
Past GT nonlinear Science courses 

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Spring 2007

Fall 2006

Spring 2006

Fall 2005

Spring 2005

Fall 2004

Spring 2004

Fall 2003

Spring 2003

Fall 2002

Spring 2002

Fall 2001

Spring 2001
[
GT nonlinear graduate courses

undergrad info
]
(sorry, a bit incomplete)
Fall 2006
Renormalization Group Theory  Predrag Cvitanović
PHYS 8803  Advanced graduate level course providing
introduction to Renormalization Group Theory and its applications to
phase transitions, bifurcations, etc.
Statistical
Mechanics  Bellissard
PHYS 7123  Principles of nonequilibrium statistical
mechanics,
both classical and quantum. Emphasis is on the dynamics of
fluctuations, their
measurement, and their relationship to transport
properties.
Introduction
to Continuum PhysicsRoman Grigoriev
PHYS 4421 The course aims
to redress the balance by offering a modern,
unified introduction to the basic concepts and phenomenology of
continuous
systems.
The course is
intended for physics, biology,
math, engineering and geophysics
advanced undergraduates, starting graduate students. The mathematical
prerequisites are modest and are developed further as the need arises.
Dynamics of
Turbulence  P.K.
Yeung
AE 6080 This is a secondlevel course on
turbulence, building on the introductory material presented in AE
6012. The emphasis is on fundamental physical understanding, and
on the
use of this knowledge in building
turbulence models. Students are encouraged to explore the
literature on current research developments, including largescale
numerical computations.
Biophysics  Ron
Fox
PHYS 4802  The course will cover cellular and subcellular
biophysical mechanisms that are crucial to life. Some mechanisms may
have
applications in nanotechnology. Advanced undergraduates and graduate
students
are welcome. No prior knowledge of the material is required.
Spring 2006
Nonlinear
Dynamics & Chaos  Predrag Cvitanović
PHYS 4267/6268  graduate/advanced undergraduate level. The
material covered includes differential equations, their stability and
bifurcations, iterated maps, deterministic chaos, fractals, and strange
attractors with applications to physical, chemical, and biological
systems.
Enforced Prerequisites MATH 2403 OR MATH 2413 OR MATH 24X3 OR MATH
3308. Basic
knowledge of computer programing required.
Spatiotemporal
Dynamics and Pattern Formation
 Roman Grigoriev
PHYS 8803RG  This advanced graduate level course will
develop
a
general theory of pattern formation in nonequilibrium systems using
linear
stability theory, bifurcations and symmetry analysis. A broad variety
of
physical, chemical, and biological systems will be used as examples.
Knowledge
of partial differential equations (at the level of MATH 4581 or PHYS
6124) is required. The continuum mechanics course PHYS 4421 and
introduction to nonlinear dynamics PHYS 4267, although not
prerequisites, will provide helpful background.
ChaosBook.org study group:
Chaos, and what to do about it
PHYS 8901PC 
Jan to Apr 2006, Man, Wed 4:055:25pm in Howey W505
Nonlinear
Journal
Club
PHYS 8901PC 
Jan to May 2006, 3 to 7 Special Problems credits
Fall 2005
Continuum mechanics
 Roman Grigoriev
PHYS 4421/8803  for graduates and advanced undergrads from
physics, engineering, math, atmospheric sciences.
Statistical Mechanics II  Kurt
Wiesenfeld
PHYS 7123  Principles of nonequilibrium statistical
mechanics,
both classical and quantum. Emphasis is on the dynamics of
fluctuations, their
measurement, and their relationship to transport properties.
Biophysics  Ron
Fox
PHYS 4251  The course will cover cellular and subcellular
biophysical mechanisms that are crucial to life. Some mechanisms may
have
applications in nanotechnology. Advanced undergraduates and graduate
students
are welcome. No prior knowledge of the material is required.
Fall 2004
TR 09:3510:55, Howey Physics S106
Statistical
Mechanics II  Kurt
Wiesenfeld
PHYS 7123  Principles of nonequilibrium statistical
mechanics,
both classical and quantum. Emphasis is on the dynamics of
fluctuations, their
measurement, and their relationship to transport properties.
TR 08:009:55, Howey Physics S204
Biophysics
 Ron
Fox
PHYS 4802  The course will cover cellular and subcellular
biophysical mechanisms that are crucial to life. Some mechanisms may
have
applications in nanotechnology. Advanced undergraduates and graduate
students
are welcome. No prior knowledge of the material is required.
MWF
11:4512:35
PHYSICS
8803C  This
course is a broad introduction to quantum information theory and
quantum communication theory. Topics to be covered include:
closed and
open quantum
system dynamics, mathematical
formulation of a quantum channel, the complete positivity constraint on
quantum channels, measurements in closed and
open quantum systems, the
classical channel capacity of a quantum
channel, the quantum state channel capacity of a quantum channel,
quantum state compression,
quantum state
coding theory, and open questions in Quantum Information Theory.
The
discussion of each topic will begin with an overview of the classical
concept, and proceed to
the quantum version.
MWF 11:0011:55,
Skiles MATH 240
Numerical
Methods: Partial Differential Equations  Liu
MATH 6640  The goal of this course is to cover the
fundamental
issues of numerical solution of DE's, with examples from different
physical
contexts. Our intent is to examine various methods of numerical
