Difference between revisions of "Math 425: Mathematical Biology"

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Math 425
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== Catalog Information ==
 
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Title 
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 +
=== Title === 
 
Mathematical Biology.
 
Mathematical Biology.
  
 
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=== (Credit Hours:Lecture Hours:Lab Hours) ===
(Credit Hours: Lecture Hours: Lab Hours)
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+
 
(3:3:0)
 
(3:3:0)
  
 +
=== Offered ===
 +
W (odd years)
  
Prerequisite
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=== Prerequisite ===
 +
[[Math 334]].
  
112
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=== Description ===
 +
Using tools in mathematics to help biologists.  Motivating new mathematics with questions in biology.
  
 +
== Desired Learning Outcomes ==
  
Description
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Students should gain a familiarity with how the disciplines of mathematics and biology can complement each other.
  
How tools in mathematics can help biologists. How questions in biology can motivate new mathematics.
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=== Prerequisites ===
  
 +
A knowledge of calculus (and the mathematical maturity that having passed [[Math 112]] entails) should suffice.
  
Desired Learning Outcomes
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=== Minimal learning outcomes ===
  
Students should gain a familiarity with how the disciplines of mathematics and biology can complement each other.
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Students should become familiar with 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. Possible topics include:
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<div style="-moz-column-count:2; column-count:2;">
  
Prerequisites
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# Signal Transduction
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#* Menten Michaelis enzyme dynamics
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#* Law of mass action
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#* Dynamical systems
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#* Bifurcation
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# Example systems
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#* Fitzhugh-Nagumo
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#* Nerve and heart dynamics
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#* Cell cycle model
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#* cAMP
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# Population models
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#* Continuous predator-prey
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#* Age structured models
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#* Discrete dynamical systems
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#* Time delayed differential equations
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#* Stochastic models
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</div>
  
A knowledge of calculus (and the mathematical maturity that having passed M112 entails) shoud suffice.
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=== Textbooks ===
  
Minimal learning outcomes
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Possible textbooks for this course include (but are not limited to):
  
Students should be familiar with the following discrete and continuous models of biological
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* A Course in Mathematical Biology.  Quantitative Modeling with Mathematical and Computational Methods. By Gerda de Vries, Thomas Hillen, Mark Lewis, Johannes Muller, Birgitt Schonfisch
  
phenomena. They should know the technical terms, and be able to implement the procedures
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=== Additional Topics ===
taught in the course to solve problems based on these models.
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+
 
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Basic notions concerning: Subcellular molecular systems. Cellular behavior. Physiological
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problems. Population biology. Developmental biology. Mathematical techniques of phase
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plane analysis, bifurcation theory, scientific computation, difference equations,
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and stochastic processes.
+
 
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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.
 
These are at the discretion of the instructor as time allows.
  
  
Courses for which this course is prerequisite
+
=== Courses for which this course is prerequisite ===
  
 
None.
 
None.
 
 
Discrete and continuous models of biological phenomena will be introduced including subcellular molecular systems, cellular behaviour, physiological problems
 
  
 
[[Category:Courses|425]]
 
[[Category:Courses|425]]

Latest revision as of 09:51, 14 November 2019

Catalog Information

Title

Mathematical Biology.

(Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

Offered

W (odd years)

Prerequisite

Math 334.

Description

Using tools in mathematics to help biologists. Motivating new mathematics with questions in biology.

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 Math 112 entails) should suffice.

Minimal learning outcomes

Students should become familiar with 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. Possible topics include:

  1. Signal Transduction
    • Menten Michaelis enzyme dynamics
    • Law of mass action
    • Dynamical systems
    • Bifurcation
  2. Example systems
    • Fitzhugh-Nagumo
    • Nerve and heart dynamics
    • Cell cycle model
    • cAMP
  3. Population models
    • Continuous predator-prey
    • Age structured models
    • Discrete dynamical systems
    • Time delayed differential equations
    • Stochastic models

Textbooks

Possible textbooks for this course include (but are not limited to):

  • A Course in Mathematical Biology. Quantitative Modeling with Mathematical and Computational Methods. By Gerda de Vries, Thomas Hillen, Mark Lewis, Johannes Muller, Birgitt Schonfisch

Additional Topics

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


Courses for which this course is prerequisite

None.