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TITLE: Mathematicians
DEFINITION: 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.
TASKS:
1. Conducts research in fundamental mathematics and in application of mathematical techniques to science, management and other fields.
2. Conceives or directs ideas for application of mathematics to wide variety of fields, including science, engineering, military planning, electronic data processing, and management.
3. Conducts research in such branches of mathematics as algebra, geometry, number theory, logic and topology.
4. Performs computations and applies methods of numerical analysis.
5. Studies and test hypotheses and alternative theories.
6. Applies mathematics or mathematical methods of numerical analysis, and operates or directs operation of desk calculators and mechanical and other functional areas.
7. Utilizes knowledge of such subjects or fields as physics, engineering, astronomy, biology, economics, business and industrial management, or cryptography.
8. Operates or directs operation of desk calculators and mechanical and electronic computation machines, analyzers, and plotters in solving problem support of mathematical, scientific or industrial research.
9. Acts as advisor or consultant to research personnel concerning mathematical methods and applications.
KNOWLEDGE:
Knowledge elements are ranked by importance.
100 Mathematics
Knowledge of numbers, their operations, and interrelationships including arithmetic, algebra, geometry, calculus, statistics, and their applications
50 Computers and Electronics
Knowledge of electric circuit boards, processors, chips, and computer hardware and software, including applications and programming
46 Administration and Management
Knowledge of principles and processes involved in business and organizational planning, coordination, and execution. This includes strategic planning, resource allocation, manpower modeling, leadership techniques, and production methods
42 Engineering and Technology
Knowledge of equipment, tools, mechanical devices, and their uses to produce motion, light, power, technology, and other applications
42 Physics
Knowledge and prediction of physical principles, laws, and applications including air, water, material dynamics, light, atomic principles, heat, electric theory, earth formations, and meteorological and related natural phenomena
42 English Language
Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar
38 Biology
Knowledge of plant and animal living tissue, cells, organisms, and entities, including their functions, interdependencies, and interactions with each other and the environment
38 Education and Training
Knowledge of instructional methods and training techniques including curriculum design principles, learning theory, group and individual teaching techniques, design of individual development plans, and test design principles
29 Communications and Media
Knowledge of media production, communication, and dissemination techniques and methods including alternative ways to inform and entertain via written, oral, and visual media
29 Economics and Accounting
Knowledge of economic and accounting principles and practices, the financial markets, banking, and the analysis and reporting of financial data
21 Personnel and Human Resources
Knowledge of policies and practices involved in personnel/human resource functions. This includes recruitment, selection, training, and promotion regulations and procedures; compensation and benefits packages; labor relations and negotiation strategies; and personnel information systems
17 Production and Processing
Knowledge of inputs, outputs, raw materials, waste, quality control, costs, and techniques for maximizing the manufacture and distribution of goods
17 Psychology
Knowledge of human behavior and performance, mental processes, psychological research methods, and the assessment and treatment of behavioral and affective disorders
17 Sociology and Anthropology
Knowledge of group behavior and dynamics, societal trends and influences, cultures, their history, migrations, ethnicity, and origins
13 Design
Knowledge of design techniques, principles, tools and instruments involved in the production and use of precision technical plans, blueprints, drawings, and models
13 Therapy and Counseling
Knowledge of information and techniques needed to rehabilitate physical and mental ailments and to provide career guidance including alternative treatments, rehabilitation equipment and its proper use, and methods to evaluate treatment effects
13 Mechanical
Knowledge of machines and tools, including their designs, uses, benefits, repair, and maintenance
8 Clerical
Knowledge of administrative and clerical procedures and systems such as word processing systems, filing and records management systems, stenography and transcription, forms design principles, and other office procedures and terminology
8 Food Production
Knowledge of techniques and equipment for planting, growing, and harvesting of food for consumption including crop rotation methods, animal husbandry, and food storage/handling techniques
4 Telecommunications
Knowledge of transmission, broadcasting, switching, control, and operation of telecommunications systems
4 Customer and Personal Service
Knowledge of principles and processes for providing customer and personal services including needs assessment techniques, quality service standards, alternative delivery systems, and customer satisfaction evaluation techniques
4 Public Safety and Security
Knowledge of weaponry, public safety, and security operations, rules, regulations, precautions, prevention, and the protection of people, data, and property
4 Chemistry
Knowledge of the 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
4 Philosophy and Theology
Knowledge of different philosophical systems and religions, including their basic principles, values, ethics, ways of thinking, customs, and practices, and their impact on human culture
SKILLS:
Skills elements are ranked by importance.
