MATH 411 - Mathematical Modeling
Instructor- Lou Gross
INDIVIDUAL PROJECTS
The purpose of this assignment is to allow each student to develop
expertise in some area of mathematical modeling by analyzing in some
detail a particular model or group of models. The essential elements of
this project must be: (i) a literature review of appropriate
background material related to the topic chosen; (ii) some type of
analysis, which may be numerical, of the model or group of models;
(iii) a carefully written report on your investigation; and (iv) an
oral report to the class, of approximately 20 minutes, based upon your
investigation. A brief 5 minute presentation by each participant on the
area they have chosen will be given in class on Wednesday October 30 -
the purpose is for the instructor and class to give feedback on your
oral presentation as well as on the topic described (this brief report
will not be graded, except that it is a required part of the
coursework).
Some details on each of these:
(i) The literature review should consist of more than merely looking at
one paper or book on the topic. You should make use of the library as
well as distributed information systems (e.g. WWW). You need to
sufficiently investigate the topic so as to have a basic understanding
of the issues being addressed, why the models or groups of models are
potentially useful, and what the purpose or purposes are for
constructing the models.
(ii) Your project should should not merely repeat verbatim what was in
a published paper. You may wish to: compare the assumptions underlying
several different models developed for the same underlying problem and
compare the behavior of these models, investigate either analytically
or numerically modified formulations of one or more models, and discuss
how you would go about producing a new model and what the advantages
would be of doing so.
(iii) The report should be a minimum of 15-20 double-spaced pages in
length, not counting references or figures. It should be written in
standard technical writing format: including an abstract or summary, an
introductory section that briefly describes the underlying problem, a
literature review section that describes previous work in some detail,
a methods and analysis section (which may have several subsections)
which describes in detail what you have done to analyze the model, and
a conclusions section that describes the results of your analysis. In
your conclusions section, you should critique the models discussed and
elaborate suggestions for future improvements of them, and/or ways to
test them using data.
(iv) The oral report should be carefully planned, and practiced
beforehand. You may use visual aids (including overheads, 35 mm slides,
and/or the computer) to aid in the presentation. You may wish to hand
out materials during the presentation. It should include a clear,
concise description of the underlying problem, a summary of what
modeling approaches have been taken, then a careful description of what
model you've investigated.
The instructor is available to meet individually with each participant
to discuss any of the above, including helping to understand any
technical aspects of a particular model.