AMATH 422  |  Schedule  |  Instructors  |  Assistants  |  Content  |  Textbooks  |  References  |  Prerequisites  |  Grading  |  Calendar  |  Notes  |  Homework  
  
     

AMATH 422

Introduction to Mathematical Biology
Fall 2007

Schedule


SLN: 10203
Days: T, Th
Time: 3:30-4:50 pm
Room: Loew Hall 113

Instructors


Name: Mark Kot
Office: 415G Guggenheim Hall
Phone: (206) 543-0908
Fax: (206) 685-1440
Email: kot@amath.washington.edu


Office Hours: M, W, F
3:00-4:00 pm


Name: Hong Qian
Office: 415E Guggenheim Hall
Phone: (206) 543-2584
Fax: (206) 685-1440
Email: qian@amath.washington.edu


Office Hours: M, W
3:00-4:30 pm

Assistants


Name: Justine GunOg Seo
Office: Guggenheim 407
Fax: (206) 685-1440
Email: justine@amath.washington.edu


Office Hours: M, W 2:00-3:00 pm (in Guggenheim 415L)

Content

Course Catalog 





Mathematical biology is an active and fast-growing interdisciplinary field in which mathematical concepts,
techniques, and models are applied to problems in biology and medicine.  Many biological processes can
be described by differential equations and difference equations.  This course introduces students
to the construction and analysis of these models.  We will cover a wide variety of topics including
single-species models, nonlinear dynamics and chaos, (predator-prey and competition) models for
interacting populations, enzyme kinetics, biological oscillators, neural and physiological models (excitability,
testoserone secretion), pharmacokinetics, and models from epidemiology.



  • 
Continuous-time population dynamics

  • 
Population models with age structure

  • 
Discrete-time population dynamics

  • 
Tumour growth and cell proliferation

  • 
Continuous-time interacting population models

  • 
Discrete-time models for interacting populations

  • 
Enzyme kinetics

  • 
Simple oscillatory reactions

  • 
Hodgkin-Huxley theory and neural networks

  • 
Belousov-Zhabotinskii reaction

  • 
Coupled oscillators

  • 
Epidemiology models and dynamic diseases

  • 
Pharmacokinetics and drug action

  • 
Blood flow and dynamics



Textbooks



The course does not require a textbook,



but see the next section for some helpful books in our library.



We will provide lecture notes for many of the course topics.

References






Helpful Reference Books:




  • 
Allen, L. J. S.  (2007)

    
An Introduction to Mathematical Biology 

    
Pearson Prentice Hall, Upper Saddle River, NJ.

    

UW Library Catalog

    


  • 
Brauer, F. and Castillo-Chavez, C.  (2001)

    
Mathematical Models in Population Biology and Epidemiology 

    
Springer, New York, NY.

    

UW Library Catalog

    


  • 
Britton, N. F.  (2005)

    
Essential Mathematical Biology 

    
Springer, London, UK.

    

UW Library Catalog

    


  • 
Edelstein-Keshet, L.  (1988)

    
Mathematical Models in Biology 

    
Random House, New York, NY.

    

UW Library Catalog

    

Edelstein-Keshet, L.  (2005)

    
Mathematical Models in Biology 

    
SIAM, Philadelphia, PA.

    

UW Library Catalog

    


  • 
Fall, C. P., Marland, E., Wagner, J., and Tyson, J.  (2002)

    
Computational Cell Biology 

    
Springer, New York, NY.

    

UW Library Catalog

    


  • 
Hoppensteadt, F. C. and Peskin, C. S.  (2002)

    
Modeling and Simulation in Medicine and the Life Sciences 

    
Springer, New York, NY.

    

UW Library Catalog

    


  • 
Keener, J. and Sneyd, J.  (1998)

    
Mathematical Physiology 

    
Springer, New York, NY.

    

UW Library Catalog

    


  • 
Kot, M.  (2001)

    
Elements of Mathematical Ecology 

    
Cambridge University Press, Cambridge, UK.

    

UW Library Catalog

    


  • 
Mangel, M.  (2006)

    
The Theoretical Biologist's Toolbox: 

    
Quantitative Methods for Ecology and Evolutionary Biology 

    
Cambridge University Press, Cambridge, UK.

    

UW Library Catalog

    


  • 
Mazumdar, J. (1989, 2006)

    
An Introduction to Mathematical Physiology and Biology 

    
Cambridge University Press, Cambridge, UK.

    

UW Library Catalog

    


  • 
Murray, J. D.  2002 (3rd Edition)

    
Mathematical Biology I: An Introduction 

    
Springer, Berlin, Germany

    

UW Library Catalog

    




Prerequisites



You should have had at least one of the following three courses:

  • 
Amath 351

    

Introduction to Differential Equations and Applications

    


  • 
Math 136

    

Honors Accelerated Calculus

    


  • 
Math 307

    

Introduction to Differential Equations



Grading



Your grade will be based on your homework and your final term paper



Your homework accounts for 70% of the final grade.  



A 10-15 page term paper accounts for 30% of your final grade



Homework problems will be assigned on a regular basis and are due one week from the date of assignment.  



Homeworks must be done alone; they are not group projects!

Calendar



Important Dates







September 26
-

Wednesday

-
First Day of Classes
      



November 12
-

Monday

-
Veterans Day (No Class)
      



November 22
-

Thursday

-
Thanksgiving (No Class)
      



November 23
-

Friday

-
Thanksgiving (No Class)
      



December 7
-

Friday

-
Last Day of Lectures
      



December 12
-

Wednesday

-
Term Papers Due
      








Notes



Exponential and logistic growth



Harvest models and bifurcations



Discrete-time models



A classical predator-prey model



To cycle or not to cycle



Simple competition



Chemical kinetics (for lectures 1 and 2)



Enzyme kinetics (for lectures 3 and 4)



Enzyme kinetics (additional reading excerpted from the book: "Chemical Biophysics", Cambridge)



Cellular Signaling Switches



Biochemical Oscillations



Cell Electrophysiology and Hodgkin-Huxley Model



Molecular and Cellular Mechanics

Homework



Homework problems will be assigned on a regular basis and are due one week from the date of assignment.  


Homeworks constitute 70% of the final grade.


Write up your homework alone, not as a group!