100 Mathematics
Using mathematics to solve problems
79 Reading Comprehension
Understanding written sentences and paragraphs in work related documents
79 Active Learning
Working with new material or information to grasp its implications
79 Learning Strategies
Using multiple approaches when learning or teaching new things
75 Information Organization
Finding ways to structure or classify multiple pieces of information
75 Critical Thinking
Using logic and analysis to identify the strengths and weaknesses of different approaches
75 Information Gathering
Knowing how to find information and identifying essential information
71 Idea Generation
Generating a number of different approaches to problems
71 Solution Appraisal
Observing and evaluating the outcomes of a problem solution to identify lessons learned or redirect efforts
67 Writing
Communicating effectively with others in writing as indicated by the needs of the audience
63 Problem Identification
Identifying the nature of problems
63 Synthesis/Reorganization
Reorganizing information to get a better approach to problems or tasks
58 Active Listening
Listening to what other people are saying and asking questions as appropriate
58 Speaking
Talking to others to effectively convey information
58 Idea Evaluation
Evaluating the likely success of an idea in relation to the demands of the situation
54 Implementation Planning
Developing approaches for implementing an idea
50 Science
Using scientific methods to solve problems
46 Visioning
Developing an image of how a system should work under ideal conditions
46 Monitoring
Assessing how well one is doing when learning or doing something
42 Operations Analysis
Analyzing needs and product requirements to create a design
42 Systems Evaluation
Looking at many indicators of system performance, taking into account their accuracy
38 Instructing
Teaching others how to do something
33 Judgment and Decision Making
Weighing the relative costs and benefits of a potential action
33 Testing
Conducting tests to determine whether equipment, software, or procedures are operating as expected
29 Programming
Writing computer programs for various purposes
29 Identification of Key Causes
Identifying the things that must be changed to achieve a goal
29 Product Inspection
Inspecting and evaluating the quality of products
25 Technology Design
Generating or adapting equipment and technology to serve user needs
21 Identifying Downstream Consequences
Determining the long-term outcomes of a change in operations
21 Coordination
Adjusting actions in relation to others' actions
21 Systems Perception
Determining when important changes have occurred in a system or are likely to occur
21 Equipment Selection
Determining the kind of tools and equipment needed to do a job
21 Time Management
Managing one's own time and the time of others
17 Service Orientation
Actively looking for ways to help people
17 Troubleshooting
Determining what is causing an operating error and deciding what to do about it
17 Operation and Control
Controlling operations of equipment or systems
13 Social Perceptiveness
Being aware of others' reactions and understanding why they react the way they do
13 Persuasion
Persuading others to approach things differently
13 Management of Financial Resources
Determining how money will be spent to get the work done, and accounting for these expenditures
8 Repairing
Repairing machines or systems using the needed tools
8 Equipment Maintenance
Performing routine maintenance and determining when and what kind of maintenance is needed
8 Operation Monitoring
Watching gauges, dials, or other indicators to make sure a machine is working properly
8 Negotiation
Bringing others together and trying to reconcile differences
4 Management of Personnel Resources
Motivating, developing, and directing people as they work, identifying the best people for the job
4 Management of Material Resources
Obtaining and seeing to the appropriate use of equipment, facilities, and materials needed to do certain work .
ABILITIES:
Abilities elements are ranked by importance.
95 Mathematical Reasoning
The ability to understand and organize a problem and then to select a mathematical method or formula to solve the problem
95 Number Facility
The ability to add, subtract, multiply, or divide quickly and correctly
75 Deductive Reasoning
The ability to apply general rules to specific problems to come up with logical answers. It involves deciding if an answer makes sense.
70 Oral Comprehension
The ability to listen to and understand information and ideas presented through spoken words and sentences
70 Written Comprehension
The ability to read and understand information and ideas presented in writing
70 Inductive Reasoning
The ability to combine separate pieces of information, or specific answers to problems, to form general rules or conclusions. It includes coming up with a logical explanation for why a series of seemingly unrelated events occur together.
65 Written Expression
The ability to communicate information and ideas in writing so others will understand
65 Information Ordering
The ability to correctly follow a given rule or set of rules in order to arrange things or actions in a certain order. The things or actions can include numbers, letters, words, pictures, procedures, sentences, and mathematical or logical operations.
60 Fluency of Ideas
The ability to come up with a number of ideas about a given topic. It concerns the number of ideas produced and not the quality, correctness, or creativity of the ideas.
60 Memorization
The ability to remember information such as words, numbers, pictures, and procedures
55 Near Vision
The ability to see details of objects at a close range (within a few feet of the observer)
50 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
45 Oral Expression
The ability to communicate information and ideas in speaking so others will understand
45 Speech Clarity
The ability to speak clearly so that it is understandable to a listener
40 Category Flexibility
The ability to produce many rules so that each rule tells how to group (or combine) a set of things in a different way.
35 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.
