# Real-Life Applications of Mathematics

- 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