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.
- 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 new principles and new relationships between existing mathematical principles to advance mathematical science.
- Perform computations and apply methods of numerical analysis to data.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
- Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
- 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.
- Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
- Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
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.
- Complex Problem Solving - Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
- 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.
- 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).
In 2016, the average annual wage in Pennsylvania was $97,590 with most people making between $47,520 and $181,840
During 2010, this occupation employed approximately 60 people in Pennsylvania. It is projected that there will be 60 employed in 2020.
This occupation will have about 1 openings due to growth and about 3 replacement openings for approximately 4 total annual openings.