BMA 567 Modeling of Biological Systems provides an introduction to quantitative modeling in biology. This stand-alone course emphasizes practical skills, including computer simulation techniques, and is designed to be accessible to a wide range of students. The biological focus of the course will depend on the instructor, so different topics, such as ecology or physiology, will be presented in different semesters.
BMA 771 Biomathematics I focuses on differential and difference equation models in biomathematics. This course examines linear and nonlinear dynamics, and develops techniques that are used to understand the qualitative behavior of mathematical models.
BMA 772 Biomathematics II introduces stochastic models.
Both BMA 771 and BMA 772 can be taken as stand-alone courses. Together they provide an overview of the types of models that are most commonly used in biomathematics. Completion of both BMA 771 and 772 is required for biomath Masters students.
BMA 773 Stochastic Modeling looks in more detail at models that involve randomness, building upon material introduced in BMA 772.
BMA 774 Partial Differential Equation Modeling in Biology develops approaches that can be used to study a wide range of biological systems, including spatially distributed systems, solid and fluid systems. This course builds upon the PDE component of BMA 772.
Together, the four semester sequence BMA 771, 772, 773 and 774 gives a wide-ranging survey of the models and techniques that are used in biomathematics and conveys the breadth of the area of research that is biomathematics. Doctoral students in the biomath program would typically complete all four of these courses.
BMA 801 Biomathematics Graduate Seminar involves student and faculty presentations. These seminars illustrate the wide range of biological problems that can be illuminated by mathematical and statistical approaches. The seminars are also intended to provide an opportunity to improve presentation skills.
Other BMA Courses
BMA 815B Mathematical Modeling of Infectious Diseases introduces disease modeling from a population biology viewpoint. This course uses a variety of deterministic and stochastic models, as introduced in BMA 771 and 772, to explore the transmission dynamics of infectious disease. (This course is not offered every year.)
Complete Course Catalog
Please note that the TRACS information about some of our courses is outdated. The information that appears above is more reliable, and if there is any question over course content or prerequisites, please contact the course instructor.
- TRACS listing of Fall semester BMA courses
- TRACS listing of Spring semester BMA courses
- Registration & Records listing of BMA courses
Abbreviations used for cross-listed courses are as follows: MA – Mathematics, OR – Operations Research, and ST – Statistics. An example of credit information is: 4(3-2). The 4 indicates the number of semester hours credit awarded for successful completion of the course. The (3-2) indicates that the course normally meets for three hours of lecture and two hours of problem session per week. The abbreviations F, S, and Sum indicate courses normally offered in the fall and spring semester and in the summer terms, respectively.
BMA 567 Modeling of Biological Systems.
Prereq: 1 semester of calculus (e.g., MA 112) 4(3-2) F. An introduction to quantitative modeling in biology. Compartment models, Forrester diagrams, probabilistic and deterministic descriptions of dynamic processes, development of model equations, simulation methods, criteria for model evaluation. Readings from current literature on applications of modeling and simulation in biology. Laboratory sessions emphasize the scientific computing skills used in biological modeling. An individual modeling project, preferably related to the student’s research interests, is required.
BMA 610 Special Topics.
Offered from time to time during Fall or Spring semesters.
BMA (ST, MA) 771 Biomathematics I.
Preq.: Advanced calculus (including matrix algebra) and reasonable background in biology, or consent of the Instructor. 3(3-0)F. Mathematical methods for dynamic state variable models in biomathematics, especially difference and differential equations, with applications including models for population dynamics, pattern formation, and enzyme kinetics. Emphasis is placed on determining the qualitative behavior of solutions rather than on explicit solutions or numerical computation.
BMA (ST,MA) 772 Biomathematics II.
Prereq.: BMA 771, elementary probability theory. 3(3-0)S. Continuation of BMA 771. Methods for analyzing nonlinear models, concepts of local and global stability, periodic and non-periodic solutions. Comparison of deterministic and stochastic models. Survey of applications and some discussion of recent research.
BMA (ST,OR,MA) 773 Stochastic Modeling.
Prereq.: BMA 772 or ST 746. 3(3-0) F. Survey of modeling approaches and analysis methods for data from continuous state random processes. Emphasis on differential and difference equations with noisy input. Doob-Meyer decomposition of process into signal and noise components. Examples from biological and physical sciences, and engineering. A student project is required. (Offered F 2000 and alt. years.)
BMA (MA,OR) 774 Partial Differential Equation Modeling in Biology.
Prereq.: BMA 771 or MA/OR 731; BMA 772 or MA 401 or MA 501 3(3-0)S. Modeling with and analysis of partial differential equations as applied to real problems in biology. Review of diffusion and conservation laws. Waves and pattern formation. Chemotaxis and other forms of cell and organism movement. Introduction to solid and fluid mechanics/dynamics. Introductory numerical methods. Scaling. Perturbations, Asymptotics, Cartesian, polar and spherical geometries. Case studies.
BMA 801 Biomathematics Graduate Seminar.
Prereq.: Grad standing 1(1-0) F, S. Student and faculty presentations of current research in biomathematics. Purposes are to broaden perspective on the field of biomathematics and research opportunities, and to give students practice in seminar presentation. Students make one presentation per year. For Ph.D. candidates, two of these presentations must concern thesis research, one near the start of the work, and the other near the completion of the thesis. Attendance is required.
BMA 815 Advanced Special Topics.
Offered from time to time in the Fall and Spring semesters.
BMA 893 Research.
Consent of instructor 1-3 F,S, Sum.