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)
|
|
|
|
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
- G. H. Hardy, 1908. Mendelian
proportions
in a mixed population, Science, N. S. Vol. XXVIII: 49-50.
- A. J. Lotka, 1920. Analytical
Note on Certain Rhythmic Relations in Organic Systems. PNAS, 6:410-415.
- R. Pearl and L.J. Reed, 1920. On
the rate of growth of the population of the United States
since 1790 and its mathematical representation. PNAS,
6:275-288.
- W. O. Kermack and A. G. McKendrick, 1927. A
Contribution to the Mathematical Theory of Epidemics.
Pro. Royal Soc. London. Series A, Vol. 115, No. 772,
700-721.
- V. Volterra, 1926. Variazioni e fluttuazioni del numero
d'individui in specie animali conviventi," Mem. R.
Accad. Naz. dei Lincei 2: 31-113. (Variations and fluctuations of the number of
individuals in animal species living together).
- V. Volterra, 1926. Fluctuations in the
abundance of a species considered mathematically. Nature
118: 558-60.
- G.F. Gause, 1934. The Struggle for
Existence, Baltimore: Williams & Wilkins.
- R.A. Fisher, 1937. The
wave of advance of advantageous gene, Ann. Eugen. 7: 355-369.
- C. Elton and M. Nicholson, 1942. The
Ten-Year Cycle in Numbers of the Lynx in Canada. Jour.
Anim. Ecol., Vol. 11, No. 2, 215-244.
- P.H. Leslie, 1945. On
the use of matrices in certain population mathematics.
Biometrica, Vol. 33,183-212.
- A. L. Hodgkin and A. F. Huxley, 1952. A
quantitative description of membrane current and its
application to conduction and excitation in nerve, J Physiol. 117(4): 500–544.
- A. Turing, 1952. The
chemical basis of morphogenesis, Phil. Tran. Royal
Soc. London, Series B, No.641, Vol. 237, 37-72.
- C.B. Huffaker, C.B. 1958, Experimental
Studies
on Predation: Dispersion factors and predator-prey
oscillations, Hilgardia 27 343-383.
- P.H. Leslie, J.C. Gower, 1960. The
properties of a stochastic model for the predator-prey
type of interaction between two species. Biometrica,
47, 219-234.
- M.L. Rosenzweig, 1971. Paradox
of
enrichment: destabilization of exploitation ecosystems in
ecological time, Science
29, 385-387.
- A. Gierer, H. Meinhardt, 1972. A
theory of biological pattern formation. Biological
Cybernetics, Vol. 12, 30-39.
- R.M. May, 1976. Simple
mathematical models with very complicated dynamics, Nature,
Vol. 261, 459-467.
- R.M. May, 1977. Thresholds
and breakpoints in ecosystems with a multiplicity of
stable states, Nature, Vol. 269, 471-477.
- R. M Anderson and R.M. May, 1979. Population biology of
infectious diseases: Part
I, Nature, Vol. 280, 361-367. Part
II, Nature Vol. 280, 455-461.
Project topics:
- Mackey-Glass model of physiological control systems.
paper
1, paper 2 (see page 37 of textbook), web
(physiology, differential equations) Niraj
- Backward
bifurcation in epidemic model (epidemiology,
differential equations) Meaghan
- FitzHugh-Nagumo
model
in neural science (original
paper in 1961) (neuron science,differential
equations) Arjun
- Killer whale population model. Paper
(ecology, difference equations) Nicholas
- Flour beetle model. paper
1, paper
2 (ecology, difference equations) Hanzhang
- Spotted owl model. paper (ecology, difference
equations)
- Cannibalism model paper
(ecology, difference equations) Alton
- Feedback control in biochemical pathways paper
(biochemistry,differential equations)
- Chaos in food chain model paper
(ecology, differential equations) Will
- Oyster model paper
(marine sci, differential equations) Junping
- Reproduction and distribution rates of T-cells in
syphilis paper (disease) Kristina
- HIV model paper
(disease, differential equations) Teresa
- Fishery management paper
(fishery, differential equations) Yilin
- Fairy rings paper
paper
paper
(plant) Yiqing
- Quorum sensing model paper
(bacteria) Marshall
- Hypercycle model paper
(origin of life) Margaret
- Mathematics of Darwin’s theory of evolution paper
(evolution) Ben
- Yellowstone wolf population model paper
(ecology) Kajsa
- Ebola epidemics (epidemiology, differential
equations) Rachel
- 1918 influenza paper paper paper (epidemiology,
differential equations) Dan
- Lead in the human body paper
(biochemistry, differential equations) also see
textbook page 160 (problem 29)
- Glucose-insulin model (medical application,
differential equations) (see Chapter 4, page 158-159,
problems 26-28)
- Genetics model for breast cancer Evan
- Chaos in simple food web models with Omnivory paper
(ecology, differential equations) Avery
- Cooperativity effects on Ligand Fluctuations in mGluR Jeffery