Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
Perform computations and apply methods of numerical analysis to data.
Assemble sets of assumptions and explore the consequences of each set.
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.