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Mathematicians
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CheckoutCareers.com
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Mathematicians
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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.
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Degrees
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Abilities
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Mathematical Reasoning| | The ability to choose the right mathematical methods or formulas to solve a problem. |
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Oral Comprehension| | The ability to listen to and understand information and ideas presented through spoken words and sentences. |
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Written Comprehension| | The ability to read and understand information and ideas presented in writing. |
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Number Facility| | The ability to add, subtract, multiply, or divide quickly and correctly. |
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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. |
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Deductive Reasoning| | The ability to apply general rules to specific problems to produce answers that make sense. |
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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). |
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Inductive Reasoning| | The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events). |
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Oral Expression| | The ability to communicate information and ideas in speaking so others will understand. |
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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). |
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Written Expression| | The ability to communicate information and ideas in writing so others will understand. |
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Speed of Closure| | The ability to quickly make sense of, combine, and organize information into meaningful patterns. |
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Category Flexibility| | The ability to generate or use different sets of rules for combining or grouping things in different ways. |
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Near Vision| | The ability to see details at close range (within a few feet of the observer). |
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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. |
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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. |
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Speech Clarity| | The ability to speak clearly so others can understand you. |
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Selective Attention| | The ability to concentrate on a task over a period of time without being distracted. |
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Visualization| | The ability to imagine how something will look after it is moved around or when its parts are moved or rearranged. |
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Speech Recognition| | The ability to identify and understand the speech of another person. |
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Perceptual Speed| | The ability to quickly and accurately compare similarities and differences among sets of letters, numbers, objects, pictures, or patterns. The things to be compared may be presented at the same time or one after the other. This ability also includes comparing a presented object with a remembered object. |
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Finger Dexterity| | The ability to make precisely coordinated movements of the fingers of one or both hands to grasp, manipulate, or assemble very small objects. |
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Memorization| | The ability to remember information such as words, numbers, pictures, and procedures. |
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Far Vision| | The ability to see details at a distance. |
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Time Sharing| | The ability to shift back and forth between two or more activities or sources of information (such as speech, sounds, touch, or other sources). |
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Hearing Sensitivity| | The ability to detect or tell the differences between sounds that vary in pitch and loudness. |
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Visual Color Discrimination| | The ability to match or detect differences between colors, including shades of color and brightness. |
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Depth Perception| | The ability to judge which of several objects is closer or farther away from you, or to judge the distance between you and an object. |
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Auditory Attention| | The ability to focus on a single source of sound in the presence of other distracting sounds. |
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Trunk Strength| | The ability to use your abdominal and lower back muscles to support part of the body repeatedly or continuously over time without 'giving out' or fatiguing. |
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Wrist-Finger Speed| | The ability to make fast, simple, repeated movements of the fingers, hands, and wrists. |
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Interests
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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. |
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Second Interest High-Point| | Secondary-Cutoff/Rank Descriptiveness |
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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. |
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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. |
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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. |
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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. |
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First Interest High-Point| | Primary-Rank Descriptiveness |
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Social| | Social occupations frequently involve working with, communicating with, and teaching people. These occupations often involve helping or providing service to others. |
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Knowledge
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Mathematics| | Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications. |
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Computers and Electronics| | Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming. |
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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. |
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English Language| | Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar. |
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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. |
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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. |
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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. |
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Biology| | Knowledge of plant and animal organisms, their tissues, cells, functions, interdependencies, and interactions with each other and the environment. |
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Production and Processing| | Knowledge of raw materials, production processes, quality control, costs, and other techniques for maximizing the effective manufacture and distribution of goods. |
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Design| | Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models. |
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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. |
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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. |
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Foreign Language| | Knowledge of the structure and content of a foreign (non-English) language including the meaning and spelling of words, rules of composition and grammar, and pronunciation. |
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Clerical| | Knowledge of administrative and clerical procedures and systems such as word processing, managing files and records, stenography and transcription, designing forms, and other office procedures and terminology. |
