Real life Application 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 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

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 simulation

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)

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

Statistics

 Statistics is the science of dealing with Data or It’s the mathematical science involving the collection, analysis and interpretation of data.

There are several fields of Application of Statistics:

  • Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insuranceand finance industries.
  • Astrostatistics is the discipline that applies statistical analysis to the understanding of astronomical data.
  • Biostatistics is a branch of biology that studies biological phenomena and observations by means of statistical analysis, and includes medical statistics.
  • Business analytics is a rapidly developing business process that applies statistical methods to data sets (often very large) to develop new insights and understanding of business performance & opportunities.
  • Chemometrics is the science of relating measurements made on a chemical system or process to the state of the system via application of mathematical or statistical methods.
  • Demography is the statistical study of all populations. It can be a very general science that can be applied to any kind of dynamic population, that is, one that changes over time or space.
  • Econometrics is a branch of economics that applies statistical methods to the empirical study of economic theories and relationships.
  • Environmental statistics is the application of statistical methods to environmental science. Weather, climate, air and water quality are included, as are studies of plant and animal populations.
  • Epidemiology is the study of factors affecting the health and illness of populations, and serves as the foundation and logic of interventions made in the interest of public health and preventive medicine.
  • Geostatistics is a branch of geography that deals with the analysis of data from disciplines such as petroleum, geologyhydrogeologyhydrologymeteorologyoceanographygeochemistrygeography.
  • Machine learning is the subfield of computer science that formulates algorithms in order to make predictions from data.
  • Operations research (or operational research) is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems.
  • Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment.
  • Psychometrics is the theory and technique of educational and psychological measurement of knowledge, abilities, attitudes, and personality traits.
  • Quality control reviews the factors involved in manufacturing and production; it can make use of statistical sampling of product items to aid decisions in process control or in accepting deliveries.
  • Quantitative psychology is the science of statistically explaining and changing mental processes and behaviors in humans.
  • Reliability engineering is the study of the ability of a system or component to perform its required functions under stated conditions for a specified period of time.
  • Statistical finance, an area of econophysics, is an empirical attempt to shift finance from its normative roots to a positivist framework using exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets.
  • Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.
  • Statistical physics is one of the fundamental theories of physics, and uses methods of probability theory in solving physical problems.
  • Statistical signal processing utilizes the statistical properties of signals to perform signal processing tasks.
  • Statistical thermodynamics is the study of the microscopic behaviors of thermodynamic systems using probability theory and provides a molecular level interpretation of thermodynamic quantities such as workheatfree energy, and entropy.

 

References : University of Northern British Columbia, Wikipedia, University of Oxford, “Graduate PROSPECT Ltd” UK