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Mathematics Overview - Preparation - Day In The Life - Application -
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Application Spectrum
The spectrum of the field is perhaps best illustrated by observing the role of mathematics as it applies to different products.  For further information, explore the Mathematical Moments Program which offers more examples of the role mathematics plays in science, nature, technology, and human culture.

Aerosol Can
Chlorofluorocarbons (CFCs), like the freon used in aerosol cans and air conditioning systems, could destroy stratospheric ozone, which protects the earth from biologically damaging ultraviolet radiation. Mathematical models, simulations and the numerical solution of a special set of differential equations, called "stiff" differential equations, are used to identify safer replacements from the members of hydrohalocarbon (HHC) family.

Oil Rig
Accurate models of oil reservoirs, including the simulations of oil and water moving through porous rock, sometimes covering hundreds of acres, are used by the petroleum industry to make decisions on where to drill. These problems are solved by reducing complex multidimensional differential equations to a sequence of simpler one-dimensional problems that are solved numerically

Airport
Operations research is used throughout the airline industry to make sure seats are sold and the airlines make money. Yield management, including mathematical models, optimization techniques, and probability calculations, is used for setting up automated reservation systems and complex systems of connecting routes.

Communications Satellite
Models based on computing solutions to partial differential equations are used to solve problems in signal processing and filtering of noise.

Circuit
The design of a circuit uses the concept of a graph, like a schematic map, with lines, called edges and intersections, called nodes. Systematic searches of the nodes are used to determine the most efficient connection from one node to another.

Aircraft
The design of an aircraft requires computational fluid dynamics, partial differential equations, and grid generation on complex geometries.

CD
CD players, digital audio tape and digital television read digital information that consists of "bits" -- 0's and 1's. Occasionally these devices confuse the two and error-correction codes, like Reed-Soloman codes, are needed. Mathematically, Reed-Solomon codes are based on the arithmetic of finite fields.

Fingerprint
The law enforcement community is interested in developing quick ways to match fingerprints with the database of fingerprints held by the Federal Bureau of Investigation. The problem is the FBI holds approximately 200 million fingerprint cards. They have now adopted a standard for digital fingerprint image compression that will allow the fingerprints to be stored electronically.

Space Vehicle
The equations of motion of a space vehicle are systems of ordinary differential equations. One may wish to solve an initial value problem, say where the initial position and velocity of the spacecraft is given and you want to determine the trajectory for some period of time. Boundary value problems also arise, for example when you want to design an orbit transfer maneuver between two different orbits. In that case you have beginning and end point constraints on the maneuver.

Submarine
The search for enemy submarines requires the application of a number of fields of mathematics, including probability, game theory and optimization.

Space Shuttle
The problem of separation of the space shuttle fuel tank involves ordinary differential equations and numerical solution methods.

Fabric
Color is the result of the combination of a light source, an object that it illuminates, and a visual system to perceive the color which is usually the eye and the brain of a human being working together. Color is commonly described by the attributes of lightness, chroma, and hue. Standardized color descriptions use values assigned to these three attributes to identify the color.

Crystal
Crystal growth can be modeled using partial differential equations.

Note: Some resources in this section are provided by the American Mathematical Society, Mathematical Association of America, Society for Industrial and Applied Mathematics, and the US Department of Labor, Bureau of Labor Statistics.
 


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