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.
Tasks
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.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
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 new principles and new relationships between existing mathematical principles to advance mathematical science.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
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.
Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
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.
Skills
Mathematics
Using mathematics to solve problems.
Active Learning
Understanding the implications of new information for both current and future problem-solving and decision-making.
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.
Science
Using scientific rules and methods to solve problems.
Writing
Communicating effectively in writing as appropriate for the needs of the audience.
Judgment and Decision Making
Considering the relative costs and benefits of potential actions to choose the most appropriate one.
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.
Oral Comprehension
The ability to listen to and understand information and ideas presented through spoken words and sentences.
Deductive Reasoning
The ability to apply general rules to specific problems to produce answers that make sense.
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.
Oral Expression
The ability to communicate information and ideas in speaking so others will understand.
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).
Written Expression
The ability to communicate information and ideas in writing so others will understand.
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).
Work Activities
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.
Analyzing Data or Information
Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
Updating and Using Relevant Knowledge
Keeping up-to-date technically and applying new knowledge to your job.
Getting Information
Observing, receiving, and otherwise obtaining information from all relevant sources.
Interacting With Computers
Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
Making Decisions and Solving Problems
Analyzing information and evaluating results to choose the best solution and solve problems.
Identifying Objects, Actions, and Events
Identifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events.
Communicating with Supervisors, Peers, or Subordinates
Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
Estimating the Quantifiable Characteristics of Products, Events, or Information
Estimating sizes, distances, and quantities; or determining time, costs, resources, or materials needed to perform a work activity.
Work Context
Electronic Mail
How often do you use electronic mail in this job?
Indoors, Environmentally Controlled
How often does this job require working indoors in environmentally controlled conditions?
Freedom to Make Decisions
How much decision making freedom, without supervision, does the job offer?
Importance of Being Exact or Accurate
How important is being very exact or highly accurate in performing this job?
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?
Spend Time Sitting
How much does this job require sitting?
Face-to-Face Discussions
How often do you have to have face-to-face discussions with individuals or teams in this job?
Impact of Decisions on Co-workers or Company Results
How do the decisions an employee makes impact the results of co-workers, clients or the company?
Work With Work Group or Team
How important is it to work with others in a group or team in this job?
Telephone
How often do you have telephone conversations in this job?
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.
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.
Integrity
Job requires being honest and ethical.
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.
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.
Initiative
Job requires a willingness to take on responsibilities and challenges.
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 Values
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 employees 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.
