# Math 425: Mathematical Biology

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.

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