University of Waterloo Complex Systems Courses

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 332: An Introduction to Complex Systems (Winter Term)

Lecture T/Th 3:30 - 5 p.m. | Tutorial Th 5-6 p.m. 

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, topic 1: Algebraic Structure of Discrete Dynamical Systems (Winter Term)

T 1:30 - 3 / Th 10-11:30 a.m. (in E5 room 6002)

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: Modern Computational Approaches to Human-Natural Systems Modelling  (Winter 2020)

      M 1:30 -3 p.m

Description: Ability to model coupled human-natural systems involing feedbacks has been boosted by recent computational advances in solving large scale systems using agent-based modelling, machine intelligence, big data, in addition to traditional differential equations models. This course will explore sociohydrology as an example. Sociohydrology is a relatively new field and was formulated to study the feedback effects of the hydrologic cycle on people and people on the hydrologic cycle. The study of co-evolution between hydrologic and socio-economic systems is necessary to assess how these systems interact and evolve. Many domain experts will present their work in this course.This an advanced level course of material in SYDE 332.


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

MW 10-11:30 a.m.


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

MW 10-11:30 am


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