Math 425: Mathematical Biology

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Math 425


Title

Mathematical Biology.


(Credit Hours: Lecture Hours: Lab Hours)

(3:3:0)


Prerequisite

112


Description

How tools in mathematics can help biologists. How questions in biology can motivate new mathematics.


Desired Learning Outcomes

Students should gain a familiarity with how the disciplines of mathematics and biology can complement each other.

Prerequisites

A knowledge of calculus (and the mathematical maturity that having passed M112 entails) shoud suffice.

Minimal learning outcomes

Students should be familiar with the following discrete and continuous models of biological

phenomena. They should know the technical terms, and be able to implement the procedures
taught in the course to solve problems based on these models.


Basic notions concerning: Subcellular molecular systems. Cellular behavior. Physiological
problems. Population biology. Developmental biology. Mathematical techniques of phase 

plane analysis, bifurcation theory, scientific computation, difference equations,

and stochastic processes.

Topics that will be covered within this program include

Signal transduction:

  Menten Michaelis enzyme dynamics
  Law of mass action
  Dynamical systems
  Bifurcation

Example systems:

  Fitzhugh-Nagumo
  Nerve and heart dynamics
  Cell cycle model
  cAMP

Population models:

  Continuous predator-prey
  Age structured models
  Discrete dynamical systems
  Time delayed differential equations

Stochastic models.


Additional Topics

These are at the discretion of the instructor as time allows.


Courses for which this course is prerequisite

None.


Discrete and continuous models of biological phenomena will be introduced including subcellular molecular systems, cellular behaviour, physiological problems