solution,
investigate their strengths and limitations, and understand the
approximations
and errors involved. A major part of the course will be final projects
in which
each student conducts a computational investigation on a problem of
special
interest to the student. The course is divided roughly into four parts:
(1)
Ordinary Differential Equations (2) Finite Difference Methods (3)
Finite
Element Methods (4) Pseudospectral Methods
TR 01:3502:55, Instr. Center 217
Introduction
to Fluid Mechanics  Neitzel
ME 6601  The fundamentals of fluid mechanics. Derivation of
the governing equations of motion. An introduction to viscous,
inviscid,
turbulent, and boundarylayer flows.
TR 3:25  4:55, Skiles (TBA)
Modeling
and Dynamics
(i.e., Introduction to Dynamical Systems for Life Sciences)  Mason Porter
MATH 6705 
An introduction to dynamical systems with a focus on the
life sciences, specifically aimed towards people with
appropriate majors related to biology or chemistry. It requires only
calculus I and II, so we'll be doing ODE's from a dynamical systems
perspective. The problems will come from the life sciences, so we'll be
looking at things like predatorprey models, disease dynamics,
excitable
media. Towards the end of the class, we'll get into things like
synchronization, reactiondiffusion systems, and perhaps even a bit of
biology systems on networks.
Note: Credit only
for individuals in the biological sciences
MWF 2:002:55, Skiles MATH 246
Dynamics
and Bifurcations I  Chow
MATH 4541  A broad introduction to the local and global
behavior of nonlinear dynamical systems arising from maps and ordinary
differential equations.
MWF 1:05 
1:55, Skiles MATH 271
MATH 6307 
Graduate level ODE: This sequence develops the qualitative theory
for systems of
ordinary differential equations. Topics include stability,
Lyapunov
functions,
Floquet theory, attractors,
invariant
manifolds, bifurcation theory, and normal forms.
MWF 2:05 
2:55, Skiles MATH 270
MATH 6514 
Applied mathematics techniques to solve realworld problems.
Topics include mathematical modeling, asymptotic analysis,
differential equations and
scientific computation.
MWF 12:05 
22:55, Skiles MATH 256
MATH 6584 
Special Functions of Higher Mathematics
Gamma function; exponential function; orthogonal
polynomials; Bessel, Legendre, and hypergeometric
functions;
application to singular ordinary differential equations; and
separation of variables for partial differential
equations.
Spring 2004
TR 12:051:25, Howey Physics S104
Continuum mechanics
 Predrag Cvitanovic'
PHYS 4421
 for grads and advanced undergrads from physics, engineering, math,
atmospheric sciences.
Text: Benny Lautrup,
Continuum
Physics, Exotic and everyday Phenomena in the Macroscopic World,
the only modern advanced undergraduate
textbook introduction into the subject.
TR 01:352:55, Howey Physics S106
Quantum Info and Computation
 Jean Bellissard
MATH 4803 BDG
 Only for College of Science. Graduate students can register without prerequisie override.
Undergraduate students must register for MATH4803BDU, CRN24286.
TR 01:352:55, Howey Physics S106
Quantum Info and Computation
 Jean Bellissard
MATH 4803 BDU
 Only DMTH MATH majors. Graduate students must register for MATH4803BDG, CRN24293.
Taught jointly with CS4803QIC, CRN 21345, and PHYS 4803A, CRN 24576.
MWF 01:0501:55, Skiles (TBA)
Intro to Mathematical Modeling
 Mason Porter
MATH 4803 POR
 Undergraduate and graduate students wanted. Prerequisites: Calculus I  IV and a willingness to work hard.
The purpose of this course is to introduce undergraduates in math, science and engineering (and interested graduate students)
to the rudiments of mathematical modeling with a case study approach. Continuous and discrete systems and applications from numerous
scientific disciplines will be considered.
MW 03:054:25, Skiles 108A
Computational Homology
 Konstantin Mischaikow
MATH 4432 A
 Enforced prerequisite: MATH 4317
Course aimed at a broad audience including students from mathematics, physics,
computer science and engineering.
Prerequisites are minimal, a solid understanding of linear algebra and continuous functions.
MWF 11:05  11:55, Cherry Emerson 204
Theoretical Ecology
 Christopher Klausmeier
BIOL 4423/8803B
 Theoretical foundations of ecology, from the population to the community and ecosystem levels.
Topics: Singlespecies models; TwoSpecies Interactions; Community Modules; Food Webs; Biodiversity Effects;
Spatial Processes; Nonequlibrium Processes; Ecological Stoichiometry; Allometry; Ecosystem Links; Evolutionary Ecology;
Community Assembly.
From Professor Klausmeier: If any students and/or postdocs are interested in applying nonlinear dynamics to ecological
problems, this class will provide the necessary background. I would love to see
some physicists show up. . .no previous biology needed.
MWF 09:05  09:55, Howey Physics S204
Thermodynamics
 Ronald Fox
PHYS 3141 Enforced Prerequisites PHYS 2212 or PHYS 2232 or PHYS 2123 AND
MATH 2403 or MATH 2413 or MATH 24X3 or MATH 3308.
MWF 09:05  09:55, Howey Physics S106
Nonlinear Dynamics & Chaos
 Kurt Wiesenfeld
PHYS 4267 Enforced Prerequisites MATH 2403 OR MATH 2413 OR MATH 24X3 OR MATH 3308. Basic knowledge of computer programing required.
MWF 12:05  12:55, Howey Physics S104
Classical Mechanics II
 Ray Flannery
PHYS 6102 Enforced Prerequisites PHYS 6101
Fall 2003
Spring 2003

