Modeling Complex Systems

Course Content and Objectives:
This seminar is ideal for assisting students develop unique and nontrivial theories of politics and society together with mathematical model specifications that exactly match those theories. Helping students develop theories and specifications useful for thesis research is a key component of the course. The subject is taught with an extremely user-friendly approach, and students should have little or no trouble mastering the course content. High school algebra is all that is required to begin. Substantively, the course focuses on a system's view of modeling, and students will learn a great many practical tools that help to bridge the divide between a verbally-stated theory and its mathematical representation.

The core of this course involves the study of graph algebra as it is applied to complex systems. Complex systems typically involves linear and nonlinear systems models, variously intermixing forced oscillators, fractals, chaos theory, and catastrophe theory. People study complex systems with respect to political and social phenomena because such systems are often closer parallels to real-world phenomena than simple linear models. Complex systems are also more fun.

Graph algebra allows you to create sophisticated mathematical models of social and political processes by simply sketching and connecting boxes and arrows that describe the phenomenon being investigtated. Graph algebra helps translate social theory into mathematical form. Mathematical model building can now be a relatively straightforward process, and students can develop their own unique models with a combination of ease and sophistication that will normally surprise those who have no background in graph algebra. Computer aided graphics are also taught in this course that bridge the model building and analysis components of social research.

COMPUTERS PROGRAMS: This course uses R, a free mathematics and statistics language that all students can load on their laptops. R is easy to use, and knowledge of this language is a great selling point on any resume. The course also uses Phaser, a graphics program that is available in a variety of locations on campus, as well as PowerPoint and MS Word.

Class Requirements:

This course is a seminar. Weekly reading and writing assignments are matched with class discussions, all focusing on the interpretation of various approaches to mathematical modeling with respect to society and politics. There is a final writing project that is submitted in three drafts. The course grade depends on the evaluation of all writing assignments, as well as class participation and attendance. Graduate students will meet with the instructor outside of class during lunch to go over assignments and to provide individual guidance, usually once a week.

There are no exams. The grades are determined as follows:

10% Attendance (Two absences are permitted without penalty.)
40% Weekly writing assignments (Graduate students need to complete all of these assignments.)
25% Final Project writing assignment (All three drafts are required.)
25% Class participation (students will make presentations to the class)

The Honor Code is strictly enforced in this course. Plagiarism is an honor code violation. Signature forgeries on attendance are an honor code violation.

Podcast Policy:

Podcasting courses can assist students tremendously. Students can listen to lectures more than once, and they can catch up on classes that were missed for, say, reasons of illness or religious obligation. I record and podcast many of the classes in this course. By taking this course, all students are automatically giving their permission to be recorded during class participation. No further written permission is required.

Disabilities Statement:

It is the policy of Emory University to make reasonable accommodations for qualified students with disabilities. All students with special requests or need for accommodations should make this request in person as soon as possible after first visiting the Office of Disabilities.

Required Texts:

Brown, Clifford, and Larry Liebovitch. 2010. Fractal Analysis. Thousand Oaks, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 165.

Brown, Courtney. 2008 (Published July 2007). Graph Algebra: Mathematical Modeling with a Systems Approach. Thousand Oaks, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 151.

Brown, Courtney. 2007. Differential Equations: A Modeling Approach. 2007. Thousand Oaks, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 150.

Brown, Courtney. 1995. Chaos and Catastrophe Theories. Thousand Oaks, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 107.

Huckfeldt, R. Robert, C. W. Kohfeld, and Thomas W. Likens. 1982. Dynamic Modeling: An Introduction. Newbury Park, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 27.

Ostrom, Charles W. 1990. Time Series Analysis, 2nd Edition. Thousand Oaks, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 9.

Reserve Readings:

Brown, Courtney. 1995. Serpents in the Sand: Essays on the Nonlinear Nature of Politics and Human Destiny. Ann Arbor, Michigan: University of Michigan Press.

Brown, Courtney. 1991. Ballots of Tumult: A Portrait of Volatility in American Voting. Ann Arbor, Michigan: University of Michigan Press.

Cortés, Fernando, Adam Przeworski, and John Sprague. 1974. Systems Analysis for Social Scientists. New York: John Wiley & Sons.

Goldstein, Larry J., David I. Schneider, and Martha J. Siegel. 1988. Finite Mathematics and Its Applications, 3rd Ed., Englewood Cliffs: Prentice-Hall.

Lave, Charles A., and James G. March. 1993(1975). An Introduction to Models in the Social Sciences. New York: University Press of America.

Mooney, Douglas, and Randall Swift. A Course in Mathematical Modeling. 1999. The Mathematical Association of America. (Recommended reading, but not on Reserve.)

Przeworski, Adam. 1975. Institutionalization of Voting Patterns, or is Mobilization the Source of Decay, American Political Science Review, 69:49-67.

Przeworski, Adam and Glaucio A. D. Soares. 1971. Theories in Search of a Curve: A Contextual Interpretation of Left Vote. American Political Science Review 65:51-65.

Simon, Herbert A. 1957. Models of Man: Social and Rational. New York: John Wiley & Sons.

Sprague, John. 1984(1981). "One-Party Dominance in Legislatures." In The Research Process in Political Science, W. Phillips Shively (Editor), pp. 225-67. Itasca, Illinois: F. E. Peacock Publishers, Inc. Also reprinted from Legislative Studies Quarterly, Vol. VI, No. 2, May 1981.

