This is the preliminary (or launch) version of the 2024-2025 VCU Bulletin. Courses that expose students to cutting-edge content and transformative learning may be added and notification of additional program approvals may be received prior to finalization. General education program content is also subject to change. The final edition and full PDF version will include these updates and will be available in August prior to the beginning of the fall semester.

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

  1. Gain a solid foundation in the theory and application of applied mathematics, and demonstrate a comprehensive understanding of these concepts
  2. Learn to perform appropriate collection, modeling and analysis of data using statistical methods
  3. Demonstrate the ability to identify situations in which mathematics can be applied and model the situation
  4. Demonstrate the ability to solve a wide variety of mathematics using the software commonly used in industry
  5. Demonstrate the ability to write code using appropriate research programming environments to implement research ideas
  6. Learn how to interpret the analysis from mathematical models to draw meaningful conclusions about the systems being studied
  7. Gain the ability to successfully communicate research ideas through writing and presentations
  8. 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 today.

Admission requirements

Degree: Semester(s) of entry: Deadline dates: Test requirements:
Ph.D. Fall Feb 1
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. The GRE General exam is optional. Applicants must provide three letters of recommendation, a statement of purpose and a resume/CV. 

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.

  1. 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.
  2. 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.
  3. Doctoral candidacy: Admission to candidacy is made by evaluation of a qualifying portfolio, including exams and project work from courses, research products 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. Students must present their research in a department-sponsored seminar. The candidacy committee will evaluate the student’s readiness to begin their dissertation work. Supplementary examination may be required by the committee.
  4. 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.
  5. Dissertation defense: The student must complete 18 credit hours in SYSM 798 or HUMS 701 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.

Curriculum requirements

Course Title Hours
Program core
MATH 535Introduction to Dynamical Systems (Program Core)3
MATH 556Graph Theory3
OPER 527Optimization I3
STAT 513Mathematical Statistics I3
SYSM 681Research Exploration1
Concentration courses
MATH 507Bridge to Modern Analysis3
MATH 515Numerical Analysis3
MATH 615Iterative Numerical Methods3
or MATH 632 Ordinary Differential Equations I
or MATH 633 Partial Differential Equations
or MATH 715 Numerical Solutions for Differential Equations
MATH 640Mathematical Biology I3
or MATH 769 Topics in Applied Mathematics: ____
or SYSM 780 Stochastic Methods in Mathematical Biology
Select courses from the applied mathematics electives list below. 26
Research requirements
SYSM 697Systems Research 12
SYSM 798Dissertation Research18
or HUMS 701 Post-candidacy Doctoral Research
Select 500-, 600- or 700-level MATH, OPER, STAT or SYSM courses with the exception of those in the list below. 26
Total Hours57

Students must complete at least nine credit hours at the 700-level. Electives will be determined based on a student’s research interests and in consultation with their advisers and the graduate program director. 


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

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

Applied mathematics electives

Course Title Hours
MATH 610Advanced Linear Algebra3
MATH 615Iterative Numerical Methods3
MATH 632Ordinary Differential Equations I3
MATH 633Partial Differential Equations3
MATH 640Mathematical Biology I3
MATH 715Numerical Solutions for Differential Equations3
MATH 732Ordinary Differential Equations II3
MATH 769Topics in Applied Mathematics: ____3
SYSM 780Stochastic Methods in Mathematical Biology3

Elective exceptions

These courses may not count as electives for this program.

Course Title Hours
MATH 505Modern Geometry3
MATH 592Teaching and Communicating Mathematics1
MATH 593Internship in Mathematical Sciences3,6
MATH 661Number and Operations3
MATH 662Geometry and Measurement3
MATH 663Functions and Algebra3
MATH 664Statistics and Probability3
MATH 665Rational Numbers and Proportional Reasoning3
MATH 667Functions and Algebra II3
MATH 668Modeling With Mathematics3
MATH 690Research Seminar2
MATH 697Directed Research1-3
MATH 698Thesis1-3
OPER 696Applied Project1-3
OPER 697Directed Research1-3
OPER 698Thesis1-3
STAT 508Introduction to Social Statistics3
STAT 543Statistical Methods I3
STAT 608Statistics for Social Research3
STAT 696Applied Project1-3
STAT 697Directed Research1-3
STAT 698Thesis1-3
SYSM 697Systems Research2
SYSM 798Dissertation Research1-12

Angela Reynolds, Ph.D.
Professor, Department of Mathematics and Applied Mathematics, and graduate program director
Phone: (804) 828-6565

Program website: