The main tasks and work activities of Mathematicians are to 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. In general, for the Mathematicians, mathematics, reading Comprehension, complex Problem Solving, critical Thinking and other 10 skills are required.

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). |
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Related 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. |

Job 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. |

Example | These occupations often involve coordinating, training, supervising, or managing the activities of others to accomplish goals. Very advanced communication and organizational skills are required. Examples include pharmacists, lawyers, astronomers, biologists, clergy, neurologists, and veterinarians. |

The following chart shows the education/training levels for Mathematicians jobs.

- 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.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.

- Interacting With ComputersUsing computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
- Analyzing Data or InformationIdentifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
- Making Decisions and Solving ProblemsAnalyzing information and evaluating results to choose the best solution and solve problems.
- Getting InformationObserving, receiving, and otherwise obtaining information from all relevant sources.
- Thinking CreativelyDeveloping, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.
- Processing InformationCompiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
- Updating and Using Relevant KnowledgeKeeping up-to-date technically and applying new knowledge to your job.
- Communicating with Supervisors, Peers, or SubordinatesProviding information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
- Interpreting the Meaning of Information for OthersTranslating or explaining what information means and how it can be used.
- Identifying Objects, Actions, and EventsIdentifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events.

- 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.
- Design computer modeling or simulation programs.
- Develop scientific or mathematical models.
- Develop computer or information security policies or procedures.
- Analyze security of systems, network, or data.
- Prepare analytical reports.
- Present research results to others.

- MathematicsUsing mathematics to solve problems.
- Reading ComprehensionUnderstanding written sentences and paragraphs in work related documents.
- Complex Problem SolvingIdentifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
- Critical ThinkingUsing logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
- Active LearningUnderstanding the implications of new information for both current and future problem-solving and decision-making.
- WritingCommunicating effectively in writing as appropriate for the needs of the audience.
- Active ListeningGiving 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.
- Systems AnalysisDetermining how a system should work and how changes in conditions, operations, and the environment will affect outcomes.
- Judgment and Decision MakingConsidering the relative costs and benefits of potential actions to choose the most appropriate one.
- Learning StrategiesSelecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
- ScienceUsing scientific rules and methods to solve problems.
- SpeakingTalking to others to convey information effectively.
- Systems EvaluationIdentifying measures or indicators of system performance and the actions needed to improve or correct performance, relative to the goals of the system.

- Mathematical ReasoningThe ability to choose the right mathematical methods or formulas to solve a problem.
- Number FacilityThe ability to add, subtract, multiply, or divide quickly and correctly.
- Deductive ReasoningThe ability to apply general rules to specific problems to produce answers that make sense.
- Written ComprehensionThe ability to read and understand information and ideas presented in writing.
- Information OrderingThe ability to arrange things or actions in a certain order or pattern according to a specific rule or set of rules (e.g., patterns of numbers, letters, words, pictures, mathematical operations).
- Inductive ReasoningThe ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
- Oral ComprehensionThe ability to listen to and understand information and ideas presented through spoken words and sentences.
- Category FlexibilityThe ability to generate or use different sets of rules for combining or grouping things in different ways.
- Problem SensitivityThe ability to tell when something is wrong or is likely to go wrong. It does not involve solving the problem, only recognizing there is a problem.
- Near VisionThe ability to see details at close range (within a few feet of the observer).
- Fluency of IdeasThe ability to come up with a number of ideas about a topic (the number of ideas is important, not their quality, correctness, or creativity).
- Oral ExpressionThe ability to communicate information and ideas in speaking so others will understand.
- Written ExpressionThe ability to communicate information and ideas in writing so others will understand.
- OriginalityThe ability to come up with unusual or clever ideas about a given topic or situation, or to develop creative ways to solve a problem.
- Speech ClarityThe ability to speak clearly so others can understand you.
- Speech RecognitionThe ability to identify and understand the speech of another person.
- Flexibility of ClosureThe ability to identify or detect a known pattern (a figure, object, word, or sound) that is hidden in other distracting material.
- Selective AttentionThe ability to concentrate on a task over a period of time without being distracted.

- Desktop computerse.g. Desktop computers
- Scientific calculatore.g. Graphing calculators
- Notebook computerse.g. Laptop computers
- Read write digital versatile disc DVDe.g. Optical disk drives
- Personal computerse.g. Personal computers
- Mainframe computerse.g. Supercomputers
- High capacity removable media drivese.g. Universal serial bus USB flash drives

- MathematicsKnowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
- Computers and ElectronicsKnowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
- English LanguageKnowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.
- Engineering and TechnologyKnowledge 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.
- PhysicsKnowledge 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.