Math 570

Mathematical
Biology
 

Winter 2012
Tue, Thur, 12:30-1:50 PM

CAB 563

Lizard








Contents:

  • Predator prey models and review of dynamical systems methods
  • Parameter estimation
  • Biochemical reaction kinetics
  • Sojourn time analysis and structured population models
  • Modelling of cancer growth and treatment
  • Reaction diffusion equations
  • Chemotaxis
  • Transport equations
  • Applications to Ecology, Epidemiology, Cancer, Brain Tumors, Wolf movement, Cell Movement

Grading:

Research Project:
Each student will be given a research project to work on during the entire term.
  1. The first homework is to find a good research project for this term. Please hand in a written 2-page description of your planned project by Jan 24, 2012 in class.
  2. (Midterm 30%) On Feb 16, 2012 your research proposal is due. Please give a short 10-15 minute presentation and a 3-4 page research proposal. Your proposal should include the sections: Title, Abstract, Background, Purpose of the Research Project, Methods and Proposed Approach, Time Plan. Assume that I am a granting agency and try to convince me that I should invest lots of money into your project. 
  3. (Final 50%) on April 5, in class: each student will hand in a written documentation (about 6 -10 pages) of his/her project work in LaTeX and give a 30 minute presentation. The presentations are on April 5, 10, 12 in class; the order of presentation is selected randomly.  I will disucss in class if we want to have the final presentations in a retreat over the weekend.
  4. (Homework assignments 20 %) There will be five homework assignments of equal weight.  They are due on Jan 24, Feb 07, Mar 01, Mar 15, Mar 29 at the beginning of class. Late assignments will not be accepted.
Students with a total percentage of more than 85% will obtain A- or better. The passing grade for a graduate class is a C+, which is guaranteed with an overall performance of at least 65%.  

 

Tentative schedule:

Dr. T. Hillen
Mathematical and Statistical Sciences
University of Alberta
CAB 575
2-3395
thillen@ualberta.ca


Office hours: Tuesday and Wednesday 3:30-4:30 PM in CAB 575. Further appointments can be made as needed. 

Webpage:

www.math.ualberta.ca/~thillen/winter12/math570.html

Textbook(s): (no textbooks are required)
  •  Britton, Essential Mathematical Biology, Springer, 2003
  • Cantrell and Cosner, Spatial Ecology via Reaction-Diffusion Equations, Wiley,  
  • de Vries, Hillen, Lewis, Müller, Schönfisch A Course In Mathematical Biology, SIAM, 2006.
  • Murray I and II, Mathematical Biology, Springer 2003.
  • Thieme, Mathematics in Population Biology, Princeton Univ. Press, 2003
  • See a reference list of textbooks at the end of de Vries et al.
Assignments:

Assignment 1
Jan 24, 2012
                            
Assignment 2,
Feb 07, 2012

Assignment 3
March 01, 2012
Midterm info
Assignment 4,
March 15, 2012

Assignment 5,
March 29, 2012
Final info:


Academic integrity:


The University of Alberta is committed to the highest standards of academic integrity and honesty.  Students are expected to be familiar with these standards regarding academic honesty and to uphold the policies of the University in this respect.  Students are particularly urged to familiarize themselves with the provisions of the Code of Student Behaviour (online at http://www.ualberta.ca/secretariat/appeals.htm) and avoid any behaviour which could potentially result in suspicions of cheating, plagiarism, misrepresentation of facts and/or participation in an offence.  Academic dishonesty is a serious offence and can result in suspension or expulsion from the University.

Policy about course outlines can be found in section 23.4(2) of the University Calendar.

Date
milestones    
Topic of the day                       
Notes from Winter 2006
Jan 10

Introduction, course outline; predator prey models
12

predator prey models

17

Parameter estimation
19

Biochemical reaction kinetics
24
Assignment 1 due Biochemical reaction kinetics
26

Structured population dynamics
31

Structured population dynamics and delay equations
Feb 2

Renewal Theorem
7
Assignment 2 due Cancer Modelling
Radiation treatment
9

Tumor Control Probability
14

Tumor Control Probability
16
Research proposal due
Midterm in class

21
no class
Reading week

23
no class
Reading week

28

Reaction-Diffusion Equations
  • Derivation [ sec. 4.3.1 in de Vries et al]
  • Fundamental Solution [sec. 4.3.2 in de Vries et al]
  • Critical Domain Size Problem [sec. 4.3.3 in de Vries et al]
  • Using the Hamiltonian to calculate l*
Mar 1
Assignment 3 due Travelling waves, Epidemic waves

6

Pattern Formation
8

Chemotaxis
13

Chemotaxis, Regularizations
Chaotic patterns
15
Assignment 4 due
Transport equations
20

Perron-Frobenius and Krein-Rutmann

22

Parabolic limits

27

Anisotropic diffusion

29
Assignment 5 due
Scaling limits

April 3

Scaling limits

5

Application to brain tumors and wolf movement
10
Final report due student presentations

12

student presentations