Real-life applications of Mathematics

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