Mathematicians

This occupation is expected to grow rapidly.
Description

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.

Sample Job Titles
Agent-Based Modeler
Computational Scientist
Cryptographer
Cryptographic Vulnerability Analyst
Director of Quantitative Research
Emerging Solutions Executive
Image Scientist
Lead Simulation Modeling Engineer
Research Scientist
Scientist
Skills
Active Learning - Understanding the implications of new information for both current and future problem-solving and decision-making.
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.
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.
Judgment and Decision Making - Considering the relative costs and benefits of potential actions to choose the most appropriate one.
Learning Strategies - Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
Mathematics - Using mathematics to solve problems.
Reading Comprehension - Understanding written sentences and paragraphs in work related documents.
Science - Using scientific rules and methods to solve problems.
Writing - Communicating effectively in writing as appropriate for the needs of the audience.
Abilities
Category Flexibility - The ability to generate or use different sets of rules for combining or grouping things in different ways.
Deductive Reasoning - The ability to apply general rules to specific problems to produce answers that make sense.
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).
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).
Mathematical Reasoning - The ability to choose the right mathematical methods or formulas to solve a problem.
Near Vision - The ability to see details at close range (within a few feet of the observer).
Number Facility - The ability to add, subtract, multiply, or divide quickly and correctly.
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.
Knowledge
Administration and Management - Knowledge of business and management principles involved in strategic planning, resource allocation, human resources modeling, leadership technique, production methods, and coordination of people and resources.
Computers and Electronics - Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
Customer and Personal Service - Knowledge of principles and processes for providing customer and personal services. This includes customer needs assessment, meeting quality standards for services, and evaluation of customer satisfaction.
Design - Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models.
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.
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.
Mathematics - Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
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.
Telecommunications - Knowledge of transmission, broadcasting, switching, control, and operation of telecommunications systems.
Tasks
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.
Work Activities
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.
Documenting/Recording Information - Entering, transcribing, recording, storing, or maintaining information in written or electronic/magnetic form.
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.
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.
Processing Information - Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
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.
Personality Traits
Achievement/Effort - Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.
Adaptability/Flexibility - Job requires being open to change (positive or negative) and to considerable variety in the workplace.
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.
Dependability - Job requires being reliable, responsible, and dependable, and fulfilling obligations.
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.
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.
Persistence - Job requires persistence in the face of obstacles.