• Algebra
• Differential Equations and Fourier Analysis
• Differential and Computational Geometry
• Probability and Statistics
• Numerical Analysis
• Operations Research and Optimization

Algebra

• Computer Science
• Cryptology (and the Protection of financial accounts with encrypted codes)
• Scheduling tasks on processors in a heterogeneous multiprocessor computing network
• Alteration of pattern pieces for precise seam alignment
• Study of crystal symmetry in Chemistry (Group Theory)

Differential Equations (Ordinary and Partial) and Fourier Analysis

• Most of Physics and Engineering (esp. Electrical and Mechanical)
• Sound waves in air; linearized supersonic airflow
• Crystal growth
• Cryocooler modeling
• Casting of materials
• Materials science
• Electromagnetics analysis for detection by radar
• Material constitutive modeling and equation of state
• Underwater acoustic signal processing
• Predict the evolution of crystals growing in an industrial crystallizer
• Reentry simulations for the Space Shuttle
• Rocket launch trajectory analysis
• Trajectory prescribed path control and optimal control problems
• Motion of a space vehicle
• Aircraft landing field length
• Design and analysis of control systems for aircraft
• Underwater acoustic signal processing
• Nonlinear dynamics
• Large scale shock wave physics code development
• Material constitutive modeling and equation of state
• Molecular and cellular mechanisms of toxicity
• Transport and disposition of chemicals through the body
• Modeling of airflow over airplane bodies
• Photographic development (Eastman Kodak)
• Waves in composite media
• Immuno-assay chemistry for developing new blood tests
• Radio interferometry
• Free mesons in nuclear physics
• Seismic wave propagation in the earth (earthquakes)
• Heat transfer
• Airflow over airplane bodies (aerodynamics)

Differential and Computational Geometry

• Computer aided design of mechanical parts and assemblies
• Terrain modeling
• Molecular beam epotaxy modeling (computational geometry)
• Color balance in a photographic system
• Optics for design of a reflector
• Cryptology
• Airflow patterns in the respiratory tract

Probability and Statistics

• Calculation of insurance risks and price of insurance
• Analysis of statistical data taken by a census
• Reliability and uncertainty of large scale physical simulations
• Speech recognition
• Signal processing
• Computer network design
• Tracking and searching for submarines
• Estimation of ocean currents (geostatistics)
• Paint stripping using lasers
• Onset and progression of cancer and pre-malignant cells
• Determining launch schedules to establish and maintain prescribed satellite constellations (also uses Monte Carlo methods)
• Radar track initiation
• Aircraft survivability and effectiveness
• Color sample acceptance tolerance correlation and prediction
• Determination of sample sizes for color acceptability evaluation (uses advanced statistical methods)
• Underwater acoustic signal processing
• Reliability analysis of complex systems
• Radio interferometry

Numerical Analysis

• Estimation of ocean currents
• Modeling combustion flow in a coal power plant
• Airflow patterns in the respiratory tract (and diff. eqs.)
• Regional uptake of inhaled materials by respiratory tract
• Transport and disposition of chemicals through the body (and ODEs + PDEs)
• Molecular and cellular mechanisms of toxicity (and ODEs + PDEs)
• Reentry simulations for the Space Shuttle
• Trajectory prescribed path control and optimal control problems
• Shuttle/tank separation
• Scientific programming
• Modeling of airflow over airplane bodies
• Electromagnetics analysis for detection by radar
• Design and analysis of control systems for aircraft
• Electromagnetics
• Large scale shock wave physics code development
• Curve fitting of tabular data

Operations Research and Optimization

• Network formulation of cut order planning problem
• Shade sorting of colored samples to an acceptable tolerance by hierarchical clustering
• Inventory control for factory parts
• Search for and tracking of submarines
• Motion of a space vehicle
• Aircraft survivability and effectiveness
• Interplanetary mission analysis
• Radio interferometry
• Scheduling tasks on processors in a heterogeneous multiprocessor computing network
• Microwave measurements analysis
• Coordinate measuring machine (optimization error modeling)
• Optics for design of a reflector
• Materials science
• Reliability and uncertainty of large scale physical simulations