Applications of Mathematics to Biological Problems

Target audience:

This is a sophomore level course meeting a mathematics or a biology distribution requirement for the B.A. The course is cross listed so that mathematics majors can take it for biology credit and biology majors for mathematics credit. The course is also of interest to secondary education science majors and computer science majors.

Prerequisites:

• Intermediate Algebra (or equivalent)
• Introductory Biology

Mathematics Topics - Biology Applications:

• Logistic Equations
  • Evolution - population growth
  • Ecology - competition
• Matrix Algebra
  • Ecology - age-dependent structure
• Conditional Probability, Probability Generating Functions
  • Evolution - Hardy-Weinberg and fixation of alleles
• Linear Differential Equations
  • Ecology - population growth
  • Biochemistry - rates of reactions, enzyme kinetics
  • Human Biology - pharmacokinetics
• Nonlinear Equations
  • Ecology - predator-prey, Lotka-Volterra equations
  • Human Biology - spread of infectious disease, oscillation cycles in heart beats
• Probability
  • Evolution, - random walks
• Game Theory
  • Evolution - evolutionary stable strategies, evolution of cooperation (prisoners' dilemma)

Structure of a Course Unit

The above units are separate modules. MATLAB is used to model some of the biological systems.
With each unit, the student

• Is introduced to a biological problem;
• Visualizes the problem, usually graphically, often through discovery;
• Examines similar problems and their solutions, some in the biology literature;
• Learns about the mathematical principles and concepts behind the example;
• Works with others to solve the initial problem;
• Works with others to solve similar problems with different variables. Some of these problems are student selected.

Sample Unit

• Predator-Prey