Biomathematics

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Biomathematics is an interdisciplinary graduate program offering courses and research opportunities in basic and applied mathematical biology. Degree programs are flexible to accommodate students with backgrounds in the biological, mathematical or physical sciences. The program also offers Ph.D. and master's-level minors.

Admission Requirements

Applicants should have either a Bachelor's degree in biology with evidence of aptitude and interest in mathematics, or a bachelor's in a mathematical science with evidence of aptitude and interest in biology. Advanced (multivariate) calculus, linear algebra and general biology are prerequisites for all BMA courses, and deficiencies in these should be remedied during the first year of graduate study. The application must include a narrative statement (1-2 pages) of the applicant's goals and reasons for interest in the BMA program.

Master's Degree Requirements

The M.S. and M.BMA. degrees require BMA 771-BMA 772 and one other BMA course; two upper-level biology courses; and three courses from the mathematical sciences or statistical sciences. The M.S. degree requires a thesis, and the M.BMA. requires two additional courses and a written project.

Doctoral Degree Requirements

Course requirements consist of a "core" and a "concentration" in some area of biology or mathematical sciences. Core requirements are: BMA 771-BMA 772, BMA 773 and BMA 774; three upper-level biology courses from at least two areas (e.g., physiology and evolution); and additional courses from the mathematical or statistical sciences. Concentration consists of either a Ph.D. co-major in a biological or mathematical science or a coherent series of five graduate courses approved by the student's committee, which must include a two-semester sequence and at least one 700-level course.

Financial Assistance

TAs (generally in the Departments of Mathematics or Statistics). RAs and internships are available. Awards are based on GRE scores, transcripts, letters of recommendation, and the personal statement. RAs usually are held by continuing students. To receive full consideration for financial aid, the completed application must be received by January 15.

Other Relevant Information

All students are required to participate in the BMA Graduate Seminar. Course requirements can be met by examination or by demonstrating that an equivalent course was completed at another university.

Faculty

Full Professors

  • Kevin Gross
  • Mansoor Abbas Haider
  • Carol K. Hall
  • Jason M. Haugh
  • George R. Hess
  • Alun L. Lloyd
  • Sharon R. Lubkin
  • Spencer V. Muse
  • Mette Olufsen
  • Brian J. Reich
  • Seth M. Sullivant
  • Jeffrey L. Thorne
  • Hien Trong Tran
  • Zhaobang Zeng

Associate Professors

  • Randall Brian Langerhans
  • Cristina Lanzas
  • Charles Eugene Smith
  • Rosangela Sozzani

Assistant Professors

  • Belinda Sena Akpa
  • Kevin Bryant Flores
  • David Alan Rasmussen

Emeritus Faculty

  • William Reid Atchley
  • John William Bishir
  • Marlene L. Hauck
  • Gail G. McRae
  • Kenneth Hugh Pollock
  • Jim E. Riviere
  • Henry E. Schaffer
  • James Francis Selgrade
  • Ronald Edwin Stinner

Adjunct Faculty

  • John Edward Banks
  • Georgiy Bobashev
  • Brian Ernest Carlson
  • James W. Gilliam
  • Nicholas M. Haddad
  • Thomas D. Husmeier
  • Julia S. Kimbell
  • W. Owen McMillan III
  • Suzanne Marie Lenhart
  • Johnny T. Ottesen
  • Eric A. Stone

Courses

BMA 560/BIO 560  Population Ecology  (3 credit hours)  

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.

Co-requisite: ST 511

Typically offered in Spring only

BMA 567  Modeling of Biological Systems  (4 credit hours)  

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.

Prerequisite: MA 131

BMA 573/MA 573  Mathematical Modeling of Physical and Biological Processes I  (3 credit hours)  

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.

Prerequisite: MA 341 and knowledge of high-level programming language.

Typically offered in Fall only

BMA 574/MA 574  Mathematical Modeling of Physical and Biological Processes II  (3 credit hours)  

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.

Prerequisite: MA/BMA 573

Typically offered in Spring only

BMA 590  Special Topics  (1-6 credit hours)  

Special topics in BMA.

Typically offered in Fall, Spring, and Summer

BMA 591  Special Topics  (1-6 credit hours)  

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.

Typically offered in Fall, Spring, and Summer

BMA 610  Special Topics  (1-6 credit hours)  

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.

Typically offered in Fall, Spring, and Summer

BMA 685  Master's Supervised Teaching  (1-3 credit hours)  

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.

Prerequisite: Master's student

Typically offered in Fall, Spring, and Summer

BMA 690  Master's Examination  (1-9 credit hours)  

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.

Prerequisite: Master's student

Typically offered in Fall and Spring

BMA 693  Master's Supervised Research  (1-9 credit hours)  

Instruction in research and research under the mentorship of a member of the Graduate Faculty.

Prerequisite: Master's student

Typically offered in Fall, Spring, and Summer

BMA 695  Master's Thesis Research  (1-9 credit hours)  

Thesis research.

Prerequisite: Master's student

Typically offered in Fall and Spring

BMA 696  Summer Thesis Research  (1 credit hours)  

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.

Prerequisite: Master's student

Typically offered in Summer only

BMA 699  Master's Thesis Preparation  (1-9 credit hours)  

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.

Prerequisite: Master's student

Typically offered in Fall, Spring, and Summer

BMA 771/MA 771/ST 771  Biomathematics I  (3 credit hours)  

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.

Prerequisite: Advanced calculus, reasonable background in biology

Typically offered in Fall only

BMA 772/MA 772/ST 772  Biomathematics II  (3 credit hours)  

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.

Prerequisite: BMA 771, elementary probability theory

Typically offered in Spring only

BMA 773/MA 773/OR 773/ST 773  Stochastic Modeling  (3 credit hours)  

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.

Prerequisite: BMA 772 or ST (MA) 746

Typically offered in Spring only

BMA 774/OR 774/MA 774  Partial Differential Equation Modeling in Biology  (3 credit hours)  

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.

Prerequisite: BMA 771 or MA/OR 731; BMA 772 or MA 401 or MA 501

Typically offered in Spring only

BMA 790  Special Topics  (1-6 credit hours)  
BMA 801  Seminar  (1 credit hours)  

Graduate students in biomathematics are expected to attend through most of their residence period.

Prerequisite: Graduate standing

Typically offered in Fall and Spring

BMA 815  Advanced Special Topics  (1-6 credit hours)  

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).

Typically offered in Fall, Spring, and Summer

BMA 885  Doctoral Supervised Teaching  (1-3 credit hours)  

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.

Prerequisite: Doctoral student

Typically offered in Fall, Spring, and Summer

BMA 890  Doctoral Preliminary Exam  (1-9 credit hours)  

For students who are preparing for and taking written and/or oral preliminary exams.

Prerequisite: Doctoral student

Typically offered in Fall, Spring, and Summer

BMA 893  Doctoral Supervised Research  (1-9 credit hours)  

Instruction in research and research under the mentorship of a member of the Graduate Faculty.

Prerequisite: Doctoral student

Typically offered in Fall, Spring, and Summer

BMA 895  Doctoral Dissertation Research  (1-9 credit hours)  

Dissertation research

Prerequisite: Doctoral student

Typically offered in Fall and Spring

BMA 896  Summer Dissertation Research  (1 credit hours)  

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.

Prerequisite: Doctoral student

Typically offered in Summer only

BMA 899  Doctoral Dissertation Preparation  (1-9 credit hours)  

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.

Prerequisite: Doctoral student

Typically offered in Fall, Spring, and Summer