Math 345 Schedule (subject to change)

Date

Sections

Lecture notes

Homework

Other readings
Programs
Homework solution

8/28(R)

1.1-1.4
Lecture1

W&M BioMath
Fibonacci sequence
Fibonacci and Golden section
malthus.m
fibonacci.m
plant.m

9/2(T)
1.5-1.8
Lecture2 Homework 1 (due 9/5) :
page 29 (2b,2e,6d,9c,10,15,17)

matrixcalculation.m  graphing.m Homework 1 solution

9/4(R)

1.2-1.10
Lecture3
Leslie paper (1945)
paper on loggerhead

loggerhead.m loggerhead_1.m
loggerhead_2.m loggerhead_3.m

9/9(T)

2.1-2.2
Lecture4 Homework 2 (due 9/12):
click the link for pdf file

bellows.m  cobweb_bellows.m
Homework 2 solution
HW2 programs
HW2 simulations
HW2 extra credit problem

9/11(R)

2.3-2.4
Lecture5



9/16(T)

2.5-2.8
Lecture6 Homework 3 (due 9/19)
Logistic map May (1976)
bifurcation_logistic_model.m
bifurcation_bellows_model.m
Homework 3 solution
HW3 simulations

9/18(R)

3.1-3.6
Lecture7




9/23(T)

4.1-4.3
Lecture8
Dimension Analysis
Homework 4 (due 9/26)
Heinz von Foerster
Dimension analysis

Homework 4 solution

9/25(R)

4.4-4.6
Lecture9 project guide

bifurcation_ricker.m
ricker.m

9/30(T)

4.7-4.10
Lecture10 Homework 5 (due 10/3)

dfield8.m pplane8.m
Homework 5 solution
HW5 simulations

10/2(R)

5.1-5.8
Lecture11



10/7(T)

6.1-6.2
Lecture12 Homework 6 (due 10/10)

Lotka Volterra
Homework 6 solution
HW6 simulations

10/9(R)

6.3-6.4
Lecture13



10/14(T)

Fall Break

no class






Date
Sections
Lecture notes
Homework
Other readings
Programs
Homework solution

10/16(R)

6.6
Lecture14




10/21(T)

8.3, 8.6
Lecture15
Exam 1 (due 10/27)

Exam 1 solution

10/23(R)

exam 1 (take home)
Lecture16 (summarizing 12-15)

competition, mutualism


10/28(T)

6.6
Lecture17
Homework 7 (due 11/3)
infectious disease
epidemic pandemic
epidemic models
sir.m
predatorprey.m
hopf.m
Homework 7 solution
HW7 simulation

10/30(R)

6.6
Lecture18

R0  e is for Ebola
How memes go viral
Math of zombies
Spread of epidemic disease on networks


11/4(T)

7.1-7.5, 8.8
Lecture19
Lecture19a
Homework 8 (due 11/10)
Enzyme rate equation
autocatalytic reaction
sigmoid function Hill function

Homework 8 solution

11/6(R)

8.1-8.2, 8.5
Lecture20

action potential(1)
action potential (2)
Hodgkin–Huxley model
FitzHugh-Nagumo model
Morris-Lecar model
oscillating chemical reaction (video)


11/11(T)

9.1-9.5
Lecture21
Lecture21a
Homework 9 (due 11/17)
Diffusion Molecular diffusion 
diffusion coefficient
random walk 
Brownian motion Binomial distribution   
Normal Distribution
Einstein 1905 (Brownian)
How sneeze particles travel inside an airplane (video)
Molecular diffusion (video)
random walk 
random walk 2d
random walk 3d
Brownian motion
Binomial dis
Normal dis
heat eq 1
heat eq 2
Homework 9 solution
trinomial coefficients

11/13(R)

10.5-10.6
Lecture22

Invasive species
Fisher's equation


11/18(T)

6.4, 9.8
Lecture23
Lorenz Equation analysis
Eigenvalue of u''
Homework 10 (due 11/24)
Routh–Hurwitz stability criterion


Homework 10 solution

11/20(R)

