## Program goal

The Ph.D. in Systems Modeling and Analysis is offered jointly by the Department of Statistical Sciences and Operations Research and the Department of Mathematics and Applied Mathematics. The program focuses on the development of the mathematical and computational skills used to conceptualize and analyze real-world systems. Faculty and students will engage and collaborate to contribute to the knowledge base used in the fields of science, medicine, business and engineering. The continued development of applied mathematics, discrete mathematics, operations research and statistics is critical to scientific advancement in the 21st century. The curriculum enables students to expand the frontiers of knowledge through original, relevant research involving quantitative and qualitative complex systems derived from real, contemporary problems facing our world.

## Student learning outcomes

- Gain a solid foundation in the theory and application of optimization, stochastic processes, simulation, decision analysis and biomathematics, and demonstrate a comprehensive understanding of these concepts
- Learn to perform appropriate collection, modeling and analysis of data using statistical methods
- Demonstrate the ability to identify situations in which mathematics, operations research or statistics can be applied and model the situation
- Demonstrate the ability to solve a wide variety of mathematics, operations research or statistics problems using the software commonly used in industry
- Demonstrate the ability to write code using appropriate research programming environments to implement research ideas
- Learn how to interpret the analysis from mathematics, operations research or statistics models to draw meaningful conclusions about the systems being studied
- Gain the ability to successfully communicate research ideas through writing and presentations
- Gain the skills needed to successfully participate in research under the guidance of faculty

## VCU Graduate Bulletin, VCU Graduate School and general academic policies and regulations for all graduate students in all graduate programs

The VCU Graduate Bulletin website documents the official admission and academic rules and regulations that govern graduate education for all graduate programs at the university. These policies are established by the graduate faculty of the university through their elected representatives to the University Graduate Council.

It is the responsibility of all graduate students, both on- and off-campus, to be familiar with the VCU Graduate Bulletin as well as the **Graduate School website** and academic regulations in individual school and department publications and on program websites. However, in all cases, the official policies and procedures of the University Graduate Council, as published on the VCU Graduate Bulletin and Graduate School websites, take precedence over individual program policies and guidelines.

**Visit the academic regulations section for** **additional information on academic regulations for graduate students.**

## Degree candidacy requirements

A graduate student admitted to a program or concentration requiring a final research project, work of art, thesis or dissertation, must qualify for continuing master’s or doctoral status according to the degree candidacy requirements of the student’s graduate program. Admission to degree candidacy, if applicable, is a formal statement by the graduate student’s faculty regarding the student’s academic achievements and the student’s readiness to proceed to the final research phase of the degree program.

Graduate students and program directors should refer to the following degree candidacy policy as published in the VCU Graduate Bulletin for complete information and instructions.

**Visit the academic regulations section for** **additional information on degree candidacy requirements.**

## Graduation requirements

As graduate students approach the end of their academic programs and the final semester of matriculation, they must make formal application to graduate. No degrees will be conferred until the application to graduate has been finalized.

Graduate students and program directors should refer to the following graduation requirements as published in the Graduate Bulletin for a complete list of instructions and a graduation checklist.

**Visit the academic regulations section for** **additional information on graduation requirements.**

**Apply online at** graduate.admissions.vcu.edu**.**

## Admission requirements

Degree: | Semester(s) of entry: | Deadline dates: | Test requirements: |
---|---|---|---|

Ph.D. | Fall | Feb 1 | GRE-General |

Spring | Nov 1 | ||

Summer | Jul 1 |

**Note:** Assistantships are only available starting in the fall semester. Spring and summer semester admission deadlines are only for students not seeking an assistantship.

In addition to general admission requirements of the VCU Graduate School, the following requirements represent the minimum acceptable standards for admission: have completed an undergraduate degree with at least 30 credit hours of undergraduate-level mathematics, including calculus I and II, multivariate calculus, linear algebra, probability and statistics. Applicants also must have completed at least one upper-level mathematics class that includes mathematical reasoning, such as abstract algebra, combinatorics, graph theory, real analysis or topology.

## Degree requirements

In addition to general VCU Graduate School graduation requirements, students are required to complete course work in core and elective courses and to conduct significant research.

- Credit hour requirements: Students in the systems modeling and analysis Ph.D. program are required to earn a minimum of 57 graduate-level credit hours beyond the baccalaureate. At least one-half of the credit hours presented for graduation must be at the 600 level or higher.
- Qualifying exam: Students must pass a qualifying exam covering material from each of the first three core courses they take after admission to the program. Two attempts are allowed for each exam. This requirement must be fulfilled by the end of the semester following completion of 18 graduate credit hours. Students are exempt from a qualifying exam if they earned an A in the corresponding core course or if they took an equivalent course at another university, as determined by the Ph.D. steering committee.
- Doctoral candidacy: Admission to candidacy is made by evaluation of a qualifying portfolio, including exams and project work from courses; writing samples from the research seminars (SYSM 681, SYSM 682 and SYSM 683); research products from systems research projects (SYSM 697); and statements from faculty advisers and instructors. The portfolio can be submitted after all course work has been completed, as well as any additional preparatory course work required at admission. The candidacy committee will evaluate the student’s readiness to begin their dissertation work. Supplementary examination may be required by the committee.
- Dissertation proposal: After admission to candidacy and the completion of all course work, the student will prepare a written and oral proposal of the intended dissertation research area, including a complete literature review. A successful proposal must be completed at least three months prior to the dissertation defense.
- Dissertation defense: The student must complete 18 credit hours in SYSM 798 resulting in a publishable dissertation and a successful oral defense. The student also must have submitted at least one paper to a refereed academic journal and prepared a second manuscript or given a conference presentation on the research prior to the defense.