25 Trunk Strength
The ability to use one's abdominal and lower back muscles to support part of the body repeatedly or continuously over time without "giving out" or fatiguing
25 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
25 Visualization
The ability to imagine how something will look after it is moved around or when its parts are moved or rearranged
25 Speed of Closure
The ability to quickly make sense of information that seems to be without meaning or organization. It involves quickly combining and organizing different pieces of information into a meaningful pattern
20 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
20 Speech Recognition
The ability to identify and understand the speech of another person
20 Auditory Attention
The ability to focus on a single source of auditory (hearing) information in the presence of other distracting sounds
15 Perceptual Speed
The ability to quickly and accurately compare 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
15 Wrist-Finger Speed
The ability to make fast, simple, repeated movements of the fingers, hands, and wrists
15 Control Precision
The ability to quickly and repeatedly make precise adjustments in moving the controls of a machine or vehicle to exact positions
10 Selective Attention
The ability to concentrate and not be distracted while performing a task over a period of time
10 Arm-Hand Steadiness
The ability to keep the hand and arm steady while making an arm movement or while holding the arm and hand in one position
5 Far Vision
The ability to see details at a distance
5 Manual Dexterity
The ability to quickly make coordinated movements of one hand, a hand together with its arm, or two hands to grasp, manipulate, or assemble objects
WORK ACTIVITIES:
Work activities elements are ranked by importance.
95 Processing Information
Compiling, coding, categorizing, calculating, tabulating, auditing, verifying, or processing information or data.
90 Analyzing Data or Information
Identifying underlying principles, reasons, or facts by breaking down information or data into separate parts.
80 Getting Information Needed to Do the Job
Observing, receiving, and otherwise obtaining information from all relevant sources.
75 Identifying Objects, Actions, and Events
Identifying information received by making estimates or categorizations, recognizing differences or similarities, or sensing changes in circumstances or events.
75 Interacting With Computers
Controlling computer functions by using programs, setting up functions, writing software, or otherwise communicating with computer systems.
70 Thinking Creatively
Originating, inventing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.
65 Interpreting Meaning of Information to Others
Translating or explaining what information means and how it can be understood or used to support responses or feedback to others.
65 Updating and Using Job-Relevant Knowledge
Keeping up-to-date technically and knowing one's own jobs' and related jobs' functions.
55 Making Decisions and Solving Problems
Combining, evaluating, and reasoning with information and data to make decisions and solve problems. These processes involve making decisions about the relative importance of information and choosing the best solution.
45 Documenting or Recording Information
Entering, transcribing, recording, storing, or maintaining information in either written form or by electronic/magnetic recording.
45 Communicating With Other Workers
Providing information to supervisors, fellow workers, and subordinates. This information can be exchanged face-to-face, in writing, or via telephone/electronic transfer.
45 Estimating Needed Characteristics
Estimating the Characteristics of Materials, Products, Events, or Information: Estimating sizes, distances, and quantities, or determining time, costs, resources, or materials needed to perform a work activity.
40 Providing Consultation and Advice to Others
Providing consultation and expert advice to management or other groups on technical, systems-related, or process related topics.
40 Handling and Moving Objects
Using one's own hands and arms in handling, installing, forming, positioning, and moving materials, or in manipulating things, including the use of keyboards.
35 Establishing and Maintaining Relationships
Developing constructive and cooperative working relationships with others.
35 Developing Objectives and Strategies
Establishing long range objectives and specifying the strategies and actions to achieve these objectives.
30 Evaluating Information Against Standards
Evaluating information against a set of standards and verifying that it is correct.
30 Communicating With Persons Outside Organization
Communicating with persons outside the organization, representing the organization to customers, the public, government, and other external sources. This information can be exchanged face-to-face, in writing, or via telephone/electronic transfer.
30 Judging Qualities of Things, Services, or People
Making judgments about or assessing the value, importance, or quality of things or people.
30 Implementing Ideas or Programs
Conducting or carrying out work procedures and activities in accord with one's own ideas or information provided through directions/instructions for purposes of installing, modifying, preparing, delivering, constructing, integrating, finishing, or completing programs, systems, structures, or products.
30 Monitor Processes, Material, or Surroundings
Monitoring and reviewing information from materials, events, or the environment, often to detect problems or to find out when things are finished.
25 Teaching Others
Identifying educational needs, developing formal training programs or classes, and teaching or instructing others.
20 Controlling Machines and Processes
Using either control mechanisms or direct physical activity to operate machines or processes (not including computers or vehicles).
20 Organizing, Planning, and Prioritizing
Developing plans to accomplish work, and prioritizing and organizing one's own work.
20 Assisting and Caring for Others
Providing assistance or personal care to others.
