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Faculty: Martin Zwick Course Information

SYSC 511: Systems Theory

SySc 511 surveys fundamental systems concepts and central aspects of systems theory. The course begins with an overview of the systems paradigm and the systems field as a whole. Topics then include introductions to set- and information-theoretic multivariate relations, dynamic systems, regulation and control, model representation and simulation; decision analysis, optimization, and game theory; artificial intelligence, complex adaptive systems. Readings draw from mathematics, the natural and social sciences, and the professional disciplines (e.g., engineering, business).

The course content derives both from "classical" general systems theory, cybernetics, and operations research as well as from more contemporary systems research which is organized around the themes of nonlinear dynamics, complexity, and adaptation.

SYSC 551: Discrete Multivariate Modeling

SySc 551 focuses on information theory as a modeling framework and as a tool for discrete multivariate analysis. The course presents set- and information-theoretic methods for studying static or dynamic (time series) relations among qualitative variables or among quantitative variables having unknown nonlinear relationships. In the 'general systems' literature, this is known as 'reconstructability analysis' (RA). RA overlaps partially with log-linear statistical techniques widely used in the social sciences; both are especially valuable in data-rich applications (but RA is not exclusively statistical). RA is highly relevant to the many interrelated "projects" which go under the names of data-mining, machine learning, knowledge discovery and representation, etc.

Applied to data analysis, RA allows the decomposition and compression of multivariate probability distributions (contingency tables) and set-theoretic relations (and mappings), as well as the composition of multiple distributions/relations. These methods are very general. They are valuable in the natural and social sciences and in engineering, business, or other professional fields whenever categorical variables are useful or, for quantitative variables, where linear models are inadequate. Applied to the conceptualization of "structure" (the relations between wholes and parts) and "complexity," these set- and information-theoretic ideas are foundational for systems science.

Data Mining with Information Theory

DMIT is a project-based course that offers an opportunity to use information theoretic methods to analyze data, without having first to master the underlying theory. These methods are particularly ideal for detecting unknown non-linear relations or many-variable interaction effects. The methods are implemented in a Systems Science software package named OCCAM that will be the main analytical tool used in the course. The underlying theory is taught in SySc 551/651 Discrete Multivariate Modeling (DMM), but DMIT is stand-alone and does not have DMM as a prerequisite. Only the theory that is needed to understand OCCAM inputs and outputs will be presented; the software will otherwise be treated as a black box. DMIT does require, however, that those taking it have data to analyze. Data should be in spreadsheet format, where columns are variables (nominal or continuous) and rows are cases (that sample a population or are points in time or space). The number of cases (the sample size) should be in the 100s or preferably higher but at least in the 10s. The larger the sample size the more variables can be analyzed, but OCCAM has not yet been used for more than 100s of variables. Questions about suitability of data should be directed to

Discrete Multivariate Modeling II

SySc 510/610 will continue the presentation of DMM (SySc 551/651), and will focus on (a) projects and (b) advanced topics. In projects, students will either do either (i) an intensive analysis of some dataset or (ii) a software project that enhances the current set of RA tools. The advanced topics will include most (or all) of the following: state-based RA and k-systems analysis; RA loopless models with many variables ("dependency analysis"); identification with inconsistent data; set-theoretic RA and binary decision diagrams; intra-model analysis; modeling with latent variables; RA and genetic algorithms; Fourier-based RA techniques; binning; the OCCAM software package.

SYSC 552: Game Theory

Game theory involves the study of cooperation and competition, without regard to the particular entities involved, and issues of rationality associated with such phenomena. Sysc 552 presents the basic ideas of game theory, especially those concerning (a) 2-person zero-sum games, which the theory solves, and (b) 2- (or nequivalent-) person nonzero-sum games, which have no general solution and which often exhibit paradoxical features. Of particular substantive interest are dilemmas of collective action, which characterize many social, economic, and political problems. Of particular methodological interest are simulation techniques used to extend game-theory into domains where analytical results are impossible.

Also covered are (c) 2-person cooperative games (bargaining & arbitration), which have alternative plausible solutions; (d) coalition theory (nnon-equivalent-person games), in which analysis is complex and limited; and (e) social choice theory, which reveals the difficulties in integrating individual preferences into collective decisions. Emphasis in the course is on the findings of game theory, especially as they apply to the social sciences, rather than on the purely technical aspects of the theory.

