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Mathematics Overview - Preparation - Day In The Life - Application -
Earnings - Employment - Job Hunting Advice - Development - Career Path Forecast - Professional Organizations 

Mathematics is one of the oldest and most fundamental sciences. Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve economic, scientific, engineering, physics, and business problems. The work of mathematicians falls into two broad classes -- theoretical (pure) mathematics and applied mathematics. These classes, however, are not sharply defined and often overlap.

Theoretical mathematicians advance mathematical knowledge by developing new principles and recognizing previously unknown relationships between existing principles of mathematics. Although these workers seek to increase basic knowledge without necessarily considering its practical use, such pure and abstract knowledge has been instrumental in producing or furthering many scientific and engineering achievements. Many theoretical mathematicians are employed as university faculty, dividing their time between teaching and conducting research.

Applied mathematicians use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, engineering, and the physical, life, and social sciences. For example, they may analyze the most efficient way to schedule airline routes between cities, the effects and safety of new drugs, the aerodynamic characteristics of an experimental automobile, or the cost-effectiveness of alternative manufacturing processes.

Applied mathematicians working in industrial research and development may develop or enhance mathematical methods when solving a difficult problem. Some mathematicians, called cryptanalysts, analyze and decipher encryption systemsócodesódesigned to transmit military, political, financial, or law-enforcement-related information.

Applied mathematicians start with a practical problem, envision its separate elements, and then reduce the elements to mathematical variables. They often use computers to analyze relationships among the variables, and they solve complex problems by developing models with alternative solutions.

Individuals with titles other than mathematician also do work in applied mathematics. In fact, because mathematics is the foundation on which so many other academic disciplines are built, the number of workers using mathematical techniques is much greater than the number formally called mathematicians. For example, engineers, computer scientists, physicists, and economists are among those who use mathematics extensively. Some professionals, including statisticians, actuaries, and operations research analysts, are actually specialists in a particular branch of mathematics. Applied mathematicians frequently are required to collaborate with other workers in their organizations to find common solutions to problems.

The world is full of places to do rigorous mathematics. As you begin to identify potential outlets for your talent, it may be useful to get a sense of the dimensions of the 'field' in its entirety. Business, industry, and government use mathematical expertise, often in the context of applications.

However, the job titles often do not include the word "mathematics" or "mathematician," but do involve significant use of mathematics and/or quantitative reasoning. For people with advanced degrees in mathematics, careers involve development of new mathematical methods and theories and application to almost every area of science, engineering, industry and business. Those who major in mathematics in undergraduate institutions find a broad variety of opportunities. Some use their mathematical training directly and some use their training in rigorous thinking and analysis indirectly to solve problems in the business sector.

Many of the contributions and uses of mathematics are closely related to the need for mathematical modeling and simulation of physical phenomena on the computer. In addition, the analysis and control of processes, and optimization and scheduling of resources use significant mathematics. For example, the finance industry uses sophisticated mathematical models for pricing of securities, while the petroleum industry models the flow of oil in underground rock formations to help in oil recovery. Image processing, whether producing clear pictures from satellite imagery or making medical images (CAT, MRI) to detect and diagnose, all use significant mathematics. Industrial design, whether structural components for airplanes or automobile parts, uses a tremendous amount of mathematical modeling; much of which is embodied in CAD/CAM computer software. Such techniques were used in the design of the Boeing 777, as well as in the design of automobiles. Computational modeling is also used in airplane and automobile design to analyze the flow of air over vehicles to determine fuel economy and efficiency.

The use of mathematics is pervasive in modern industry. The result is that mathematicians are found in almost every sector of the job market, including engineering research, telecommunications, computer services and software, energy systems, computer manufacturers, aerospace and automotive, chemicals and pharmaceuticals, and government laboratories, among others.

Mathematics Resources


Degrees Options and Considerations
Day in the Life:
Typical Problems; Work Environment; Skills; Activities; Advice
Application Spectrum:
Overview and the role of mathematics as it applies to different products.
Range of compensation
Industry; Business; Government; Titles; Motivation; Specialties; Disciplines; Advice
Job Hunting Advice:
Researching Jobs, Occupations, Tips
Dual Tracks; Continuing Education; Life Outside
Career Path Forecast:
Professional Organizations:
Resources, Networking, Support
Internet Resources:
American Mathematical Society
Mathematical Association of America
Mathematical Moments Program
Society for Industrial and Applied Mathematics

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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