Conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve or direct solutions to problems in various fields by mathematical methods.

Other names for Mathematicians: Algebraist, Cipher Expert, Computational Physicist, Computational Scientist, Cryptanalyst, Cryptographer, Cryptographic Vulnerability Analyst, Emerging Solutions Executive, Engineering Mathematician, Image Scientist, Knowledge Engineer, Nanotechnologist, Numerical Analysis Group Manager, Research Computing Specialist, Research Scientist, Scientist, Systems Analyst, Systems Engineer, Technical Fellow,

• Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
• Develop computational methods for solving problems that occur in areas of science and engineering, or that come from applications in business or industry.
• Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
• Perform computations and apply methods of numerical analysis to data.
• Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
• Assemble sets of assumptions and explore the consequences of each set.
• Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
• Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
• Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
• Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.

• Desktop computers
• Calculators or accessories
• Notebook computers
• Read write digital versatile disc DVD
• Personal computers
• Mainframe computers
• High capacity removable media drives

Graphics or photo imaging software

Word processing software

Presentation software

Spreadsheet software

Desktop publishing software

Data base user interface and query software

Development environment software

Object or component oriented development software

Computer aided design CAD software

Analytical or scientific software

Internet browser software

Electronic mail software