Joseph M. Mahaffy SDSU
Math 636: Mathematical Modeling Fall 2017
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HW Assignment for Math 636

This page will give a complete listing of the reading and homework assignments that you are required to do. Some problems will be worked in WeBWorK. Instructions for logging into WeBWorK can be found at Logging into WeBWorK.

Week 8-9: Read the material in the lecture notes for Diabetes Modeling (4-Panel). Other references include the articles of Gatewood, Ackerman, Rosevear, and Molnar and Mahaffy and Keshet.
Project Time!
Find a compatible partner in class. (Exceptions will be made for the occasional individual or group of 3, but we should have about 12-13 groups from this class.) Create a two-page outline for your final group project (due by Thursday Nov. 2). The outline needs to be sufficiently detailed that I understand your sources and scope of study. This includes discussing the area of application and some idea of the mathematical techniques employed. Your final project is a modeling problem of your choice that should use some of the techniques we are teaching in this class or related material. (No statistics!) You will be producing a paper at the end of the semester that is approximately 20-25 pages (not counting appendices with programs) and giving an oral presentation (graded by your fellow students). The project can be related to projects in other courses, but must be unique from other courses and emphasize the modeling part of a problem.

Week 10-11: Lecture notes for Markov Chain Monte Carlo (4-Panel) are being developed. Old notes are available for Monte Carlo simulations, Stochastic simulations, and Stochastic birth only process. There are a few MatLab programs that were used in lecture for Monte Carlo simulations (and one additional one mentioned). 1. Population decay (pop.m and Mpop.m). 2. Integration (mcint.m and g.m). 3. Computing Pi. 4. Game of craps. (craps.m and dice.m). The link to the video for the Disney film Our Friend the Atom for a chain reaction with mousetraps and the mousetrap MatLab code simulating the stochastic model for this movie. The original article by Schmitz and Kwak on the Deaconess Hospital simulation is available.
HW Assignment: The Diabetes HW assignment (mostly from WeBWorK) can be found through this link and is due by Tuesday, Nov. 14. Reference material is listed above (Week 8-9). Homework solutions are available for ODE Models - HW5 and LV Models - HW 6.

Week 12: Lectures continue on stochastic processes. There are lecture notes for Stochastic Modeling (4-Panel) (very incomplete). Additional references for the Stochastic simulations notes are found in the work by Gillespie in 1977. The Gillespie algorithm is valuable for studying biological systems with smaller numbers of molecules. A good example is a bifurcation study by Arkin, Ross, and McAdams (1998) on the lysogenic-lytic switch in Phage Lambda infections of E. coli. There are lecture notes for Leslie Models. There are additional references on this topic about Loggerhead turtles and Semalparous organisms (and other articles by Cushing).
HW Assignment for the Monte Carlo simulations is due by Tuesday, Nov. 21.

Old Homework Assignments

Week 1: You should familiarize yourself with this webpage and how to navigate the different sections. This will be a key page where I post Reading and Homework assignments. The dates for when those assignments are due will also be listed here. We will use a variety of computer programs, but primarily MatLab and Maple. MatLab can be downloaded from SDSU. Maple is available for purchase through the Maple Adoption program. All these programs are available in our computer labs.

Read the lecture notes for Introduction (4-Panel) and Linear and Polynomial Modeling (4-Panel).
HW Assignment: The Introduction HW are available in WeBWorK, including parts that must be written (graphs and paragraphs). The written HW is due Sept. 7 (class time), while the WeBWorK problems are due Sept. 9 (4 AM).

Week 2: Read the lecture notes on Allometric and Dimensional Analysis (4-Panel). There is additional information in article for Atomic Bomb Energy Part 1 and Part 2. Also, there is information on food energy and weight (Kleiber's Law) and the relation to pulse and weight (von Bertalanffy).
HW Assignment:
There is a homework assignment on WeBWorK (due by Sat., Sept. 16) for Allometric and Dimensional Analysis along with one additional problem for Allometric models, which will be due by Thurs., Sept. 14.

You should begin finding an article in the Proceedings of the National Academy of Sciences (PNAS) from the last 5 years. You need to submit to me the title of the article, list of authors, volume number, and year by Tues. Sept. 12. A list of PNAS articles selected by the class will be regularly updated, and each student must choose a different article. You will write a 2-5 page review that summarizes the work done and discusses some mathematical modeling aspect in the article. I am primarily looking for good scientific writing and an understanding of the role of modeling in your article. Your review will be due Thurs. Sept. 28.

Week 3: Reading the material in the lecture notes under U. S. Population (4-Panel) and Discrete Dynamical Models (4-Panel). The link to the Lectures has a collection of MatLab files used to solve problems in these notes. You may use any software for your homework, but document what you use.
HW Assignment: The third Homework assignment for the Discrete models is due by Thursday, Sept. 21. (WeBWorK is due by Friday, Sept. 22 (4 AM)).

Week 4: Read the material in the lecture notes for the SIR Model for Influenza (4-Panel). Also, begin reading the material for population modeling with differential equations. The lecture notes include Continuous models: Yeast data and Malthusian growth (4-Panel).
HW Assignment: Begin the Homework assignment for SIR - HW, which includes a WeBWorK problem. This will be due by Thursday, Sept. 28. Don't forget to start work on your PNAS article review, which is due Thur. Sept. 28.
Homework solutions are available for Allometric Models - HW1.

Week 5: Read the material for population modeling with differential equations. The lecture notes include Continuous models: Yeast data and Malthusian growth (4-Panel) and Continuous models: Competition Model (4-Panel).
HW Assignment: Your next homework assignment begins with some basic ODE models, using simple population models and Newton's law of cooling, then examines two dimensional competition models. One problem takes data from A.C. Crombie on graminivorous beetles and has you repeat much of what we have done in class to create a mathematical model for this ecological system with two competing species. The Differential Equations HW assignment (including a data file) can be found through this link and is due by Tuesday, Oct. 10.

Week 6: Read the material in the lecture notes for Continuous models: Competition Model (4-Panel).
HW Assignment: (See previous week.) The
homework assignment covers with some basic ODE models, using simple population models and Newton's law of cooling, then examines two dimensional competition models.

Week 7: Read the material in the lecture notes for Lotka Volterra models (4-Panel) and Bifurcation Studies (4-Panel). Highly recommended is the PBS American Experience on Rachel Carson, which helps explain the use of pesticides on the environment and her huge impact on both the environmental movement and the awareness of women in science. (Peanuts and link.)
HW Assignment: The LV Model HW assignment can be found through this link and is due by Tuesday, Oct. 24.
The Bifurcation Analysis HW assignment is available and includes a collection to WeBWorK problems. It assignment is due Thursday, Oct. 26. Also, homework solutions are available for Discrete Models - HW 3 and SIR Models - HW4.

 

 

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