Conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve problems in various fields using mathematical methods.
- Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
- Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
- Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
- Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
- 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.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
- Perform computations and apply methods of numerical analysis to data.
- Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
- Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
People who work in this occupation generally have the interest code: ICA.
This means people who work in this occupation generally have Investigative interests, but also prefer Conventional and Artistic environments.
People who work in this occupation generally prize Achievement, but also value Recognition and Working Conditions in their jobs.
- Mathematics - Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
- Computers and Electronics - Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
- English Language - Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.
- Engineering and Technology - Knowledge of the practical application of engineering science and technology. This includes applying principles, techniques, procedures, and equipment to the design and production of various goods and services.
- Physics - Knowledge and prediction of physical principles, laws, their interrelationships, and applications to understanding fluid, material, and atmospheric dynamics, and mechanical, electrical, atomic and sub- atomic structures and processes.
- Mathematics - Using mathematics to solve problems.
- Critical Thinking - Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
- Reading Comprehension - Understanding written sentences and paragraphs in work related documents.
- Complex Problem Solving - Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
- Active Learning - Understanding the implications of new information for both current and future problem-solving and decision-making.
- Writing - Communicating effectively in writing as appropriate for the needs of the audience.
- 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.
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).
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