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Mathematicians

Description:

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

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.
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.
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.
Communications and Media
Knowledge of media production, communication, and dissemination techniques and methods. This includes alternative ways to inform and entertain via written, oral, and visual media.
Design
Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models.
Telecommunications
Knowledge of transmission, broadcasting, switching, control, and operation of telecommunications systems.

Skills

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.
Programming
Writing computer programs for various purposes.
Writing
Communicating effectively in writing as appropriate for the needs of the audience.
Science
Using scientific rules and methods to solve problems.
Speaking
Talking to others to convey information effectively.
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.

Abilities

Mathematical Reasoning
The ability to choose the right mathematical methods or formulas to solve a problem.
Deductive Reasoning
The ability to apply general rules to specific problems to produce answers that make sense.
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).
Number Facility
The ability to add, subtract, multiply, or divide quickly and correctly.
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.
Inductive Reasoning
The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
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).
Oral Comprehension
The ability to listen to and understand information and ideas presented through spoken words and sentences.
Near Vision
The ability to see details at close range (within a few feet of the observer).

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.
Interacting With Computers
Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
Getting Information
Observing, receiving, and otherwise obtaining information from all relevant sources.
Making Decisions and Solving Problems
Analyzing information and evaluating results to choose the best solution and solve problems.
Analyzing Data or Information
Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
Communicating with Supervisors, Peers, or Subordinates
Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
Processing Information
Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
Provide Consultation and Advice to Others
Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics.
Interpreting the Meaning of Information for Others
Translating or explaining what information means and how it can be used.

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?

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.

Work Style

Analytical Thinking
Job requires analyzing information and using logic to address work-related issues and problems.
Innovation
Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems.
Attention to Detail
Job requires being careful about detail and thorough in completing work tasks.
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.

Work Value

Achievement
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.
Recognition
Occupations that satisfy this work value offer advancement, potential for leadership, and are often considered prestigious. Corresponding needs are Advancement, Authority, Recognition and Social Status.
Working Conditions
Occupations that satisfy this work value offer job security and good working conditions. Corresponding needs are Activity, Compensation, Independence, Security, Variety and Working Conditions.
Independence
Occupations that satisfy this work value allow employs to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy.
Support
Occupations that satisfy this work value offer supportive management that stands behind employees. Corresponding needs are Company Policies, Supervision: Human Relations and Supervision: Technical.
Relationships
Occupations that satisfy this work value allow employees to provide service to others and work with co-workers in a friendly non-competitive environment. Corresponding needs are Co-workers, Moral Values and Social Service.

Related Occupations

Common Lay Titles