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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. |
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Personnel and Human Resources| | Knowledge of principles and procedures for personnel recruitment, selection, training, compensation and benefits, labor relations and negotiation, and personnel information systems. |
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Economics and Accounting| | Knowledge of economic and accounting principles and practices, the financial markets, banking and the analysis and reporting of financial data. |
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Telecommunications| | Knowledge of transmission, broadcasting, switching, control, and operation of telecommunications systems. |
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Psychology| | Knowledge of human behavior and performance; individual differences in ability, personality, and interests; learning and motivation; psychological research methods; and the assessment and treatment of behavioral and affective disorders. |
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Sales and Marketing| | Knowledge of principles and methods for showing, promoting, and selling products or services. This includes marketing strategy and tactics, product demonstration, sales techniques, and sales control systems. |
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Law and Government| | Knowledge of laws, legal codes, court procedures, precedents, government regulations, executive orders, agency rules, and the democratic political process. |
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Transportation| | Knowledge of principles and methods for moving people or goods by air, rail, sea, or road, including the relative costs and benefits. |
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Geography| | Knowledge of principles and methods for describing the features of land, sea, and air masses, including their physical characteristics, locations, interrelationships, and distribution of plant, animal, and human life. |
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Mechanical| | Knowledge of machines and tools, including their designs, uses, repair, and maintenance. |
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Sociology and Anthropology| | Knowledge of group behavior and dynamics, societal trends and influences, human migrations, ethnicity, cultures and their history and origins. |
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Philosophy and Theology| | Knowledge of different philosophical systems and religions. This includes their basic principles, values, ethics, ways of thinking, customs, practices, and their impact on human culture. |
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Public Safety and Security| | Knowledge of relevant equipment, policies, procedures, and strategies to promote effective local, state, or national security operations for the protection of people, data, property, and institutions. |
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Medicine and Dentistry| | Knowledge of the information and techniques needed to diagnose and treat human injuries, diseases, and deformities. This includes symptoms, treatment alternatives, drug properties and interactions, and preventive health-care measures. |
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History and Archeology| | Knowledge of historical events and their causes, indicators, and effects on civilizations and cultures. |
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Building and Construction| | Knowledge of materials, methods, and the tools involved in the construction or repair of houses, buildings, or other structures such as highways and roads. |
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Fine Arts| | Knowledge of the theory and techniques required to compose, produce, and perform works of music, dance, visual arts, drama, and sculpture. |
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Wages
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Related Careers
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Compensation, Benefits, & Job Analysis Specialists| | Conduct programs of compensation and benefits and job analysis for employer. May specialize in specific areas, such as position classification and pension programs. |
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Cost Estimators| | Prepare cost estimates for product manufacturing, construction projects, or services to aid management in bidding on or determining price of product or service. May specialize according to particular service performed or type of product manufactured. |
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Insurance Underwriters| | Review individual applications for insurance to evaluate degree of risk involved and determine acceptance of applications. |
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Operations Research Analysts| | Formulate and apply mathematical modeling and other optimizing methods using a computer to develop and interpret information that assists management with decision making, policy formulation, or other managerial functions. May develop related software, service, or products. Frequently concentrates on collecting and analyzing data and developing decision support software. May develop and supply optimal time, cost, or logistics networks for program evaluation, review, or implementation. |
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Statistical Assistants| | Compile and compute data according to statistical formulas for use in statistical studies. May perform actuarial computations and compile charts and graphs for use by actuaries. Includes actuarial clerks. |
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Statisticians| | Engage in the development of mathematical theory or apply statistical theory and methods to collect, organize, interpret, and summarize numerical data to provide usable information. May specialize in fields, such as bio-statistics, agricultural statistics, business statistics, economic statistics, or other fields. |
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Traffic Technicians| | Conduct field studies to determine traffic volume, speed, effectiveness of signals, adequacy of lighting, and other factors influencing traffic conditions, under direction of traffic engineer. |
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Skills
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Mathematics| | Using mathematics to solve problems. |
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Reading Comprehension| | Understanding written sentences and paragraphs in work related documents. |
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Critical Thinking| | Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems. |
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Active Learning| | Understanding the implications of new information for both current and future problem-solving and decision-making. |
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Complex Problem Solving| | Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions. |
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Programming| | Writing computer programs for various purposes. |
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Science| | Using scientific rules and methods to solve problems. |
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Writing| | Communicating effectively in writing as appropriate for the needs of the audience. |
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Instructing| | Teaching others how to do something. |
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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. |
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Speaking| | Talking to others to convey information effectively. |
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Operations Analysis| | Analyzing needs and product requirements to create a design. |
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Learning Strategies| | Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things. |
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Judgment and Decision Making| | Considering the relative costs and benefits of potential actions to choose the most appropriate one. |
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Systems Analysis| | Determining how a system should work and how changes in conditions, operations, and the environment will affect outcomes. |
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Persuasion| | Persuading others to change their minds or behavior. |
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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. |
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Monitoring| | Monitoring/Assessing performance of yourself, other individuals, or organizations to make improvements or take corrective action. |