Introduction to nonlinear dynamics and chaos
 Kurt Wiesenfeld
phys 4267 
a service graduate/advanced undergraduate course
course with at least 50% students outside physics.
(Should be crosslisted in other Schools)

Classical Mechanics II
 Raymond Flannery
phys 6102
 fast track grads

Spatiotemporal Dynamics and Pattern Formation

Roman Grigoriev
phys 7224  advanced graduate:
this year the emphasis is on
patterns, extended systems and spatiotemporal chaos.

Numerical Methods for Dynamical Systems
 TBA
math 6647
 advanced graduate:
Approximation of the dynamical structure of a differential equation and preservation of dynamical structure under discretization.

Quantum Information and Quantum Computing
 Jean Bellissard
PHYS 4803 A LPA 28057 Special Topics 3 0 20 TR 01350255pm  Place TBA
Secondary Title: Quantum Info and Computation
Enforced Prerequisite(s): MATH 2401
Prerequisites MATH2401 and familiarity with matrix calculus
and finite dimensional vector spaces.
Taught jointly with Math4803BDU and CS4803F

Theoretical Chemisty of Polymers
 Rigoberto Hernandez
chem 6755
 advanced graduate: Equilibrum and nonequilibrium
theories for polymers (crosslisted with CHE, MSE and TFE 6755).

Field theory

Predrag Cvitanovic'
phys 7147  Quantum Field Theory,
introduction to quantum field theory: path integrals
Feynman diagrams,
diagrammatic purtubation theory,
variational methods, renormalization theory.
Fall 2002
TR 12:00am01:00pm, Howey TBA:
(R)evolution of physics.
 David
Finkelstein
The main evolutionary leaps of 20th century
physics: spacetime theory, quantum theory, and gauge theory, at the
rudimentary level
phys 2001  Text: Smolin, Three roads to quantum gravity.
Basic Books, 2001.
TR 09:3510:55, Howey N209:
Continuum mechanics
 Predrag Cvitanovic'
phys 4421
 for grads and advanced undergrads from physics, engineering, math,
geophysics.
Text: Benny Lautrup,
Continuum
Physics, Exotic and everyday Phenomena in the Macroscopic World,
the only modern advanced undergraduate
textbook introduction into the subject.
MWF 10:0510:55, Howey L5:
Classical Mechanics I
 Ian Gatland
phys 6101
 introductory graduate course
TR 12:051:25, 108B Skiles:
Modeling and Dynamics

