Project: Playing With S3 Simulator.
This handout contains the information you need to get going on your
project. There are two parts to the handout. This first part has
information about due dates for the project, the report you will be
preparing, grading criteria, and a list of which students are doing
which projects to help you in forming a group if you choose to do so.
The second part has a brief summary of your topic and a list of key
words to help you head in the right direction. In the next couple of
weeks, you will get one more handout which will contain problems for
you to solve as part of your project.
The material I'm giving you really is just a bare-bones minimum to help
direct you. You are responsible for finding references and doing your own
investigating and learning. However please feel free to contact me, in
person or by email, for help finding references or working the problems or
for general guidance about the projects, and to give me feedback about how
it is going.
Due Dates
There are three due dates for the project, October 11th, October 30th
and November 22nd. These deadlines are explained in page 3. Turning
this material in on time will count towards points in the
determination of your total grade on the project.
On Wednesday, November 22nd your overall project report is due.
Each person will be responsible for preparing his/her own report,
including writing up his/her own solutions to the problems.
Reports and Grading Criteria
Your report should include some version of the following 5 parts. They do
not have to be arranged the way I list them here, but all should be
included in your report in some form or another.
- (10 points) General Discussion Introduction and
generalities for the project (could include why you chose this project,
background about the field of application, goals of the project),
definitions and results from Probability used in the project,
definitions and discussion of results and ideas from the field of
application used in the project. When you state mathematical results that
you use, try to explain some of the mathematics behind why the results are
true-present a derivation if you can, or, if that is too difficult, give a
sketch or an intuitive idea of how it works.
- (25 points) Solutions to Problems Give your
solutions to the problems I will provide for your topic. It is very
important not only to give a correct answer but also to give a
thorough explanation of your solution. You should have a clear
explanation of each step, an analysis of what results apply to what
step, etc. This is not like just working out a usual homework
problem-explain in words what you are doing and write sentences. If
you are going to support a theory by simulations you should attach
print outs of those realizations.
- (6 points) References A list of the references that
you used, people you consulted, people you worked with, places you
found help. Included in the 6 points will be turning things on time with respect to your deadlines.
- (2 points) Comments Your comments on how interesting you
found the project, whether you feel that the time you spent on this was
worthwhile and whether it might help you in the future or lead to anything
for you, and suggestions to me for improvements in case I do projects like
this again.
- (7 points) Presentation This includes innovation in
presenting the material of the report,
clarity and neatness, flow, design and organization of the report,
and creativity used in explaining the ideas.
Project Details
Modeling Biological phenomena is a very exciting and rich area of
research in Mathematics. Interacting particle systems is one way of
modeling. Loosely speaking in this set up, we mainly work on the
lattice(s) Z, Z^2, where particles or infections spread according
to pre-determined birth and death rates.
In this project we shall work closely with the simulator S3 to
understand these processes better. We shall try to predict (based on
simulations) properties of certain processes with regard to it initial
distribution, birth/death rates etc.
key words to learn:
- Interacting particle systems.
- Predator prey systems.
- Exponential Random variable.
- Poisson process.
- Contact process.
Plan:
- October 11th Install the simulator from the web-site: http://gumby.syr.edu. Present a print out of a simulation of your favourite process.
- October 30th Read through the Tutorial. Submit at least two
references that you have found for you project. An explanation or
definition of at least two of the key words.
http://www.math.ubc.ca/~athreya/302/projects/sim.html
[Math 302 -Projects page]
[Math 302 page]
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