CNCS Center for Nonlinear and Complex Systems
NCS 201: Survey of Topics in Nonlinear and Complex Systems

Graduate Certificate in Nonlinear and Complex Systems


The purpose of the certificate is to broaden the scope of the typical disciplinary graduate student traning program. Students are encouraged to develop interdisciplinary and transferable sets of skills in their course work and research activities.  The certificate program helps to guide students toward this broad view by requiring the completion of: 
  • a survey course (CNCS 201, Topics in Nonlinear and Complex Systems );
  • four courses from an approved list; and
  • a Ph.D. dissertation on a topic in the domain of the Center.
In addition, the student must have two members of the Center on her or his Ph.D. dissertation committee.

Obtaining the Certificate

Students are encouraged to meet together with their dissertation thesis advisor and the Associate Director of the Center (currently Prof. Virgin) early in their graduate program to help with course planning and dissertation committee selection.

The only formal paperwork that must be completed to obtain the certificate occurs when the student's Ph.D. dissertation is submitted to the Graduate School.  The student should check the box on the Graduate School "Intent to Receive Degree Form" indicating that they would like to receive the CNCS Graduate Certificate.  The student must then send the Associate Director of the Center the following information:

  • the semester(s) when CNS 201 was taken
  • the name of the four courses taken (from the approved list)
  • the Ph.D. dissertation title
  • the list of final Ph.D. dissertation committee members
  • the date of the final defense
  • the final Ph.D. dissertation abstract
  • the student's graduate transcript

Biomedical Engineering
Civil Engineering
Computer Science
Earth and Ocean Sciences
Electrical Engineering
Mechanical Engineering and Materials Science
School of the Environment


268. Ecological Theory and Data
291. Mathematical Biology
292. Population Ecology
293. Simulating Ecological and Evolutionary Systems
303. Principles of Ecological Modeling
304. Plant Growth Modeling

Biomedical Engineering

201. Electrophysiology
204. Measurement and Control of Cardiac Electrical Events
207. Transport Phenomena in Biological Systems 
212. Theoretical Electrocardiology 
213. Nonlinear Dynamics in Electrophysiology 
216. Transport Phenomena in Cells and Organs 
229. Tissue Mechanics 
231. Intermediate Biomechanics 
239. Cell Transport Mechanisms 
244. Mathematical Models of Physiological Systems 
246. Computational Methods in Biomedical Engineering 
250. Cardiovascular Mechanics 
331. Viscoelasticity 

Civil and Environmental Engineering

201. Advanced Mechanics of Solids 
303. Plasticity 
207. Transport Phenomena in Biological Systems 
210. Intermediate Dynamics 
225. Dynamic Engineering Hydrology 
237. Advanced Soil Mechanics 
245. Pollutant Transport Systems 
252. Buckling of Engineering Structures 
255. Nonlinear Finite Element Analysis 
263. Multivariable Control 
283. Structural Dynamics 

Computer Science

240. Computational Complexity 
250. Numerical Analysis 
252. Numerical Methods for Partial Differential Equations
264. Nonlinear Dynamics 
270. Artificial Intelligence 
271. Numerical Artificial Intelligence
350. Topics in Numerical Mathematics
364. Advanced Topics in Nonlinear and Complex Systems 

Earth and Ocean Sciences

203. Physical Oceanography
207. Analysis of Coastal Engineering Models
221. Hydrogeology
222. New Perspectives and Methods in the Earth Sciences
223. Computational Methods in Hydrologic Sciences
230. Advanced Structural Geology
250. Applied Mathematics for the Environmental and Earth Sciences
252. Geophysics and Crustal Dynamics

Electrical and Computer Engineering

241. Linear Systems: Theory and Control
243. Pattern Classification and Recognition
255. Mathematical Modeling for Systems Analysis I
258. Artificial Neural Networks
263. Multivariable Control
281. Random Signals and Noise
282. Digital Signal Processing
285. Signal Detection and Extraction Theory
288. Image and Array Signal Processing
289. Adaptive Filters
299. Nonlinear Control Systems (Advanced Topics)


216. Applied Stochastic Processes
221, 222. Numerical Analysis
224. Scientific Computing I
225. Scientific Computing II
226. Topics in Numerical Analysis
228. Mathematical Fluid Dynamics
231. Ordinary Differential Equations
232. Partial Differential Equations I
233. Asymptotic and Perturbation Methods
239. Mathematical Modeling
281,282. Partial Differential Equations II, III

Mechanical Engineering and Materials Science

202. Engineering Thermodynamics 
207. Transport Phenomena in Biological Systems
209. Soft Wet Materials and Interfaces
210. Intermediate Dynamics
216. Mechanical Metallurgy 
217. Fracture of Engineering Materials 
221. Compressible Fluid Flow
225. Mechanics of Viscous Fluids
226. Intermediate Fluid Mechanics
227. Advanced Fluid Mechanics
229. Computational Fluid Dynamics and Heat Transfer 
230. Modern Control and Dynamical Systems
231. Adaptive Structures 
232. Optimal Control 
235. Advanced Mechanical Vibrations
237. Aerodynamics 
238. Advanced Aerodynamics 
239. Unsteady Aerodynamics 
252. Buckling of Engineering Structures 
280. Convective Heat Transfer 
290. Physical Oceanography 
325. Aeroelasticity 
331. Nonlinear Control Systems 
335. Nonlinear Mechanical Vibration 


213. Introductory Nonlinear Dynamics
230. Mathematical Methods in Physics 
271. Quantum Optics
281. Classical Mechanics 
303. Statistical Mechanics
304. Advanced Topics in Statistical Mechanics
313. Advanced Nonlinear Dynamics
318. Fundamentals of Electromagnetism
319. Advanced Electrodynamics 

School of the Environment

216. Applied Population Ecology
290. Physical Oceanography
356. Environmental Fluid Mechanics