SYLLABUS – Math
4/5779: Math Clinic
Mathematical Models for Peace
Fall
Semester ‑ 2003
Professor: Weldon A. Lodwick
Office:
Telephone: 556‑8462 (office -
voice mail), 556‑8442 (secretary), 556-8550 (fax)
E-Mail: weldon.lodwick@cudenver.edu
Web Site:
http://www-math.cudenver.edu/~wlodwick
Office Hours: TTh
W
Other times by appointment
Students with Disabilities: If you have a disability that requires
accommodation in this course, please see me as soon as possible. I am happy to make appropriate accommodations
provided timely notice is received.
Cell Phones: You are to turn off your
cell phones prior to entering class.
1.
To
develop an understanding of mathematical models for peace by:
a.
Researching
the literature leading to an annotated bibliography,
b.
Developing
a clinic website where the bibliography, links, class reports and other items
of interest will be posted,
c.
Presenting
an oral and written report on one topic and/or one research paper,
d.
Creating
and testing a prototype mathematical world-peace model.
2.
To
develop a well-reasoned definition of peace and a taxonomy of mathematical
models for peace.
3.
To
incorporate, within group work, conflict resolution techniques.
The proposed outline is the
initial guess of the topics that will be fruitful to investigate. Research is a process of discovery when one
does not know, so the rule is that we will modify our topics during the
semester. Thus the proposed outline will
undoubtedly change as we learn more during the semester.
This semester we will study traditional and contemporary
mathematical models for peace. Of
course, we will also look at approaches that are not in the literature. The objective will be to develop and test
prototype algorithms for the analysis of world peace. NOTE: This class is one in which we will do
research toward the goals outlined above.
Research is research because we do not know what are the mathematical
models for peace. So, this class is one
in which we will explore together. I
have studied a little bit of the literature and have been in contact with
several researchers in this area so that I have a little understanding of what
are some of the prevailing views. The
proposed topics that we will try to cover include:
I.
Approaches
A.
Dynamical
system models –
1.
Jurgen
Scheffrean’s article “Calculated Security?
Mathematical Modelling of Conflict and Cooperation”
2.
Courtney
Brown’s analyses of voting behavior (Ballots of Tumult and Serpents
in the Sand) and Marcelo Anile’s notes
3.
Luenberger’s
dynamical systems text
B.
Systems
dynamic models – qualitative dynamical system models
1.
George
Backus’ article on Coping Theory
2.
Ralph
Levine’s psychological dynamic models
C.
Game
theory
1.
Axelrod’s
approach to the prisoner’s dilemma (The Complexity of Cooperation), Gary
Kochenberger’s approach to Axelrod (tabu search vs. genetic algorithms),
simulated annealing approaches
2.
Thomas
Saaty’s Mathematical Models of Arms Control and Disarmament and Thomas
Schelling’s The Strategy of Conflict
D.
Graph
theory – to be presented by Dave Brown
E.
Catastrophe
theory
F.
Fuzzy
Set Methods
1.
Rule-based
models
2.
Relational
models
3.
Clustering
G.
Others
1.
Neural
networks
2.
Inverse
problem
3.
Datamining
II.
Algorithm
Development and Testing
A.
Dynamical
Systems – systems of ODE’s
B.
System
Dynamic models ala Backus and Levine
C.
Game
theoretical approaches are probably the most readily accessible and
programmable – genetic algorithms, simulated annealing and tabu search
D.
Graph
theory – models
E.
Fuzzy
logic models – use of MATLAB’s Fuzzy Logic Toolbox and relational models
F.
Others
– catastrophe theory, neural networks, inverse methods, datamining methods,
fuzzy cluster analysis
III.
Social
sciences – Peace is a topic studied by social scientists. There are several peace universities (
The work
this semester will be divided as follows:
1.
Introduction to the problem, models, approaches and algorithms (1st
7 weeks)
2.
