# Difference between revisions of "Math 425: Mathematical Biology"

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Students should be familiar with the following discrete and continuous models of biological | 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 | 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. | taught in the course to solve problems based on these models. | ||

+ | |||

Basic notions concerning: Subcellular molecular systems. Cellular behavior. Physiological | Basic notions concerning: Subcellular molecular systems. Cellular behavior. Physiological | ||

+ | |||

problems. Population biology. Developmental biology. Mathematical techniques of phase | problems. Population biology. Developmental biology. Mathematical techniques of phase | ||

− | plane analysis, bifurcation theory, scientific computation, difference equations, | + | |

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

+ | |||

and stochastic processes. | and stochastic processes. | ||

Line 44: | Line 49: | ||

Signal transduction: | Signal transduction: | ||

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Menten Michaelis enzyme dynamics | Menten Michaelis enzyme dynamics | ||

+ | |||

Law of mass action | Law of mass action | ||

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Dynamical systems | Dynamical systems | ||

+ | |||

Bifurcation | Bifurcation | ||

Example systems: | Example systems: | ||

+ | |||

Fitzhugh-Nagumo | Fitzhugh-Nagumo | ||

+ | |||

Nerve and heart dynamics | Nerve and heart dynamics | ||

+ | |||

Cell cycle model | Cell cycle model | ||

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cAMP | cAMP | ||

Population models: | Population models: | ||

+ | |||

Continuous predator-prey | Continuous predator-prey | ||

+ | |||

Age structured models | Age structured models | ||

+ | |||

Discrete dynamical systems | Discrete dynamical systems | ||

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Time delayed differential equations | Time delayed differential equations | ||

## Revision as of 17:43, 18 August 2008

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