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.
  • Assemble sets of assumptions and explore the consequences of each set.
  • Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
  • 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.
  • 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.
Work Context
  • Electronic Mail — 88% responded "Every day".
  • Freedom to Make Decisions — 71% responded "A lot of freedom".
  • Importance of Being Exact or Accurate — 67% responded "Extremely important".
  • Structured versus Unstructured Work — 63% responded "A lot of freedom".
  • Spend Time Sitting — 55% responded "Continually or almost continually".
  • Face-to-Face Discussions — 50% responded "Once a week or more but not every day".
  • Indoors, Environmentally Controlled — 75% responded "Every day".
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Work Activities
  • Interacting With Computers — Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
  • Analyzing Data or Information — Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
  • Making Decisions and Solving Problems — Analyzing information and evaluating results to choose the best solution and solve problems.
  • Getting Information — Observing, receiving, and otherwise obtaining information from all relevant sources.
  • Thinking Creatively — Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.
  • Processing Information — Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
  • Updating and Using Relevant Knowledge — Keeping up-to-date technically and applying new knowledge to your job.
  • Communicating with Supervisors, Peers, or Subordinates — Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
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Detailed Work Activities
  • Present research results to others.
  • Prepare analytical reports.
  • Apply mathematical principles or statistical approaches to solve problems in scientific or applied fields.
  • Determine appropriate methods for data analysis.
  • Update knowledge about emerging industry or technology trends.
  • Analyze data to identify trends or relationships among variables.
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Knowledge

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.
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Skills

Mathematics
  • Using mathematics to solve problems.
Reading Comprehension
  • Understanding written sentences and paragraphs in work related documents.
Critical Thinking
  • Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
Complex Problem Solving
  • Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
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Abilities

Mathematical Reasoning
  • The ability to choose the right mathematical methods or formulas to solve a problem.
Number Facility
  • The ability to add, subtract, multiply, or divide quickly and correctly.
Deductive Reasoning
  • The ability to apply general rules to specific problems to produce answers that make sense.
Written Comprehension
  • The ability to read and understand information and ideas presented in writing.
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Personality

People interested in this work like activities that include ideas, thinking, and figuring things out.
They do well at jobs that need:
  • Achievement/Effort
  • Persistence
  • Initiative
  • Leadership
  • Cooperation
  • Concern for Others
  • Social Orientation
  • Self Control
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Technology

You might use software like this on the job:

Object or component oriented development software
  • R Hot Technology
  • Python Hot Technology
  • Practical extraction and reporting language Perl Hot Technology
  • Oracle Java Hot Technology
  • C++ Hot Technology
  • C# Hot Technology
Enterprise application integration software
  • Extensible markup language XML Hot Technology
Web platform development software
  • PHP: Hypertext Preprocessor Hot Technology
  • JavaScript Hot Technology
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Education

Master's Degree or
Doctoral Degree
usually needed

Get started on your career:

Job Outlook

New job opportunities are less likely in the future.
Salary
$110,860
$61,130
$170,150