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.

tasks jobzones knowledge skills abilities work_activities work_context interests work_styles work_values

Tasks

• 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.

• Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.

• 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.

• Perform computations and apply methods of numerical analysis to data.

• Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.

• 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.

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Job Zone

• Name: Job Zone Five: Extensive Preparation Needed

• 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.

• Education: A bachelor's degree is the minimum formal education required for these occupations. However, many also 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).

• 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.

• Examples: 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 librarians, lawyers, aerospace engineers, physicists, school psychologists, and surgeons.

• Svp range: (8.0 and above)

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Knowledge

Browse 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.

• 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.

• English Language
  Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.

• 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.

• Education and Training
  Knowledge of principles and methods for curriculum and training design, teaching and instruction for individuals and groups, and the measurement of training effects.

• Chemistry
  Knowledge of the chemical composition, structure, and properties of substances and of the chemical processes and transformations that they undergo. This includes uses of chemicals and their interactions, danger signs, production techniques, and disposal methods.

• Biology
  Knowledge of plant and animal organisms, their tissues, cells, functions, interdependencies, and interactions with each other and the environment.

• Production and Processing
  Knowledge of raw materials, production processes, quality control, costs, and other techniques for maximizing the effective manufacture and distribution of goods.

• Design
  Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models.

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Skills

Browse 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.

• Active Learning
  Understanding the implications of new information for both current and future problem-solving and decision-making.

• Complex Problem Solving
  Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.

• Programming
  Writing computer programs for various purposes.

• Science
  Using scientific rules and methods to solve problems.

• Writing
  Communicating effectively in writing as appropriate for the needs of the audience.

• Instructing
  Teaching others how to do something.

• 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.

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Abilities

Browse Abilities

• Mathematical Reasoning
  The ability to choose the right mathematical methods or formulas to solve a problem.

• Oral Comprehension
  The ability to listen to and understand information and ideas presented through spoken words and sentences.

• Written Comprehension
  The ability to read and understand information and ideas presented in writing.

• Originality
  The ability to come up with unusual or clever ideas about a given topic or situation, or to develop creative ways to solve a problem.

• Number Facility
  The ability to add, subtract, multiply, or divide quickly and correctly.

• Fluency of Ideas
  The ability to come up with a number of ideas about a topic (the number of ideas is important, not their quality, correctness, or creativity).

• Deductive Reasoning
  The ability to apply general rules to specific problems to produce answers that make sense.

• Oral Expression
  The ability to communicate information and ideas in speaking so others will understand.

• Inductive Reasoning
  The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).

• Information Ordering
  The 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).

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Work Activities

Browse Work Activities

• Thinking Creatively
  Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.

• Updating and Using Relevant Knowledge
  Keeping up-to-date technically and applying new knowledge to your job.

• Analyzing Data or Information
  Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.

• Getting Information
  Observing, receiving, and otherwise obtaining information from all relevant sources.

• Processing Information
  Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.

• Making Decisions and Solving Problems
  Analyzing information and evaluating results to choose the best solution and solve problems.

• Interacting With Computers
  Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.

• Interpreting the Meaning of Information for Others
  Translating or explaining what information means and how it can be used.

• Provide Consultation and Advice to Others
  Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics.

• 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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Work Context

• Electronic Mail
  How often do you use electronic mail in this job?

• Spend Time Sitting
  How much does this job require sitting?

• Freedom to Make Decisions
  How much decision making freedom, without supervision, does the job offer?

• Indoors, Environmentally Controlled
  How often does this job require working indoors in environmentally controlled conditions?

• Structured versus Unstructured Work
  To what extent is this job structured for the worker, rather than allowing the worker to determine tasks, priorities, and goals?

• Face-to-Face Discussions
  How often do you have to have face-to-face discussions with individuals or teams in this job?

• Importance of Being Exact or Accurate
  How important is being very exact or highly accurate in performing this job?

• Telephone
  How often do you have telephone conversations in this job?

• Work With Work Group or Team
  How important is it to work with others in a group or team in this job?

• Level of Competition
  To what extent does this job require the worker to compete or to be aware of competitive pressures?

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Interests

Browse Interests

• 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.

• 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.

• 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.

• Realistic
  Realistic occupations frequently involve work activities that include practical, hands-on problems and solutions. They often deal with plants, animals, and real-world materials like wood, tools, and machinery. Many of the occupations require working outside, and do not involve a lot of paperwork or working closely with others.

• Enterprising
  Enterprising occupations frequently involve starting up and carrying out projects. These occupations can involve leading people and making many decisions. Sometimes they require risk taking and often deal with business.

• Social
  Social occupations frequently involve working with, communicating with, and teaching people. These occupations often involve helping or providing service to others.

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Work Styles

• Analytical Thinking
  Job requires analyzing information and using logic to address work-related issues and problems.

• Attention to Detail
  Job requires being careful about detail and thorough in completing work tasks.

• Innovation
  Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems.

• Achievement/Effort
  Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.

• Persistence
  Job requires persistence in the face of obstacles.

• Initiative
  Job requires a willingness to take on responsibilities and challenges.

• Integrity
  Job requires being honest and ethical.

• Independence
  Job requires developing one's own ways of doing things, guiding oneself with little or no supervision, and depending on oneself to get things done.

• Dependability
  Job requires being reliable, responsible, and dependable, and fulfilling obligations.

• Adaptability/Flexibility
  Job requires being open to change (positive or negative) and to considerable variety in the workplace.

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Work Values

Browse Work Values

• Autonomy
  Workers on this job plan their work with little supervision.

• Ability Utilization
  Workers on this job make use of their individual abilities.

• Achievement-Mean Extent
  Occupations that satisfy this work value are results oriented and allow employees to use their strongest abilities, giving them a feeling of accomplishment. Corresponding needs are Ability Utilization and Achievement.

• Independence-Mean Extent
  Occupations that satisfy this work value allow employs to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy.

• Independence
  Workers on this job do their work alone.

• Working Conditions
  Workers on this job have good working conditions.

• Responsibility
  Workers on this job make decisions on their own.

• Achievement
  Workers on this job get a feeling of accomplishment.

• Security
  Workers on this job have steady employment.

• Creativity
  Workers on this job try out their own ideas.

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