Analysis

The study of analysis provides a basic understanding of qualitative and quantitative problem-solving techniques, the ability to analyze new areas of interest, and the ability to interact with colleagues from other disciplines in a problem-solving situation. Modern applications of analysis include biomedical modeling, image analysis, robotic control, ecology, environmental modeling, and financial engineering.

Faculty

D. Ambrose » applied analysis, scientific computing, nonlinear PDEs, free-surface problems in fluids
J. Brannan » mathematical modeling, stochastic analysis, financial mathematics
R. Fennell » applied and industrial mathematics, control theory and applications
J. Hoffacker » dynamic equations on time scales, biological modeling
T. Khan » inverse problems, parameter estimation, optical tomography, biomedical imaging, control problems
H. MacMillan » inverse problems, PDEs, multigrid, systems biology
J. Peterson » distributed computing, biological modeling, neurobiology, neuroscience
J. Reneke » decision making under uncertainty, financial mathematics
J-R Yoon » medical imaging, inverse problems, elasticity theory, seismic inversion

Curriculum

A plan of study for students concentrating in analysis will include courses in theoretical analysis, applied analysis, numerical analysis, and physical system modeling.

Courses

	linear analysis	measure and integration
	complex analysis	functional analysis
	partial differential equations	Fourier series
	dynamical systems	optimal control
	applied mathematics	numerical analysis
	neural networks	investment science
	stochastic calculus for finance	computational finance

Sample Curricula

- Sample Program for M.S. Concentration in Analysis

FALL: 810, 853, 825/826

SPRING: 805, 821, 860

SUMMER: 803

FALL: 841, 861, 825/826

SPRING: 809, 811, 831, 892

- Sample Program for M.S. Concentration in Financial Mathematics

FALL: 805, 810, 853

SPRING: 821, 860, 974

SUMMER: 803

FALL: 804, 982, MBA 846

SPRING: 809/811, ECON 855, 982, 892

Recent M.S. Graduates (master's project title)

Ethan Baldwin ("Machine Learning Using a Recurrent Neural Network")
Steven Charlesworth ("Neural Network Cluster Models")
Steven Crawford("Topology and Distributions Theory")
Bing Cui ("Option Pricing with GARCH-Based Volatility Model")
Sherlene Enriquez ("Univariate Time-Varying Volatility")
Matthew Fawcett ("Modeling 3D Worlds")
Kelly Graham ("Vector Recognition Using a Neural Network")
Dyon Hanson ("Structured Neural Networks with Performance Guarantees")
Christina Juergens ("Vibration Suppression of Simple Space Station Models Using Position and Velocity Feedback")
Somchai Liangrokapart ("Fitting Financial Models Using Limited Data")
Prasit Limbupasiriporn ("Probabilistic and Numerical Approaches for Transport in Random Flows")
Eric Lowenstein ("Testing the Lorenz Force Equation")
Erin McNelis ("Analyzing a Model for the Heartbeat")
Gaurav Narwani ("The Implications of Macroeconomic Factors on a Period Optimal Portfolio Investment Strategy")
Jun Ni ("Active Versus Passive Portfolio Management")
Kashema Rock, Jakeisha Thompson ("Decision Modeling with Risk Management Methodology")
John Paul Roop ("Motivated Autonomous Agents")
Snehanshu Saha ("Hodgkin Huxley Excitable Cell Models")
Sundeep Samson ("Performance Based Decisions Under Uncertainty for Complex Systems: A Manual")
David Szurley ("The Effect of Changing the Coriolis Force Gradient Parameter on the Escape Probability and Mean Residence Time")
Jiangxia Wang ("Estimation of Implied Volatility Smiles from S&P 500")

Recent Ph.D. Graduates (dissertation title)

Steve Benz ("Parameter Estimation in a Reproducing Kernel Hilbert Space for Linear Hereditary Systems")
Steve Black ("Coordination of Control for Large-Scale Systems")
Mark Copeland ("Neural Network Dynamical Systems for Associative Memory and Control")
Mike Grabbe ("Optimal Control of Robot Manipulators")
Edward Jennings ("Approximate Solutions of the 3-D Helmholtz Equation as Applied to Underwater Acoustic Propagation")
Belinda King ("Modeling and Control of Multiple Component Structures")
Linda Lawson ("Multigrid Dynamic Programming")
Christopher Lee ("Studies in Dynamical Systems")
Dale McIntyre ("Time Invariance and Stability of Stochastic Linear Hereditary Systems as Characterized by Their Covariance Functions")
Karin Vorwerk ("Frequency Domain Methods for Distributed Parameter Systems")
Christian Wypasek ("Stochastic Models for Workstation Utilization")

Current Ph.D. Students (dissertation advisor)

Sundeep Samson (J. Reneke)
Alan Thomas (T. Khan)

Additional Analysis Links

Last Updated: July 7, 2005
Send comments to: shierd@clemson.edu