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, on the other hand, 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 systems—codes—designed 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 solve complex problems by developing models with alternative solutions.
Individuals with titles other than mathematician do much of the 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 are frequently required to collaborate with other workers in their organizations to find common solutions to problems.
Work environment. Mathematicians usually work in comfortable offices. They often are part of interdisciplinary teams that may include economists, engineers, computer scientists, physicists, technicians, and others. Deadlines, overtime work, special requests for information or analysis, and prolonged travel to attend seminars or conferences may be part of their jobs.
Mathematicians who work in academia usually have a mix of teaching and research responsibilities. These mathematicians may conduct research alone or in close collaboration with other mathematicians. Collaborators may work together at the same institution or from different locations, using technology such as e-mail to communicate. Mathematicians in academia also may be aided by graduate students.
| 1. | Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields. |
| 2. | Develop computational methods for solving problems that occur in areas of science and engineering, or that come from applications in business or industry. |
| 3. | Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences. |
| 4. | Perform computations and apply methods of numerical analysis to data. |
| 5. | Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation. |
| 6. | Assemble sets of assumptions and explore the consequences of each set. |
| 7. | Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols. |
| 8. | Develop new principles and new relationships between existing mathematical principles to advance mathematical science. |
| 9. | Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code. |
| 10. | Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic. |
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