Development of a working prototype mathematical model for peace (2nd
7 weeks)
Problem
Statement
To create a mathematical model that,
1.
Describes
the dynamics of world peace
2.
Predicts
world peace
3.
Prescribes
(to lay down as a rule or course to be followed – The Random House College
Dictionary) the conditions for world peace
Outcomes:
* Note:
10% of your grade depends on your ability to work in a team. This means that you must find a way to
resolve conflicts within your assigned group.
I need to be a part of conflict resolution efforts as early as
possible. If your group “falls apart,”
then your highest grade possible is a B+ or an A- depending on the nature of
the problem(s) arising in your group.
Individual Responsibility
Group Responsibility
EVALUATION
Individual
report and in-class individual presentations (3 per class period
beginning October 9th):
Written reports are due no later than the day that the last presentation
is made. This part is worth 45% of your grade and is broken down as follows.
Proposal – a three page (maximum) written research
proposal is due by the end of class on September 16th and it
outlines what you intend to research, present and report. Prior to your writing the proposal, set up an
appointment with me to discuss what you are thinking. Note that your report will typically be an
aspect of your team’s project and can be worked out in conjunction with your
team’s DOL.
Depth and breadth –
graduate students will need to tackle tougher approaches and/or go into topics
more in depth and to a greater depth than undergraduate students. This is a topic for our individual meeting.
Examples, illustrations, graphics, tables –
since the subject of mathematical models for peace is a broad and complex
topic, you will be expected to be specific in your presentations and toward
this end, use a variety of means (including those mentioned above) to express
what you are researching.
Clarity – please share your understanding in a way
that we all can comprehend while at the same time does not insult our intelligence.
Participation – this is a small class and your
contribution(s) are important both in terms of your presence as well as your
ideas. You are expected to attend all
classes and group meetings. We will have
guest speakers and it is especially important that you are a part of these
presentations. I will keep a record of
your participation.
Group report
and in-class presentations (finals week – December 9th and/or
11th) is the written chapter in the clinic report and an in-class
presentation of group projects. This
part is worth 45% of your grade. All
individuals in a group, if they complete their portion of the DOL successfully,
will receive the same grade (exceptions are noted below).
Group
functionality – 10% of your grade.
Note: Graduate students will
be held to higher standards as mentioned above.
The grade assignments are on the 10 percent scale (A = 90%-100%, B =
80%-89%, C = 70%-79%, D = 60-69%).
MY APPROACH TO TEACHING
I
believe that teaching is a process that involves an active partnership. My role is that of a guide to your
learning. Therefore, I am responsible to
open the way, to encourage, and to nudge you toward your own learning. I will help guide you toward this learning by
providing mathematics for you to experience.
It is my aim to communicate mathematics in a way that is supportive and
nurturing of your efforts. Your role is to find a way to experience and
articulate the mathematics that is presented and that you encounter. I believe that it is your responsibility to
let me know when you find yourself not understanding mathematical concepts that
are presented in class. Once you make
this known, it is our responsibility to work on trying to attain clarity. I will try to be as proactive as
possible. I believe that results on
projects give us the opportunity to clearly see where the areas of mathematical
understanding are and what areas need more attention.
OUTCOMES
By the end of the semester you should be able to
read, understand and apply appropriate methods associated with aspects of
mathematical models for peace we’ve studied this semester to correctly solve
associated problems. Secondly, given a
problem in the area of mathematical models for peace that we have studied this
semester, you should be able to: (i) translate the description of the problem
into an algorithm, (ii) choose and apply the appropriate software method(s),
(iii) obtain the workable solution(s), and (iv) (correctly) interpret and
display results. Lastly, by the end of
the semester you should be able to judge, for yourself, the veracity of statements
made in the areas of our study.
