Spring Semester 2009

It is widely anticipated that Biology and Medicine will be the premier sciences of the 21st century. The complexities of the biological sciences make interdisciplinary involvement essential and the increasing use of mathematics in biology is inevitable as biology becomes more quantitative. In 1905, Charles Darwin wrote that people with an understanding "of the great leading principles of mathematics seem to have an extra sense."

Why is Mathematical Models in Biology relevant now?

2003 - NATURE published an article entitled "Mathematical Oncology: Cancer Summed Up" where the authors stated, "understanding the complex, non-linear systems in cancer biology will require ongoing interdisciplinary, interactive research in which mathematical models, informed by extant data and continuously revised by new information, guide experimental design and interpretation."

- 2004, mathematician wrote a paper (good reading!) claiming "Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better."

- September 8th, 2008, Dr. Doron Levy, an Associate Professor of Mathematics at the University of Maryland - College Park and at the Center for Scientific Computation and Mathematical Modeling addressed the U.S. Congress on "Can Mathematics Cure Leukemia?"

In MTH 265, mathematical models that suggest possible mechanisms that may underlie specific biological processes are developed and analyzed. We will investigate how these models can be used to predict what may follow under currently untested conditions. By the end of this course students will be able to derive, interpret, solve, understand, discuss, and critique deterministic and stochastic models of biological systems.

MTH 265 is a 4 credit course covering the following topics

 I. Discrete Models
      A. Linear and nonlinear difference equations
             1.  Population models, drug concentration, and other applications
      B.  System of difference equations
             1.  Introduction to linear algebra
      C.  Equilibrium, stability and the qualitative behavior of solutions
II. Continuous Models
      A.  Introduction to first and second order ordinary differential equations
      B.  Steady-state solutions, stability and linearization.
      C.  Phase-plane methods and qualitative solutions.
III. Probabilistic and Stochastic Models
      A.  Quantitative genetics
      B.  Independence and Markov chains.
      C.  Random variables and inferential statistics.
      D.  Probability distributions

Check back later in the Fall for a syllabus and more information.