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.
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.
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.
Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
Disseminate research by writing reports, publishing papers, or presenting at 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.
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.
Work Context
Electronic Mail — 88% responded "Every day".
Freedom to Make Decisions — 71% responded "A lot of freedom".
Importance of Being Exact or Accurate — 67% responded "Extremely important".
Structured versus Unstructured Work — 63% responded "A lot of freedom".
Spend Time Sitting — 55% responded "Continually or almost continually".
Face-to-Face Discussions — 50% responded "Once a week or more but not every day".
Interacting With Computers — Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
Analyzing Data or Information — Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
Making Decisions and Solving Problems — Analyzing information and evaluating results to choose the best solution and solve problems.
Getting Information — Observing, receiving, and otherwise obtaining information from all relevant sources.
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.
Updating and Using Relevant Knowledge — Keeping up-to-date technically and applying new knowledge to your job.
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.
Interpreting the Meaning of Information for Others — Translating or explaining what information means and how it can be used.
Identifying Objects, Actions, and Events — Identifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events.
Documenting/Recording Information — Entering, transcribing, recording, storing, or maintaining information in written or electronic/magnetic form.
Organizing, Planning, and Prioritizing Work — Developing specific goals and plans to prioritize, organize, and accomplish your work.
Provide Consultation and Advice to Others — Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics.
Training and Teaching Others — Identifying the educational needs of others, developing formal educational or training programs or classes, and teaching or instructing others.
Developing Objectives and Strategies — Establishing long-range objectives and specifying the strategies and actions to achieve them.
Communicating with Persons Outside Organization — Communicating with people outside the organization, representing the organization to customers, the public, government, and other external sources. This information can be exchanged in person, in writing, or by telephone or e-mail.
Establishing and Maintaining Interpersonal Relationships — Developing constructive and cooperative working relationships with others, and maintaining them over time.
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.
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.
Writing
Communicating effectively in writing as appropriate for the needs of the audience.
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.
Speaking
Talking to others to convey information effectively.
Science
Using scientific rules and methods to solve problems.
Learning Strategies
Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
Judgment and Decision Making
Considering the relative costs and benefits of potential actions to choose the most appropriate one.
Systems Analysis
Determining how a system should work and how changes in conditions, operations, and the environment will affect outcomes.
Systems Evaluation
Identifying measures or indicators of system performance and the actions needed to improve or correct performance, relative to the goals of the system.
The ability to choose the right mathematical methods or formulas to solve a problem.
Number Facility
The ability to add, subtract, multiply, or divide quickly and correctly.
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).
Written Comprehension
The ability to read and understand information and ideas presented in writing.
Inductive Reasoning
The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
Oral Comprehension
The ability to listen to and understand information and ideas presented through spoken words and sentences.
Problem Sensitivity
The 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 Vision
The ability to see details at close range (within a few feet of the observer).
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).
Category Flexibility
The ability to generate or use different sets of rules for combining or grouping things in different ways.
Oral Expression
The ability to communicate information and ideas in speaking so others will understand.
Written Expression
The ability to communicate information and ideas in writing 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.
Speech Recognition
The ability to identify and understand the speech of another person.
Speech Clarity
The ability to speak clearly so others can understand you.
Flexibility of Closure
The ability to identify or detect a known pattern (a figure, object, word, or sound) that is hidden in other distracting material.
Selective Attention
The ability to concentrate on a task over a period of time without being distracted.
