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.

• Mathematician

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

• advise clients or customers
• advise governmental or industrial personnel
• analyze scientific research data or investigative findings
• analyze social or economic data
• collect scientific or technical data
• collect statistical data
• communicate technical information
• compile numerical or statistical data
• confer with engineering, technical or manufacturing personnel
• confer with research personnel
• confer with scientists
• consult with managerial or supervisory personnel
• create mathematical or statistical diagrams or charts
• develop mathematical ideas or interpretations
• develop mathematical or computer languages
• develop mathematical simulation models
• develop new products based on scientific research results
• develop or maintain databases
• develop scientific or mathematical hypotheses, theories, or laws
• develop tables depicting data
• direct and coordinate activities of workers or staff
• direct and coordinate scientific research or investigative studies
• explain complex mathematical information
• make decisions
• make presentations
• perform statistical modeling
• plan scientific research or investigative studies
• prepare reports
• prepare technical reports or related documentation
• provide expert testimony on research results
• recommend further study or action based on research data
• resolve engineering or science problems
• use computers to enter, access or retrieve data
• use interpersonal communication techniques
• use knowledge of investigation techniques
• use library or online Internet research techniques
• use mathematical or statistical methods to identify or analyze problems
• use oral or written communication techniques
• use quantitative research methods
• use relational database software
• use scientific research methodology
• use spreadsheet software
• use word processing or desktop publishing software
• write scholarly or technical research papers