Internet Resources:

General Math -
A great web site on fractal geometry and chaos
Professor Strang's Linear Algebra Class Lecture Videos (MIT)
Professor Strang's Web Programs for Linear Algebra (MIT)

Data and Statistical -
The Cran Home Page: This is where you get R
Wikipedia's discussion of the R programming language
UCLA's R Resources Page
A discussion in a political methodology journal about the use of R
John Fox's methods class page
The Quick-R page, a great resource for SAS and SPSS users
The "Kickstarting R" Intro Manual
Hugh C. Pumphrey's course notes on R
Thomas Lumley's course notes on R
Rob Cribbie's course notes on R
Frank McCown's easy intro to graphing using R
The R Graphical Manual: A really comprehensive collection of graphics methods
The American Phytopathological Society has published a great introduction to R
Emory University Library's Political Methodology Research Guide
Emory University's Electronic Data Center
Gary King's excellent advice on writing your first publishable paper
How to Use a Codebook, from Princeton University
Inter-University Consortium for Political and Social Research (ICPSR)
National Election Studies, The University of Michigan
Rice Virtual Lab in Statistics
SAS Documentation for version 8.2
SAS Documentation for version 9.1 (This is the one we use in class.)
Statistical Abstract of the United States
Statistics Calculators from UCLA
SticiGui Online Statistics Text, by Philip B. Stark, University of California, Berkeley
Surf Stat, an online statistics text

Simulations
Robert Hanneman's list of useful links
Wikipedia on complex systems
Wikipedia on complexity theory and organizations
Wikipedia on complexity economics

WEEKLY OUTLINE

Week 1
Presentation and Discussion: Difference Equations
Readings:
Goldstein, Schneider, and Siegel (chapter 11)
Lave and March (chapter 1)
Huckfeldt, Kohfeld, and Likens (chapter 1)
Graph Algebra (chapters 1 & 2)
Fractal Analysis (Preface)

Week 2
Presentation and Discussion: Graph Algebra I - An Introduction
Readings:
Lave and March (chapter 2)
Cortés, Przeworski, and Sprague (chapters 1 & 2)
Graph Algebra (chapters 3 & 4)
Fractal Analysis (chapter 1)

Week 3
Presentation and Discussion: Graph Algebra II - Discrete Time Operators
Readings:
Lave and March (chapter 3)
Cortés, Przeworski, and Sprague (chapters 3 & 4)
Graph Algebra (chapters 5 & 6)
Fractal Analysis (chapter 2)
Written Assignment Due: Assignment #1

Week 4
Presentation and Discussion: Graph Algebra II - Discrete Time Operators (Continued)
Readings: Cortés, Przeworski, and Sprague (chapter 5)
Graph Algebra (chapters 7 & 8)
Fractal Analysis (chapter 3)
Written Assignment Due: Assignment #2

Week 5
Presentation and Discussion: Dynamic Modeling I
Readings:
Huckfeldt, Kohfeld, and Likens, chapters 1 & 2, Sprague
Graph Algebra (chapter 9)
Fractal Analysis (chapter 4)
Written Assignment Due: Assignment #3

Week 6
Presentation and Discussion: Dynamic Modeling II
Readings:
Lave and March, chapter 7
Huckfeldt, Kohfeld, and Likens, chapter 3
Differential Equations (chapters 1 & 2)
Fractal Analysis (chapter 5)
Written Assignment Due: Assignment #4

Week 7
Presentation and Discussion: Dynamic Modeling III
Readings:
Huckfeldt, Kohfeld, and Likens, chapter 4
Ballots of Tumult, chapters 1 & 7
Differential Equations (chapter 3)
Fractal Analysis (chapter 6)
Written Assignment Due: Assignment #5

Week 8
Presentation and Discussion: Graph Algebra III - Graph Algebra II - Working with Systems
Readings:
Huckfeldt, Kohfeld, and Likens, continue with chapter 4
Chaos and Catastrophe Theories, chapters 1&2
Differential Equations (chapter 4)
Written Assignment Due: Assignment #6

Week 9
Presentation and Discussion: Graph Algebra IV - Operators for Continuous Time
Readings:
Huckfeldt, Kohfeld, and Likens, finish chapter 4
Ballots of Tumult, chapter 2
Chaos and Catastrophe Theories, chapters 3&4
Differential Equations (chapter 5)
Written Assignment Due: Assignment #7

Week 10
Presentation and Discussion: Richardson's Arms Race Model
Readings:
Huckfeldt, Kohfeld, and Likens, begin chapter 5
Ballots of Tumult, chapter 2
Chaos and Catastrophe Theories, chapters 5&6
Differential Equations (chapter 6)
Written Assignment Due: Assignment #8

Week 11
Presentation and Discussion: Working with Systems using Phaser I
Readings:
Huckfeldt, Kohfeld, and Likens, continue with chapter 5
Ballots of Tumult, chapters 3-6
Chaos and Catastrophe Theories, chapter 7; Differential Equations (chapter 7)
Ostrom, chapters 1&2
Written Assignment Due: Assignment #9

Week 12
Presentation and Discussion: Working with Systems using Phaser II
Readings:
Huckfeldt, Kohfeld, and Likens, finish chapter 5
Serpents in the Sand, chapter 2-4
Differential Equations (chapter 8)
Ostrom, chapter 3
Written Assignment Due: Assignment #10

Week 13
Presentation and Discussion: Working with Systems using Phaser III
Readings:
Huckfeldt, Kohfeld, and Likens, chapter 6
Serpents in the Sand, chapters 1, 5, & 6
Ostrom, chapter 4
Written Assignment Due: Assignment #11

Week 14
Presentation and Discussion: Graph Algebra and Nonlinear Systems Topic
Readings:
Ballots of Tumult, chapter 8
Serpents in the Sand, chapter 7
Written Assignment Due: Assignments #12 and #13