University of Waterloo Complex Systems Courses

!NEW! PLAN 474/674: Introduction to Agent-Based Modeling Online Course (Winter 2023)

T 1:30 - 2:50 p.m. | Th 10:30-11:30 a.m., 1:30-2:30 p.m.

Description: An online training course offered by the University of Waterloo via the SMART Healthy Cities program, this course helps students to learn about Agent-Based Modeling (ABM), which is a computational simulation framework that explores how natural and social phenomena emerge from micro-level components.

Participants will learn about complex systems, explore and expand existing models using a simple programming platform (Netlogo), develop and experiment with their own model, and interact with international scholars and students from across Canada.

For more information about the course please

View the full course outline.

GGOV 622: Complexity and Global Governance (Winter 2023)

Thursdays 10 a.m. - 12:50 p.m. (BSIA 316)

Description: After introducing key concepts, theories, and tools from complexity science, this seminar explores its most recent empirical findings in several global governance domains, including environment, political economy, and security. Students will assess the value-added and policy implications of the complexity approach while developing their own research projects.

Course outline

HEALTH 654: Systems Thinking and Analysis in Health Program Planning and Evaluation

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INTEG 120: The Art and Science of Learning (Fall Term)

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INTEG 251: Creative Thinking (Fall or Winter Term)

(check availability; usually offered every other year)

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INTEG 440/640: Computational Social Science (Winter Term - online course)

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INTEG 441/641: Hard Decisions and Wicked Problems (Fall or Winter Term)

(check availability; usually offered every other year)

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SYDE 532: An Introduction to Complex Systems (Winter Term)

Description: The overwhelming majority of societal and ecological issues of pressing importance are complex systems; nonlinear interacting systems poorly characterized by linear analyses and Gaussian statistics. This course introduces the mathematics needed to understand such interactions, including nonlinear dynamics, critical and bifurcation behaviours, large-scale systems, power-law distributions, and statistical inference. The mathematical methods will be motivated by a set of case studies comprised of pressing large-scale interconnected problems such as global warming, energy shortages, desertification, overpopulation, poverty, and economic instability, to be investigated from a systems engineering perspective that will connect the mathematical analyses to real-world examples.

SYDE 710 - Topics in Mathematics: Algebraic Structure of Discrete Dynamical Systems (Winter Term)

Description: The course lays mathematical foundations for Algebraic Intelligence – an approach to Artificial Intelligence that exploits the hidden algebraic structure of any dynamical system with discrete finite spaces of states and events.  Examples have multiple types of discrete events (or inputs) transforming their states, and include finite automata, Petri nets, Boolean networks, permutation groups, transformation semigroups, and graph networks. Such discrete-event dynamical systems arise in many branches of science, engineering, artificial intelligence, computer science, and pure mathematics, and have links to invariants and conservations laws in physics, and applications to systems biology, gene regulatory and biochemical networks, reaction graphs, among other areas.   

The algebraic analysis of these systems identifies *natural subsystems* (“pools of locally reversible computation”, which are certain special permutation subgroups) and allows one algorithmically to derive *hierarchical coordinate systems* (wreath product decompositions).  Using this mathematically derived hidden algebraic structure, a human (or an AI) can understand and manipulate the given discrete-event dynamical system.   

Target topics include: Background from Abstract Algebra (Homomorphisms, Simple Groups, Permutation Groups, Transformation Semigroups, Covering Morphisms, Lagrange’s Theorem for Symmetry Structures, Wreath Products); Coarse-to-Fine Graining and Hierarchical Manipulation; Frobenius-Lagrange Coordinates on Permutation Groups, and Applications to Permutation Puzzles (e.g. Rubik’s Cube); Natural Subsystems of Discrete Event Systems (plus their Permutator Semigroups and Holonomy Groups); Global Hierarchical Coordinate Systems (Holonomy Decomposition, Krohn-Rhodes Prime Decomposition); Selected Topics from: Computer Algebraic Implementations, Complexity Measures, Complete Invariants for Graphs, Generalizations to Growing and Changing Networks, and AI applications

SYDE 730: Complex Systems

Description: Nonlinear interacting dynamic systems represent a fascinating domain in systems engineering.  Although a rigorous analysis of such complex systems can be tremendously difficult, at a systems level there are quite common themes which emerge, and which can offer a significant degree of conceptual understanding.

This seminar/reading course seeks to explore advanced topics in the understanding and high-level properties of complex systems, particularly as motivated by an exploration of societal and environmental systems, particularly the interaction of people with their physical environment.  Examples of such problems are all around us, including global warming, water dead zones, soil desertification, food production, and poverty, none of which can be understood or solved on the basis of examining single pieces of an interlocking puzzle.

SYDE 750 topic 37 / ECE 750 topic 33: Artificial Life - Biology & Computation (Spring 2019)

SYDE 750 topic 38 / ECE 750 topic 34: Artificial Life - Embodied Intelligence (Fall 2019)