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Troubleshooting| | Determining causes of operating errors and deciding what to do about it. |
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Quality Control Analysis| | Conducting tests and inspections of products, services, or processes to evaluate quality or performance. |
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Time Management| | Managing one's own time and the time of others. |
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Coordination| | Adjusting actions in relation to others' actions. |
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Technology Design| | Generating or adapting equipment and technology to serve user needs. |
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Equipment Selection| | Determining the kind of tools and equipment needed to do a job. |
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Social Perceptiveness| | Being aware of others' reactions and understanding why they react as they do. |
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Negotiation| | Bringing others together and trying to reconcile differences. |
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Management of Financial Resources| | Determining how money will be spent to get the work done, and accounting for these expenditures. |
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Service Orientation| | Actively looking for ways to help people. |
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Management of Personnel Resources| | Motivating, developing, and directing people as they work, identifying the best people for the job. |
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Management of Material Resources| | Obtaining and seeing to the appropriate use of equipment, facilities, and materials needed to do certain work. |
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Installation| | Installing equipment, machines, wiring, or programs to meet specifications. |
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Operation Monitoring| | Watching gauges, dials, or other indicators to make sure a machine is working properly. |
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Operation and Control| | Controlling operations of equipment or systems. |
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Repairing| | Repairing machines or systems using the needed tools. |
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Equipment Maintenance| | Performing routine maintenance on equipment and determining when and what kind of maintenance is needed. |
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Tasks
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| Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields. |
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| Develop computational methods for solving problems that occur in areas of science and engineering, or that come from applications in business or industry. |
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| Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences. |
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| Perform computations and apply methods of numerical analysis to data. |
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| Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation. |
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| Assemble sets of assumptions and explore the consequences of each set. |
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| Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols. |
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| Develop new principles and new relationships between existing mathematical principles to advance mathematical science. |
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| Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code. |
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| Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic. |
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Career Activities
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| Thinking Creatively |
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| create mathematical or statistical diagrams or charts |
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| develop mathematical ideas or interpretations |
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| develop mathematical or computer languages |
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| develop mathematical simulation models |
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| develop new products based on scientific research results |
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| develop scientific or mathematical hypotheses, theories, or laws |
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| Updating and Using Relevant Knowledge |
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| use interpersonal communication techniques |
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| use knowledge of investigation techniques |
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| use library or online Internet research techniques |
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| use mathematical or statistical methods to identify or analyze problems |
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| use oral or written communication techniques |
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| use quantitative research methods |
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| use scientific research methodology |
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| Analyzing Data or Information |
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| analyze scientific research data or investigative findings |
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| analyze social or economic data |
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| perform statistical modeling |
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| Getting Information |
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| collect scientific or technical data |
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| collect statistical data |
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| Processing Information |
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| compile numerical or statistical data |
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| develop tables depicting data |
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| Making Decisions and Solving Problems |
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| make decisions |
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| resolve engineering or science problems |
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| Interacting With Computers |
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| develop or maintain databases |
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| use computers to enter, access or retrieve data |
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| use relational database software |
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| use spreadsheet software |
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| use word processing or desktop publishing software |
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| Interpreting the Meaning of Information for Others |
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| explain complex mathematical information |
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| write scholarly or technical research papers |
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| Provide Consultation and Advice to Others |
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| advise clients or customers |
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| advise governmental or industrial personnel |
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| provide expert testimony on research results |
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| recommend further study or action based on research data |
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| Communicating with Supervisors, Peers, or Subordinates |
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| confer with engineering, technical or manufacturing personnel |
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| confer with research personnel |
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| consult with managerial or supervisory personnel |
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| Communicating with Persons Outside Organization |
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| communicate technical information |
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| confer with scientists |
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| make presentations |
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| Organizing, Planning, and Prioritizing Work |
