Careers in Mathematics & Statistics

Mathematics and statistics allow us to "see" things that are, otherwise, invisible -- from cognitive processes to the fluid flows that keep airplanes in the air, and they better people's lives by helping us solve important problems.

Every e-mail message follows routes based on graph theoretic analyses, and search engines rely on matrix theory to rank web sites. Weather is forecasted and endangered species populations are predicted using mathematical and statistical models that often involve computers and differential equations. The nation's economy is guided by principles of mathematical game theory and statistical decision-making techniques. Public policy and social programs are developed with the aid of experiments conducted by statisticians, and the foundations of medical tomography are firmly planted in the mathematics of functional analysis.

Mathematicians and statisticians are employed by industrial firms, financial companies, and others to help design, develop, produce, market and distribute products. And they are employed by various branches of government that are charged with responsibilities too grand for a single company (e.g., space exploration, interpretation of census data, national security, managing our environment, etc.).

The American Mathematical Society (AMS) has a nice collection of "mathematical moments" that describe various ways that mathematics is used in science, technology and culture. (A link to their site is provided below.) The Society for Industrial and Applied Mathematics (SIAM) also has a great brochure about careers in mathematics. Other examples have been listed here (thsee lists are by no means comprehensive, but are meant to provide a sampling of various employment opportunities that focus on mathematics and statistics).

	Canon, and other imaging companies employ mathematicans to help them improve the quality of their ink jet printers. Partial differential equations are used to model the settling and absorbtion of the ink, and account for qualities such as surface tension and viscosity. 1		Lucent Technologies, AT&T, and other large communications companies maintain technical staff who conduct research in the areas of statistics, mathematics of networks, performance analysis, mathematical foundations of computing, infrmation theorey, and operations research (among others).2
	Mathematicians at companies such as Lockheed-Martin and Boeing use numerical analysis to study the effects of shock waves and the resonance of aircraft wings in trans-sonic flows. This image is shows a U.S. Navy fighter breaking the sound barier. The white cloud is water that has condensed as the shock wave passed through the air.3		Panasonic and Siemens use algorithms developed by mathematicians to identify people from the patter of their irises. These algorithms use the recently developed mathematical theory of wavelet bases. Wavelets are also used to compress fingerprint libraries and to analyze sonar data.4
	NASA, JPL, and the United States Military rely on the ability to process data collected by parabolic dishes and radio telescopes. This requires significant knowledge of multivariate analysis and spatial point processes. Integral transforms are used to purge noise from the signal (noise can arise from a variety of sources, including atmospheric variations between the satellite and the dish).5		The National Security Agency is the largest employer of mathematicians in the country. Mathematicians who work for the NSA use abstract (modern) algebra, combinatorics and graph theory to attack cryptographic problems. Though the problems addressed by the NSA have to do with national security, the same techniques are used to design encryption systems for internet security and cell phone transmission.6
	Organizations charged with managing the environment, such as the United States Department of the Interior, use integer programming and cutting plane techniques to solve nonlinear problems such as determining the optimal placement of monitoring stations.7		Mathematicians at Intel, IBM and others companies model problems in plasma etching, which is a fundamental fabrication method in computer chip technology.8
	Honeywell, Raytheon, and other companies employ mathematicians to model micro-machines (1-100 microns in size). These machines are used in machines like ink jet printers and accelerometers in air bags.9		Merck, Pfizer, Johnson & Johnson and other pharmacutical companies that want FDA approval of their newest drugs must use statistical techniques to prove that the drugs are safe. They also use advanced methods of ordinary differential equations to design assays by which to analyze the concentration of various drug compounds in a patient's system.10
	The U.S. Geological Survey uses statistical methods to analyze accelerogram data. From their conclusions, they provide short-term warnings of ground shaking from strong earthquakes and real-time estimations of an earthquake's size.11		Companies like Melles Griot and GrinTech use mathematical modeling and computer simulation in the field of Photonics, the practical application of light. Geometry and Ordinary Differential Equations are used, for example, in the design of GRIN (GRadient INdex) lenses.12
	The amount of DNA sequence data available to biologists has grown immensely in recent years. Companies like Celera Genomics use mathematicians to solve the combinatorial problems involved in sequencing and analyzing DNA.13		Mathematicians at car companies such as General Motors and Ford model the aerodynamics of vehicles, including drag and lift. Vortices (which can be seen when the roads are covered with a light dusting of snow) are the result of drag. 14
	Statisticians at financial firms such as Merril Lynch use quasi-Monte carlo methods to estimate multivariate integrals that determine the present value of a financial derivative. 16

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