IMPORTANT DATES:
August
20th – September 15th: set up appointment with me to
discuss your individual reports
and presentations
September 16th –
individual proposals
September 30th –
last day to sign up for in-class the individual presentations
October 9th –
group DOL, set up group meetings with me to go over the DOL’s
October 9th –
begin individual reports, written reports are due no later than the day of the
last presentation
December 9th and
11th – group presentations
December 12th – last day to turn in the group reports
General advice: Keep all materials that I turn back in case you think I have not
credited you with the points you earned.
I can only correct your score if you have what I have turned back to
you. It is a good idea to copy anything that you turn in just in case I lose
what you turn in. Please check to make sure that the points you earned are the
points I have recorded. Note: The
statistics that I have read about correctness of professors in recording grades
state that there is a 6% error rate in our recording of your grades. Please make sure that I have correctly
recorded your points.
POLICIES
Adds, drops and incomplete grades:
See Schedule of Courses for the
relevant dates with respect to adding and dropping this course. Given the budget cuts facing universities,
you must be registered by the dated specified or you will not get credit. The incomplete policy of the Mathematics
Department and the
Legitimate Excuses: Legitimate excuses
are for reasons that are beyond your control.
You may be required to produce an official, signed excuse. If you are needed in a wedding, for example,
you must talk to me prior to the
(blessed) event. If you are legally
arrested, then this is not a legitimate excuse.
For matters that are within your control, the general rule is that it is
not excused. However, talk to me prior to the event.
Teams:
If all
items of the "Division of Labor" are correctly fulfilled by the
responsible person(s), then all members of the team will receive the same point
distribution. An individual in a team
will be rated differently for one or more of the following reasons:
·
The individual's share of the labor as outlined in the "Division
of Labor" is not fulfilled
·
The individual's portion is incomplete
·
The individual's part is poorly completed
· The individual failed to meet with the team to plan and carry out the project
INSTRUCTIONS FOR PROJECTS: A project consists of:
1. Proposal and division of labor – Each project will be divided into tasks and
assigned to each group so that the assignment is equitable. These tasks and assignments need to be
written up and submitted to me. Once the
tasks have been identified, assigned and approved, a division of labor is
written by each of the groups. A DOL is a list of tasks and subdivided into subtasks that are assigned
to individuals in the group along with associated due-dates. A DOL is a formal contract between the
members of the group and the clinic professor.
Once the tasks have been approved and a written division of labor
submitted, the group needs to schedule of meeting with me so that we can go
over the DOL, its associated responsibilities and expectations.
2. Software
a. Code - the actual computer implementation of the project. Attention must be paid to efficiency,
readability and portability.
b. User interface – the way information is passed to the software must
be compelling to the client.
c. Data and inputs
d. Execution - the algorithm as run must correctly perform what it
was designed to do.
e. Output - relevant, clear display of solution (tables, graphs,
images).
f. Ease – ease of use.
g. Documentation – an in-line and hardcopy of the documentation on how
to use the software needs to be written.
Moreover, help files must be part of the software.
3. Testing and analysis
a. Testing - this part in the context of
our clinic consists of running the software developed on the test problems and
comparing results to Monte Carlo simulations of the same set of problems. We will be compiling a set of test problems
as a part of our clinic.
b.
Analysis - the purpose of an
analysis is to get you to critically
evaluate the results obtained from the software as it was run on the test
problems. Part of an analysis is a
critique of the software.
4. The Clinic Report – Each team will need to be responsible for parts of
the final clinic report that will be delivered to our sponsor and is a part of
the mathematics department’s published Clinic Report Series. This will be done in MS-Word or Latex. The final report will (subject to
modifications we uncover) consist of:
a. Introduction – clinic director
b. Project 1
i.
Theoretical
foundations – theory, application,
algorithms
ii.
Software – description
iii.
Results – conclusions, limitations and improvements
c. Project 2 (same as project 1)
…
d. Project N (same as project 1)
e. Opportunities for further research
f.
Conclusions
g. Bibliography
h. Appendices (Source code, test problems,
documentation)