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| plan scientific research or investigative studies |
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| Coordinating the Work and Activities of Others |
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| direct and coordinate activities of workers or staff |
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| direct and coordinate scientific research or investigative studies |
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| Performing Administrative Activities |
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| prepare reports |
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| prepare technical reports or related documentation |
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Career Context
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| Indoors, Environmentally Controlled |
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| Electronic Mail |
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| Spend Time Sitting |
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| Freedom to Make Decisions |
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| Face-to-Face Discussions |
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| Importance of Being Exact or Accurate |
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| Structured versus Unstructured Work |
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| Telephone |
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| Work With Work Group or Team |
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| Contact With Others |
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| Importance of Repeating Same Tasks |
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| Level of Competition |
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| Spend Time Using Your Hands to Handle, Control, or Feel Objects, Tools, or Controls |
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| Coordinate or Lead Others |
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| Letters and Memos |
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| Extremely Bright or Inadequate Lighting |
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| Sounds, Noise Levels Are Distracting or Uncomfortable |
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| Spend Time Making Repetitive Motions |
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| In an Enclosed Vehicle or Equipment |
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| Consequence of Error |
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| Deal With External Customers |
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Career Styles
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Analytical Thinking| | Job requires analyzing information and using logic to address work-related issues and problems. |
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Attention to Detail| | Job requires being careful about detail and thorough in completing work tasks. |
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Innovation| | Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems. |
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Achievement/Effort| | Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks. |
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Persistence| | Job requires persistence in the face of obstacles. |
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Initiative| | Job requires a willingness to take on responsibilities and challenges. |
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Integrity| | Job requires being honest and ethical. |
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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. |
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Dependability| | Job requires being reliable, responsible, and dependable, and fulfilling obligations. |
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Adaptability/Flexibility| | Job requires being open to change (positive or negative) and to considerable variety in the workplace. |
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Cooperation| | Job requires being pleasant with others on the job and displaying a good-natured, cooperative attitude. |
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Stress Tolerance| | Job requires accepting criticism and dealing calmly and effectively with high stress situations. |
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Leadership| | Job requires a willingness to lead, take charge, and offer opinions and direction. |
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Self Control| | Job requires maintaining composure, keeping emotions in check, controlling anger, and avoiding aggressive behavior, even in very difficult situations. |
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Concern for Others| | Job requires being sensitive to others' needs and feelings and being understanding and helpful on the job. |
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Social Orientation| | Job requires preferring to work with others rather than alone, and being personally connected with others on the job. |
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Career Needs
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Autonomy| | Workers on this job plan their work with little supervision. |
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Ability Utilization| | Workers on this job make use of their individual abilities. |
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Independence| | Workers on this job do their work alone. |
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Working Conditions| | Workers on this job have good working conditions. |
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Responsibility| | Workers on this job make decisions on their own. |
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Achievement| | Workers on this job get a feeling of accomplishment. |
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Creativity| | Workers on this job try out their own ideas. |
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Security| | Workers on this job have steady employment. |
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Moral Values| | Workers on this job are never pressured to do things that go against their sense of right and wrong. |
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Activity| | Workers on this job are busy all the time. |
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Company Policies and Practices| | Workers on this job are treated fairly by the company. |
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Social Status| | Workers on this job are looked up to by others in their company and their community. |
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Recognition| | Workers on this job receive recognition for the work they do. |
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Compensation| | Workers on this job are paid well in comparison with other workers. |
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Advancement| | Workers on this job have opportunities for advancement. |
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Supervision, Human Relations| | Workers on this job have supervisors who back up their workers with management. |
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Co-workers| | Workers on this job have co-workers who are easy to get along with. |
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Authority| | Workers on this job give directions and instructions to others. |
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Variety| | Workers on this job have something different to do every day. |
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Supervision, Technical| | Workers on this job have supervisors who train their workers well. |
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Social Service| | Workers on this job have work where they do things for other people. |
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Career Values
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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. |
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Independence| | Occupations that satisfy this work value allow employs to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy. |
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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. |
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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. |
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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. |
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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. |
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