## Curriculum requirements

Course | Title | Hours |
---|---|---|

Choose three from the following foundation courses: | 9 | |

Introduction to Dynamical Systems | ||

Graph Theory | ||

Optimization I | ||

Mathematical Statistics I | ||

SYSM 681 | Systems Seminar I | 1 |

SYSM 682 | Systems Seminar II | 1 |

SYSM 683 | Systems Seminar III | 1 |

SYSM 697 | Systems Research ^{1} | 3 |

SYSM 798 | Dissertation Research | 18 |

Electives (Choose courses from lists below.) ^{2} | 24 | |

Total Hours | 57 |

^{1}

Students are required to take SYSM 697 with a faculty adviser before admission to candidacy.

^{2}

Students must complete at least nine credit hours at the 700-level and must complete courses in at least two of the following subject areas: discrete mathematics, mathematical biology, operations research and statistics from the lists below. Electives will be determined based on a student’s research interests and in consultation with their advisers and the graduate program director.

**The minimum total of graduate credit hours required for this degree is 57.**

#### Elective courses in discrete mathematics

Course | Title | Hours |
---|---|---|

MATH 750 | Topics in Combinatorics: ____ | 3 |

MATH 756 | Topics in Graph Theory: ____ | 3 |

#### Elective courses in mathematical biology

Course | Title | Hours |
---|---|---|

MATH 715 | Numerical Solutions for Differential Equations | 3 |

MATH 732 | Ordinary Differential Equations II | 3 |

MATH 769 | Topics in Applied Mathematics: ____ | 3 |

SYSM 780 | Stochastic Methods in Mathematical Biology | 3 |

#### Elective courses in operations research

Course | Title | Hours |
---|---|---|

OPER 731 | Discrete Optimization | 3 |

OPER 732 | Optimization Under Uncertainty | 3 |

OPER/STAT 736 | Mathematics of Knowledge and Search Engines | 3 |

OPER 741 | Advanced Stochastic Simulation | 3 |

OPER 743 | Decision Analysis II | 3 |

OPER 791 | Special Topics in Operations Research | 1-3 |

#### Elective courses in statistics

Course | Title | Hours |
---|---|---|

STAT 725 | Advanced Multivariate Statistical Methods | 3 |

STAT/OPER 736 | Mathematics of Knowledge and Search Engines | 3 |

STAT 742 | Design and Analysis of Experiments II | 3 |

STAT 744 | Regression II | 3 |

STAT 745 | Advanced Bayesian Statistics | 3 |

STAT 746 | Spatial Data Analysis | 3 |

STAT 791 | Special Topics in Statistics | 1-3 |

SYSM 780 | Stochastic Methods in Mathematical Biology | 3 |

#### Other electives

Course | Title | Hours |
---|---|---|

Select 500-, 600- or 700-level MATH, OPER, STAT or SYSM courses except the following: | ||

MATH 505 | Modern Geometry | 3 |

MATH 593 | Internship in Mathematical Sciences | 3,6 |

MATH 661 | Number and Operations | 3 |

MATH 662 | Geometry and Measurement | 3 |

MATH 663 | Functions and Algebra | 3 |

MATH 664 | Statistics and Probability | 3 |

MATH 665 | Rational Numbers and Proportional Reasoning | 3 |

MATH 667 | Functions and Algebra II | 3 |

MATH 690 | Research Seminar | 2 |

MATH 697 | Directed Research | 1-3 |

MATH 698 | Thesis | 1-3 |

OPER 696 | Applied Project | 1-3 |

OPER 697 | Directed Research | 1-3 |

OPER 698 | Thesis | 1-3 |

STAT 508 | Introduction to Social Statistics | 3 |

STAT 543 | Statistical Methods I | 3 |

STAT 608 | Statistics for Social Research | 3 |

STAT 696 | Applied Project | 1-3 |

STAT 697 | Directed Research | 1-3 |

STAT 698 | Thesis | 1-3 |

SYSM 697 | Systems Research | 3 |

**Graduate program director**

Angela Reynolds, Ph.D.

Associate professor, Department of Mathematics and Applied Mathematics

Email: areynolds2@vcu.edu

Phone: (804) 828-6565

**Program website:** sysm.vcu.edu