SYSC 557: Artificial Life

"Artificial Life" (ALife) is a name given to theoretical, mathematical, and computationally "empirical" studies of phenomena commonly associated with "life," such as replication, metabolism, morphogenesis, learning, adaptation, and evolution. It focuses on the materiality-independent, i.e., abstract, bases of such phenomena. As such, it overlaps extensively with "theoretical biology" and, less extensively, with certain areas of physics and chemistry and the social sciences. It also raises important philosophical questions. It is part of a larger research program into "complex adaptive systems," one stream of contemporary systems theory.

In its intersection with computer science, ALife is the newest example of "the sciences of the artificial" (Herbert Simon). ALife is to life what AI is to intelligence. Christopher Langton writes that "Artificial Life ... complements the traditional biological sciences ... by attempting to synthesize life-like behaviors within computers and other artificial media." The purpose is twofold: to understand these phenomena better and to develop new computational technologies.

SySc 557 will sample the research literature in this field, and will be organized in a seminar format. Topics to be emphasized are: (1) discrete dynamics: cellular automata and random networks, (2) ecological & evolutionary dynamics, (3) genetic algorithm optimization and adaptation, (4) agent-based simulation. Other topics will include: artificial and real chemistry (metabolism, reproduction, & origin of life), "complex adaptive systems," autonomous agents, and philosophical issues.

SYSC 521: Systems Philosophy

This seminar will consider some philosophical issues central to the systems field. Fundamental to these issues is Bunge's conception of systems science as a research program aimed at the construction of "an exact and scientific metaphysics," that is, a set of concepts, models, and theories of broad generality and philosophical import, which are applicable to the sciences, and which are cast (or capable ultimately of being cast) in the exact language of mathematics.

The course will present a broad range of systems ideas (from information theory, game theory, thermodynamics, non-linear dynamics, decision theory, and many other areas) and attempt to integrate these ideas into a coherent framework. These ideas will be organized around the theme of fundamental "problems," that is, difficulties (imperfections, modes of failure) encountered by many systems of widely differing types. While most of these ideas are mathematically-based, they will be approached in this course primarily at a conceptual level (with mathematical details provided as requested). Many of these systems ideas derive from the natural sciences and engineering, but they apply as well to the social sciences and to fields of professional practice (business, the helping professions, etc.). It is primarily their relevance to the human domain -- to individuals, groups, organizations, and societies -- and to technology which motivates this theoretical/philosophical inquiry. Certain of these ideas pertain also to the arts and humanities.

SYSC 510: Systems Ideas & Sustainability

This course will examine systems-theoretic ideas that bear on sustainability. These ideas come from graph theory, non-linear dynamics, game and decision theory, thermodynamics, theories of complex adaptive systems, and from systems-oriented theories in the earth sciences, ecology, sociology, and history. The ideas shed light on the causes of sustainability problems and on the principles that might guide attempts to solve these problems. A talk introducing these ideas and their relevance to sustainability is at Many of the systems ideas covered in this course are mathematically-based, but the ideas will be presented mainly at a conceptual level (with mathematical details provided as requested).

Topics will include

  • macro-historical perspectives on the sustainability challenge
  • world systems and earth systems models
  • the classic limits to growth studies, updated
  • the Panarchy model of adaptation in ecological & social systems
  • the Tragedy of the Commons and its possible solutions
  • energy and entropy dimensions of sustainability.



Table 1. Degree of mathematical content and topic specialization of courses

Topic Specialization

low (survey course)

high (one topic course)

Math Content


Discrete Multivariate Modeling1



Systems Theory

Artificial Life

Data Mining with Information Theory

Game Theory


Systems Philosophy

Systems Ideas & Sustainability

SP: 510/610; ST: 511/611; AL: 557/657; DMM: 551/651; GT: 552/652

I am comparing the relative mathematical content only of my own courses; I'm not quantifying how mathematical my courses are compared to courses given by other faculty.

1Although the Discrete Multivariate Modeling course is listed as having "high" mathematical content, it is accessible to social science students who have taken courses in probability and statistics. Calculus is not needed for DMM.