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Details for Mathematicians


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.


  • 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.


  • Investigative - Investigative occupations frequently involve working with ideas, and require an extensive amount of thinking. These occupations can involve searching for facts and figuring out problems mentally.
  • Artistic - Artistic occupations frequently involve working with forms, designs and patterns. They often require self-expression and the work can be done without following a clear set of rules.
  • Conventional - Conventional occupations frequently involve following set procedures and routines. These occupations can include working with data and details more than with ideas. Usually there is a clear line of authority to follow.

Education, Training, Experience

  • Education - Most of these occupations require graduate school. For example, they may require a master's degree, and some require a Ph.D., M.D., or J.D. (law degree).
  • Training - Employees may need some on-the-job training, but most of these occupations assume that the person will already have the required skills, knowledge, work-related experience, and/or training.
  • Experience - Extensive skill, knowledge, and experience are needed for these occupations. Many require more than five years of experience. For example, surgeons must complete four years of college and an additional five to seven years of specialized medical training to be able to do their job.



  • Reading Comprehension - Understanding written sentences and paragraphs in work related documents.
  • Active Listening - Giving full attention to what other people are saying, taking time to understand the points being made, asking questions as appropriate, and not interrupting at inappropriate times.
  • Writing - Communicating effectively in writing as appropriate for the needs of the audience.
  • Speaking - Talking to others to convey information effectively.
  • Mathematics - Using mathematics to solve problems.
  • Science - Using scientific rules and methods to solve problems.
  • Critical Thinking - Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
  • Active Learning - Understanding the implications of new information for both current and future problem-solving and decision-making.
  • Learning Strategies - Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
  • Instructing - Teaching others how to do something.
  • Complex Problem Solving - Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
  • Judgment and Decision Making - Considering the relative costs and benefits of potential actions to choose the most appropriate one.
  • Systems Analysis - Determining how a system should work and how changes in conditions, operations, and the environment will affect outcomes.

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