11.4-11.7
Lecture24
animal coat
Exam 2
Alan Turing pattern formation
Gierer-Meinhardt model
The Imitation Game (trailer) (video)
pattern formation (video) more
Gierer-Meinhardt model spot (video)
Gierer-Meinhardt labyrinth (video)


11/25(T)

presentation
Kajsa, Dan, Evan,Yiqing, Kristina, Alton











11/27(R)
Thanksgiving

Thanksgiving



12/2(T)

presentation
Avery, Jeffrey, Ben, Nicolas,
Arjun, Margaret, Marshall, Rachel




12/4(R)

presentation
Niraj, Will, Meaghan, Hanzhang, Ashley,  Teresa, Yilin, Alex




12/12(F)



Exam 2 (due 12/12)




12/16(T)


project paper (due 12/16)




Project Abstracts

General Articles in Mathematical biology

Modeling of Biological Systems, A Workshop at the National Science Foundation in 1996

Mathematics, Biology, and Physics: Interactions and Interdependence  Michael C. Mackey and Moisés Santillán, Notices of American Mathematical Society, Sept, 2005.

Why Is Mathematical Biology So Hard?  Michael C. Reed, Notices of American Mathematical Society, March, 2004.

Uses and Abuses of Mathematics in Biology  Robert M. May, Science,  February 6, 2004.
A webpage about Brahe, Kepler and Newton's story

Mathematical Challenges from Genomics and Molecular Biology Richard M. Karp, Notices of American Mathematical Society, May, 2002.

Mathematical Challenges in Spatial Ecology Claudia Neuhauser, Notices of American Mathematical Society, Dec. 2001.

Linking Mind to Brain: The Mathematics of Biological Intelligence  Stephen Grossberg, Notices of American Mathematical Society, Dec. 2000.

We Got Rhythm: Dynamical Systems of the Nervous System Nancy Kopell, Notices of American Mathematical Society, Jan. 2000.

Getting Started in Mathematical Biology  Frank Hoppensteadt, Notices of American Mathematical Society,  Sept. 1995.

Some Advice to Young Mathematical Biologists  Kenneth Lange, (from internet), date unknown.

How the leopard gets its spots?  James Murray, Scientific American, 258(3): 80-87, 1988.


Some Classical Papers of Mathematical Biology

Project topics:

  1. Mackey-Glass model of physiological control systems. paper 1, paper 2 (see page 37 of textbook), web (physiology, differential equations) Niraj
  2. Backward bifurcation in epidemic model (epidemiology, differential equations) Meaghan
  3. FitzHugh-Nagumo model in neural science  (original paper in 1961) (neuron science,differential equations) Arjun
  4. Killer whale population model. Paper (ecology, difference equations) Nicholas
  5. Flour beetle model. paper 1, paper 2 (ecology, difference equations) Hanzhang
  6. Spotted owl model. paper (ecology, difference equations)
  7. Cannibalism model paper (ecology, difference equations) Alton
  8. Feedback control in biochemical pathways paper (biochemistry,differential equations)
  9. Chaos in food chain model paper (ecology, differential equations) Will
  10. Oyster model paper (marine sci, differential equations) Junping
  11. Reproduction and distribution rates of T-cells in syphilis paper (disease) Kristina
  12. HIV model paper (disease, differential equations) Teresa
  13. Fishery management  paper (fishery, differential equations) Yilin
  14. Fairy rings paper paper paper (plant) Yiqing
  15. Quorum sensing model paper (bacteria) Marshall
  16. Hypercycle model paper (origin of life) Margaret
  17. Mathematics of Darwin’s theory of evolution paper (evolution) Ben
  18. Yellowstone wolf population model paper (ecology) Kajsa
  19. Ebola epidemics (epidemiology, differential equations) Rachel
  20. 1918 influenza paper paper paper (epidemiology, differential equations) Dan
  21. Lead in the human body paper (biochemistry, differential equations) also see textbook page 160 (problem 29)
  22. Glucose-insulin model (medical application, differential equations) (see Chapter 4, page 158-159, problems 26-28)
  23. Genetics model for breast cancer Evan
  24. Chaos in simple food web models with Omnivory paper (ecology, differential equations) Avery
  25. Cooperativity effects on Ligand Fluctuations in mGluR Jeffery