stochastic Models

AMS 553/CSE 529 Simulation and Modeling

One course in statistics (AMS 570 - 586)

AMS 595 Fundamentals of Computing (1 credit)

Four elective courses (12 credits total) chosen from AMS 542-556; one of these may be substituted by an additional statistics course (AMS 570-586), and one may be substituted by a quantitative finance course (AMS 511-523)

4. Statistics

AMS 510 Analytical Methods for Applied Mathematics and Statistics

AMS 507 Introduction to Probability

AMS 570 Mathematical Statistics I

AMS 572 Exploratory Data Analysis

AMS 573 Design & Analysis of Categorical Data

AMS 578 Regression Theory

AMS 582 Design of Experiments

AMS 597 Statistical Computing

Two elective courses (6 credits total) chosen in consultation with advisor

5. Quantitative Finance

AMS 507 Introduction to Probability

AMS 510 Analytical Methods for Applied Mathematics and Statistics

AMS 511 Foundations of Quantitative Finance

AMS 512 Capital Markets & Portfolio Theory

AMS 513 Financial Derivatives and Stochastic Calculus

AMS 514 Computational Finance

AMS 516 Statistical Methods in Finance

AMS 517 Quantitative Risk Management

AMS 518 Advanced Stochastic Models, Risk Assessment & Portfolio Optimization

AMS 572 Data Analysis I

FIN 539 Investment Analysis

One elective course (3 credits total) chosen in consultation with advisor

*Elective Requirements for the M.S. Degree*Unless otherwise specified, any graduate-level AMS or other graduate-level courses in a related discipline approved by the graduate program director may be used to satisfy the credit requirement beyond the core course requirement.

**B. Final Recommendation**

Upon the fulfillment of the above requirements, the faculty of the graduate program will recommend to the dean of the Graduate School that the Master of Science degree be conferred or will stipulate further requirements that the student must fulfill.**C. Time Limit**

All requirements for the Master of Science degree must be completed within three years of the student’s first registration as a full-time graduate student.Requirements for the Ph.D. Degree in Applied Mathematics and Statistics

**A. Course Requirements**

The course of study prescribed for the M.S. degree provides basic guidelines for doctoral study. The student pursues a program of study planned in consultation with an academic advisor. The program and any subsequent modifications require approval of the graduate program director.**B. Qualifying Examination**

A student must pass a two-part qualifying examination to be allowed to continue toward the Ph.D. degree. Each component of the qualifying examination is given twice a year at the beginning and the end of the Spring semester and is designed to test the student’s preparation to do research in applied mathematics. Each student must demonstrate competency in linear algebra and analysis and in-depth knowledge in one of the following areas:Computational Applied Mathematics

Computational Biology

Operations Research

Quantitative Finance

Statistics

**C. Research Advisor**

After completion of at least one year of full-time residence and prior to taking the preliminary examination, the student must select a research advisor who agrees to serve in that capacity.**D. Preliminary Examination**

This is an oral examination administered by a committee and given to the student when he or she has developed a research plan for the dissertation. The plan should be acceptable to the student’s research advisor.**E. Mathematical Writing Requirement**

The mathematical writing requirement is associated with the preliminary oral examination. The student must submit a document, typically 20 to25 double-spaced pages long, containing the research plan for the dissertation, including a wellreferenced synopsis of the relevant background literature, as well as a summary of research work accomplished to date. It must be given to the members of the Preliminary Examination committee at least one week before the oral presentation.The document must be approved for satisfactory written style and use of technical English as well as for intellectual content; this will be assessed by the Preliminary Examination Committee, who is appointed by the graduate program director. International students may need extensive writing assistance from the ESL Tutoring Center established to provide exactly this kind of technical writing tutorial support.

Tutorial assistance in writing, if needed, will also be provided to native students.

**F. Advancement to Candidacy**

After successfully completing all requirements for the degree other than the dissertation, the student is eligible to be recommended for advancement to candidacy. This status is conferred by the dean of the Graduate School upon recommendation from the graduate program director.**G. Dissertation**

The most important requirement of the Ph.D. degree is the completion of a dissertation, which must be an original scholarly investigation. The dissertation must represent a significant contribution to the scientific literature and its quality must be comparable with the publication standards of appropriate and reputable scholarly journals.**H. Dissertation Defense**

The student must defend the dissertation before an examining committee. On the basis of the recommendation of this committee, the Department of Applied Mathematics and Statistics will recommend acceptance or rejection of the dissertation to the dean of the Graduate School. All requirements for the degree will have been satisfied upon successful defense of the dissertation. There must be at least one year between advancing to candidacy and scheduling a dissertation defense.**I. Minimum Residence**

At least two consecutive semesters of full-time study are required.**J. Time Limit**

All requirements for the Ph.D. degree must be completed within seven years after the completion of 24 graduate credits in the program. The time limits for the qualifying and preliminary examinations and advancement to candidacy are described in the departmental*Graduate Student Handbook.***K. Teaching Requirement**

One academic year long teaching experience required. - Facilities
- Faculty
- Contact
Applied Mathematics and Statistics

**Chairperson**

Joseph Mitchell, Mathematics Building P-134A (631) 632-8366**Graduate Program Director (PhD)**

Hongshik Ahn, Mathematics Building 137 (631) 632-8372**Graduate Program Director (MS, AGC)**

Wei Zhu , Mathematics Building 138 (631) 632-8374**Graduate Secretary**

Christine Rota, Mathematics Building P-141 (631) 632-8360**Advanced Graduate Certificate Awarded**

Advanced Graduate Certificate in Operations Research; Advanced Graduate Certificate in Quantitative Finance**Degrees Awarded**

M.S. in Applied Mathematics and Statistics; Ph.D. in Applied Mathematics and Statistics**Web Site**

http://www.ams.stonybrook.edu/**Application**

https://app.applyyourself.com/AYApplicantLogin/fl_ApplicantLogin.asp?id=sunysb-gs