ECE 421

Catalog Data: 

ECE 421 - Complexity (3 units)

Description: Complexity is an approach studying how interconnected parts give rise to the collective behavior of large systems and how the systems interact with their environment. It cuts across all traditional disciplines including science, engineering, medicine and management. 

Grading: Regular grades are awarded for this course: A B C D E

May be convened with ECE 521


Recommended reading list available from instructor.

Course Learning Outcomes: 

By the end of this course, the student will understand:

  1. The key issues associated with complexity
  2. The main approaches to studying complexity
  3. The ways of describing complex systems
  4. The process of formation of complex systems
  5. How local interactions give rise to global patterns of behavior
  6. Emergent phenomena
  7. Analytical and computational tools for studying complexity
  8. The main application areas of complexity
Course Topics: 


  • Introduction
  • Complexity in areas such as physics, mathematics, engineering, society, weather, traffic, and even families

Common principles and characteristics of complex systems 

  • Agents
  • Feedback
  • Learning
  • Adaptation
  • Self-organization
  • Emergence
  • Phase transitions

Approaches to complexity

  • General system theory
  • Cybernetics
  • Chaos
  • Fractals
  • Mandelbrot and Julia sets
  • Cellular automata
  • Swarms
  • Artificial intelligence
  • Search procedures
  • Dynamic programming
  • Decision heuristics
  • Artificial life and societies
  • N-person games
  • Network theory
  • Power laws
  • Neural networks
  • Evolution
  • Self-organized criticality
  • Simulated annealing
  • Models
  • Agent-based simulation
  • Criticism of complexity science

Case studies

Complexity economics

Social norms

Class/Laboratory Schedule: 

Two 75-minute lectures per week

Relationship to Student Outcomes: 

ECE 421 contributes directly to the following specific electrical and computer engineering student outcomes of the ECE department:

  • Ability to apply knowledge of mathematics, science and engineering (medium)
  • Ability to design a system, component or process to meet desired needs within realistic constraints, such as economic, environmental, social, political, ethical, health and safety, manufacturability and sustainability (medium)
  • Ability to identify, formulate and solve engineering problems (high)
  • Ability to communicate effectively (medium)
  • Broad education necessary to understand the impact of engineering solutions in a global, economic, environmental and societal context (medium)
  • Ability to use the techniques, skills and modern engineering tools necessary for engineering practice (high)
Prepared by: 
Miklos Szilagyi
Prepared Date: 

University of Arizona College of Engineering