BMA - Biomathematics


BMA (BIO) 560Population EcologyUNITS: 3 - Offered in Spring Only, Offered Alternate Odd Years
Co-requisite: ST 511
Dynamics of natural populations. Current work, theories and problems dealing with population growth, fluctuation, limitation and patterns of dispersion, species interactions, community structure and ecological genetics. One semester of calculus and a junior/senior level ecology course are required.


BMA 567Modeling of Biological SystemsUNITS: 4 - Offered Alternate Years
Prerequisite: MA 131
An introduction to quantitative modeling in biology. Use of Forrester diagrams, probabilistic and deterministic description of dynamic processes, development of model equations, simulation methods and criteria for model evaluation. Examination of current literature dealing with application of models and simulation in biology. Individual and class modeling projects.


BMA (MA) 573Mathematical Modeling of Physical and Biological Processes IUNITS: 3 - Offered in Fall Only
Prerequisite: MA 341 and knowledge of high-level programming language.
Introduction to model development for physical and biological applications. Mathematical and statistical aspects of parameter estimation. Compartmental analysis and conservation laws, heat transfer, and population and disease models. Analytic and numerical solution techniques and experimental validation of models. Knowledge of high-level programming languages required.


BMA (MA) 574Mathematical Modeling of Physical and Biological Processes IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA/BMA 573
Model development, using Newtonian and Hamiltonian principles, for acoustic and fluid applications, and structural systems including membranes, rods, beams, and shells. Fundamental aspects of electromagnetic theory. Analytic and numerical solution techniques and experimental validation of models.


BMA 590Special TopicsUNITS: 1-3 - Offered in Fall Spring Summer
Special topics in BMA.


BMA 591Special Topics - Offered in Fall Spring Summer
Directed readings, problem sets, written and oral reports as dictated by need and interest of student, e.g., cellular, molecular and physiological modeling; new 500-level courses during the developmental phase.


BMA 610Special TopicsUNITS: 1-3 - Offered in Fall Spring Summer
Directed readings, problem sets, written and oral reports as dictated by need and interest of student, e.g., cellular, molecular and physiological modeling; new 500-level courses during the developmental phase.


BMA 685Master's Supervised TeachingUNITS: 1-3 - Offered in Fall Spring Summer
Prerequisite: Master's student
Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.


BMA 688Non-Thesis Masters Continuous Registration - Half Time RegistrationUNITS: 1 - Offered in Fall Spring Summer
Prerequisite: Master's student
For students in non-thesis master's programs who have completed all credit hour requirements for their degree but need to maintain half-time continuous registration to complete incomplete grades, projects, final master's exam, etc.


BMA 689Non-Thesis Master Continuous Registration - Full Time RegistrationUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: Master's student
For students in non-thesis master's programs who have completed all credit hour requirements for their degree but need to maintain full-time continuous registration to complete incomplete grades, projects, final master's exam, etc. Students may register for this course a maximum of one semester.


BMA 690Master's ExaminationUNITS: 1-5 - Offered in Fall and Spring
Prerequisite: Master's student
For students in non thesis master's programs who have completed all other requirements of the degree except preparing for and taking the final master's exam.


BMA 693Master's Supervised ResearchUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Master's student
Instruction in research and research under the mentorship of a member of the Graduate Faculty.


BMA 695Master's Thesis ResearchUNITS: 1-9 - Offered in Fall and Spring
Prerequisite: Master's student
Thesis research.


BMA 696Summer Thesis ResearchUNITS: 1 - Offered in Summer
Prerequisite: Master's student
For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.


BMA 699Master's Thesis PreparationUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Master's student
For students who have completed all credit hour requirements and full-time enrollment for the master's degree and are writing and defending their theses.


BMA (MA) (ST) 771Biomathematics IUNITS: 3 - Offered in Fall Only
Prerequisite: Advanced calculus, reasonable background in biology
Role of theory construction and model building in development of experimental science. Historical development of mathematical theories and models for growth of one-species populations (logistic and off-shoots), including considerations of age distributions (matrix models, Leslie and Lopez; continuous theory, renewal equation). Some of the more elementary theories on the growth of organisms (von Bertalanffy and others; allometric theories; cultures grown in a chemostat). Mathematical theories oftwo and more species systems (predator-prey, competition, symbosis; leading up to present-day research) and discussion of some similar models for chemical kinetics. Much emphasis on scrutiny of biological concepts as well as of mathematical structureof models in order to uncover both weak and strong points of models discussed. Mathematical treatment of differential equations in models stressing qualitative and graphical aspects, as well as certain aspects of discretization. Difference equation models.


BMA (MA) (ST) 772Biomathematics IIUNITS: 3 - Offered in Spring Only
Prerequisite: BMA 771, elementary probability theory
Continuation of topics of BMA 771. Some more advanced mathematical techniques concerning nonlinear differential equations of types encountered in BMA 771: several concepts of stability, asymptotic directions, Liapunov functions; different time-scales. Comparison of deterministic and stochastic models for several biological problems including birth and death processes. Discussion of various other applications of mathematics to biology, some recent research.


BMA (MA) (OR) (ST) 773Stochastic ModelingUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: BMA 772 or ST (MA) 746
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 its signal and noise components. Examples from biological and physical sciences, and engineering. Student project.


BMA (MA) (OR) 774Partial Differential Equation Modeling in BiologyUNITS: 3 - Offered in Spring Only
Prerequisite: BMA 771 or MA/OR 731; BMA 772 or MA 401 or MA 501
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 790Special Topics


BMA 801SeminarUNITS: 1 - Offered in Fall and Spring
Prerequisite: Graduate standing
Graduate students in biomathematics are expected to attend through most of their residence period.


BMA 815Advanced Special TopicsUNITS: 1-3 - Offered in Fall Spring Summer
Directed readings, problem sets, written and oral reports as dictated by need and interest of student; new 600-level courses during the development phase (currently includes courses in stochastic modeling and biophysical theory).


BMA 885Doctoral Supervised TeachingUNITS: 1-3 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.


BMA 890Doctoral Preliminary ExamUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
For students who are preparing for and taking written and/or oral preliminary exams.


BMA 893Doctoral Supervised ResearchUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
Instruction in research and research under the mentorship of a member of the Graduate Faculty.


BMA 895Doctoral Dissertation ResearchUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
Dissertation research


BMA 896Summer Dissertation ResearchUNITS: 1 - Offered in Summer
Prerequisite: Doctoral student
For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.


BMA 899Doctoral Dissertation PreparationUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
For students who have completed all credit hours, full-time enrollment, preliminary examination, and residency requirements for the doctoral degree, and are writing and defending their dissertations.