Mathematicians

What they do:

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.

On the job, you would:

  • 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.

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.
  • Telecommunications
  • Knowledge of transmission, broadcasting, switching, control, and operation of telecommunications systems.
  • Design
  • Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models.

Skills

  • Mathematics
  • Using mathematics to solve 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.
  • 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.
  • Learning Strategies
  • Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
  • 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.
  • Science
  • Using scientific rules and methods to solve problems.
  • Writing
  • Communicating effectively in writing as appropriate for the needs of the audience.

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.
  • Written Comprehension
  • The ability to read and understand information and ideas presented in writing.
  • Number Facility
  • The ability to add, subtract, multiply, or divide quickly and correctly.
  • 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).
  • Inductive Reasoning
  • The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
  • 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.
  • Oral Comprehension
  • The ability to listen to and understand information and ideas presented through spoken words and sentences.
  • 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).
  • 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.

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.
  • Second Interest High-Point
  • Secondary-Cutoff/Rank Descriptiveness
  • 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.
  • Third Interest High-Point
  • Tertiary-Cutoff/Rank Descriptiveness
  • First Interest High-Point
  • Primary-Rank Descriptiveness
  • 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 Styles

  • 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.