Math 345 Schedule (subject to change)

Date

Sections

Lecture notes

Homework

Other readings
Programs

8/30(R)

1.1-1.4
Lecture1

W&M BioMath
mathematical model 2
Fibonacci sequence
Fibonacci and Golden section
malthus.m
fibonacci.m
plant.m
9/4(T)
1.5-1.8
Lecture2 Homework 1 (due 9/7) :


matrixcalculation.m  graphing.m

9/6(R)

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

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

9/11(T)

2.1-2.2
Lecture4  



9/13(R)

Florence




9/18(T)

2.3-2.8
Lecture5
Lecture6
Homework 2 (due 9/21) Logistic map May (1976)
period 3 implies chaos
bellows.m  cobweb_bellows.m
bifurcation_bellows_model.m

9/20(R)

3.1-3.6
Lecture7


bifurcation_logistic_model.m

9/25(T)

4.1-4.3
Lecture8
Dimension Analysis
Homework 3 (due 9/28) Heinz von Foerster
Dimension analysis

9/27(R)

4.4-4.6
Lecture9 project guide

bifurcation_ricker.m
ricker.m

10/2(T)

4.7-4.10
Lecture10 Homework 4 (due 10/5) direction field plotter 1 2 3
phase portrait plotter 1 2 3
dfield8.m pplane8.m

10/4(R)

5.1-5.8
Lecture11


10/9(T)

6.1-6.2
Lecture12 Homework 5 (due 10/12) Lotka Volterra  

10/11(R)

6.3-6.4
Lecture13
Catastrophic shifts in ecosystems
We have 12 years to limit climate change catastrophe, warns UN
Eluding catastrophic shifts

10/16(T)

Fall Break

no class





Date
Sections
Lecture notes
Homework
Other readings
Programs

10/18(R)

Exam 1



1 2 3

10/23(T)

6.6
Lecture14 Homework 6 (due 10/26)

10/25(R)

8.3, 8.6 Lecture15
Lecture16 (summarizing 12-15)

competition and mutualism

10/30(T)

6.6
Lecture17
Homework 7 (due 11/2) infectious disease
epidemic pandemic
epidemic models
CDC outbreak page
sir.m
predatorprey.m
hopf.m
hiv.m

11/1(R)

6.6
Lecture18
Lecture18a

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

11/6(T)

7.1-7.5, 8.8
Lecture19
Lecture19a
Homework 8 (due 11/9) Enzyme rate equation
autocatalytic reaction
sigmoid function Hill function

11/8(R)

8.1-8.2, 8.5
Lecture20

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

11/13(T)

9.1-9.5
Lecture21
Lecture21a
Homework 9 (due 11/16) 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

11/15(R)

10.5-10.6
Lecture22

Invasive species
Fisher's equation

11/20(T)

6.4, 9.8
Lecture23
Lecture23a

Routh–Hurwitz stability criterion


11/22(R)

Thanksgiving no class



11/27(T)

11.4-11.7 Lecture24
animal coat
Lecture24a
Homework 10 (due 11/30) 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)
schnakenberg model simulation
11/29(R)

Berry, Briggs(Wong), Gaines, Gizaw, Hauk,
Hwang, James, 



12/4(T)


Kean,Larson(Stevenson), Lin, Liu, McKay,
Miller, Noll, Raj,



12/6(R)


Roy, Shang, Song, Stevenson(Larson),
Stolting, Tseng, Wong(Briggs), Zhang



12/12(F)






12/16(T)






Project Abstracts

General Articles in Mathematical biology

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

Mathematical Biology is Good for Mathematics  Michael C. Reed, Notices of American Mathematical Society, October 2015.

When Does Compromise Prevent More Pollution? C. Clemons, J. Cossey, M. Ferrara, S. Forcey, T. Norfolk, G. Obeng, D. Ricciardi, and G. Young. Notices of American Mathematical Society, October 2012.

Why Are There No 3-Headed Monsters? Mathematical Modeling in Biology  J. D. Murray. Notices of American Mathematical Society, June/July 2012.

What Is Mathematical Biology and How Useful Is It? by Avner Friedman, August 2010.

Climate Change and the Mathematics of Transport in Sea Ice by Kenneth Golden. May 2009

Climate Change: Can Mathematics Help Clear the Air? by Christopher K.R.T. Jones. April 2009

Mathematical Models in Science and Engineering by Alfio Quarteroni. January 2009

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.

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)
  2. Backward bifurcation in epidemic model (epidemiology, differential equations) Yuxin Shang
  3. FitzHugh-Nagumo model in neural science  (original paper in 1961) (neuron science,differential equations)
  4. Killer whale population model. Paper (ecology, difference equations) Hannah Stevenson-Anders Larson
  5. Flour beetle model. paper 1, paper 2 (ecology, difference equations)
  6. Spotted owl model. paper (ecology, difference equations) Alec Miller
  7. Cannibalism model paper (ecology, difference equations) Hannah Stevenson-Anders Larson
  8. Feedback control in biochemical pathways paper (biochemistry,differential equations)
  9. Chaos in food chain model paper (ecology, differential equations)
  10. Oyster model paper (marine sci, differential equations) 
  11. Reproduction and distribution rates of T-cells in syphilis paper (disease) 
  12. HIV model paper (disease, differential equations) Tiffany Tseng, Elizabeth McKay
  13. Fishery management  paper (fishery, differential equations)  Harrison McGuire
  14. Fairy rings paper paper paper (plant)
  15. Quorum sensing model paper (bacteria) 
  16. Hypercycle model paper (origin of life)
  17. Mathematics of Darwin’s theory of evolution paper (evolution) Abby Berry
  18. Yellowstone wolf population model paper (ecology) Teddy Noll
  19. Ebola epidemics (epidemiology, differential equations) 
  20. 1918 influenza paper paper paper (epidemiology, differential equations)
  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) Lulu Zhang
  23. Genetics model for breast cancer
  24. Chaos in simple food web models with Omnivory paper (ecology, differential equations) Phillip Hwang
  25. Cooperativity effects on Ligand Fluctuations in mGluR
  26. A Computational Study of Neurexin Mutations Leading to Dynamic Neuronal Network Activity Martha Gizaw
  27. The Effect of the Grey Squirrel Invasion on Red Squirrel Population in the United Kingdom Kathryn Kean
  28. Mathematical Model to Account for Relative Abundance Factor in the Success of Batesian Mimicry Lindsay Stolting
  29. Demographic and genetic consequences of environmental heterogeneity for biological control Xi Lin
  30. Detecting the Spatial Scale Limit of Lacunarity for Grey-Scale Raster and/or Point Data from a Moving Window Analysis using Differential Equations Mollie Gaines
  31. Modeling Phage Growth in Relation to Bacterial Population Dynamics Autumn Liu
  32. Panda population model Jingzheng Song
  33. Pharmacokinetic/pharmacodynamic model for aspirin Ban Hauk
  34. SIR Differential Equations Model to study Influenza Roy Rudraksh
  35. Michael James
  36. Stabilizing Fish Populations Through Pollution Tax Michael Briggs-Evan Wong
  37. Optimization of Crop Biomass Growth Through Regulating Water Supply Michael Briggs-Evan Wong