L.A. Bunimovich
TR 02:00pm03:00pm , Van Leer C457
Quantitative Electrophysiology
 Robert Butera
ECE6787/BMED6787
 a quantitative description of the dynamics of electrically excitable
cells (mostly neurons, also cardiac and muscle), both
measurement and modeling.
 NonECE students should register for
the BMED listing.
TR 08:0509:25am, Howey TBA:
Statistical mechanics II: Stochastic processes and nonequilibrium
statistical mechanics
 Ron Fox
phys 7123  advanced graduate:
this year the emphasis is on stochastic and nonequilibrium processes.
TR 01:00pm02:00, Howey TBA:
Physics of philosophy
 David
Finkelstein
phys 8802
 a physicist looks at the questions of
philosophers; the inverse of the philosophy of physics.
TR 06:00pm09:00, Howey TBA:
Quantum relativity workshop
 David
Finkelstein
phys 8803
 ongoing research into postquantum
physics, currently exploring a new concept of elementary quantum processes
Summer 2002
Spring 2002

Introduction
to nonlinear dynamics and chaos
 Roman Grigoriev
phys 4267 
a service graduate/advanced undergraduate course
course with at least 50% students outside physics.
(Should be crosslisted in other Schools)

Nonlinear dynamics: Quantum chaos

Predrag Cvitanovic
phys 7224  advanced graduate:
this year the emphasis is on semiclassical methods in quantum mechanics and
quantum chaos. It will be easier going for those who have taken
Fall 2001 phys 7123.
Text: Quantum dynamics chapters of
Classical
and quantum chaos
webbook by P. Cvitanovic' et al.

Group Theory and Quantum Mechanics

John Wood
PHYS 7143
 graduate:
Foundations of group representation theory with applications in atomic, molecular, nuclear, and solidstate physics.

Information
Theory
 Professor L.
Bunimovich
 Important in information technologies.

Algebraic
Topology

Professor Mischaikov
With a computational approach motivated by applications in
image processing, dynamics and numerical analysis.
Fall 2001
MWF 9:059:55, 108A Skiles:
Chaotic Dynamics: Operator approach

Michael Blank
math 8823  advanced graduate special topics course,
the emphasis on PerronFrobenius operators which move
probability distributions.
M. Blank,
visiting from Inst. of Information Transmission Problems, Moscow,
works and publishes with physicists and biologists, so this course is
recommended also for advanced graduate students outside mathematics.
MWF 10:0510:55, Howey L5:
Classical Mechanics I
 Raymond Flannery
phys 6101
 introductory graduate course
MWF 1:051:55, 108A Skiles:
Interacting particle systems

Markos A. Katsoulakis
math 8833  advanced graduate special topics course
on large scale limits on interacting particle systems.
TR 1:352:55, 167 Skiles:
Introduction to Numerical Methods for PDEs
 Peter J. Mucha
Mon 2:052:55, Howey N110:
Nonlinear Science Seminar
MWF 3:053:55, 108A Skiles:
Probability: Trees & networks

Russel Lyons
math 8803  advanced graduate special topics course
on dynamics of networks.
Center for Dynamical Systems and Nonlinear Studies Colloquium
TR 09:3510:55, Howey L5:
Classical Mechanics II
 Raymond Flannery
phys 6102
 fast track grads
TR 11:0512:25, Howey S106:
Statistical mechanics II: Chaos, and what to do about it

Predrag Cvitanovic
phys 7123  advanced graduate:
this year the emphasis is on chaotic dynamics, evolution operator
formalism and chaotic dynamics theory of nonequilibrium processes.
Part I of 2 semester sequence, with quantum chaos to be taken up
in phys 7224.
Can be taken in tandem with math 8823.
Text: Classical dynamics chapters of
Classical
and quantum chaos
webbook by P. Cvitanovic' et al.
Tue 12:351:25, Skiles 255:
Dynamics Informal Brown Bag Lunch Chat
Nanobiology
 Ronald Fox
phys 4802/8802
 terminology, concepts and mechanisms of biology at the nanometer scale
Spring 2001
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