20 Inspecting Equipment, Structures, or Material
Inspecting or diagnosing equipment, structures, or materials to identify the causes of errors or other problems or defects.
15 Selling or Influencing Others
Convincing others to buy merchandise/goods, or otherwise changing their minds or actions.
15 Performing Administrative Activities
Approving requests, handling paperwork, and performing day-to-day administrative tasks.
10 Repairing and Maintaining Electrical Equipment
Fixing, servicing, adjusting, regulating, calibrating, fine-tuning, or testing machines, devices, and equipment that operate primarily on the basis of electrical or electronic (not mechanical) principles.
10 Monitoring and Controlling Resources
Monitoring and controlling resources and overseeing the spending of money.
10 Performing General Physical Activities
Performing physical activities that require moving one's whole body, such as in climbing, lifting, balancing, walking, stooping, where the activities often also require considerable use of the arms and legs, such as in the physical handling of materials.
10 Repairing and Maintaining Mechanical Equipment
Fixing, servicing, aligning, setting up, adjusting, and testing machines, devices, moving parts, and equipment that operate primarily on the basis of mechanical (not electronic) principles.
10 Coordinating Work and Activities of Others
Coordinating members of a work group to accomplish tasks.
10 Coaching and Developing Others
Identifying developmental needs of others and coaching or otherwise helping others to improve their knowledge or skills.
5 Scheduling Work and Activities
Scheduling events, programs, activities, as well as the work of others.
5 Drafting and Specifying Technical Devices
Providing documentation, detailed instructions, drawings, or specifications to inform others about how devices, parts, equipment, or structures are to be fabricated, constructed, assembled, modified, maintained, or used.
5 Resolving Conflict or Negotiating with Others
Handling complaints, arbitrating disputes, and resolving grievances, or otherwise negotiating with others.
5 Developing and Building Teams
Encouraging and building mutual trust, respect, and cooperation among team members.
5 Guiding, Directing and Motivating Subordinates
Providing guidance and direction to subordinates, including setting performance standards and monitoring subordinates.
5 Staffing Organizational Units
Recruiting, interviewing, selecting, hiring, and promoting persons for the organization.
WORK CONTEXT:
Work context elements are ranked by frequency (F), importance (I), responsibility (R), amount of contact (C), how serious (S), objective vs. subjective (O), automation (A), extent of frustration (E), responsible for health and safety (H), likelihood of injury (L), degree of injury (D) .
100 (F) Indoors
How frequently does this job require the worker to work: Indoors
85 (F) Sitting
How much time in a usual work period does the worker spend: Sitting?
76 (I) Importance of Being Exact or Accurate
How important is being very exact or highly accurate in performing this job?
60 (I) Importance of Being Sure All Is Done
How important is it to be sure that all the details of this job are performed and everything is done completely?
48 (I) Coordinate or Lead Others
How important are interactions requiring the worker to: Coordinate or lead others in accomplishing work activities (not supervision)?
47 (S) Consequence of Error
How serious would the result usually be if the worker made a mistake that was not readily correctable?
40 (F) Standing
How much time in a usual work period does the worker spend: Standing?
40 (F) Using Hands on Objects, Tools, Controls
How much time in a usual work period does the worker spend: Using hands to handle, control, or feel objects, tools or controls?
36 (I) Importance of Being Aware of New Events
How important is being constantly aware of either frequently changing events (e.g. security guard watching for shoplifters) or infrequent events (e.g. radar operator watching for tornadoes) to performing this job?
30 (C) Job-Required Social Interaction
How much does this job require the worker to be in contact (face-to-face, by telephone, or otherwise) with others in order to perform it?
24 (I) Provide a Service to Others
How important are interactions requiring the worker to: Provide a service to others (e.g., customers)?
23 (R) Responsibility for Outcomes and Results
How responsible is the worker for work outcomes and results of other workers?
21 (E) Frustrating Circumstances
To what extent do frustrating circumstances ("road blocks" to work that are beyond the worker's control) hinder the accomplishment of this job?
20 (I) Deal With External Customers
How important are interactions requiring the worker to: Deal with external customers (e.g., retail sales) or the public in general (e.g., police work)?
20 (F) Making Repetitive Motions
How much time in a usual work period does the worker spend: Making repetitive motions?
20 (I) Importance of Repeating Same Tasks
How important is repeating the same physical activities (e.g., key entry) or mental activities (e.g., checking entries in a ledger) over and over, without stopping, to performing this job?
17 (O) Objective or Subjective Information
How objective or subjective is the information communicated in this job?
17 (A) Degree of Automation
Indicate the level of automation of this job.
16 (I) Supervise, Coach, Train Others
How important are interactions requiring the worker to: Supervise, coach, train, or develop other employees?
16 (I) Take a Position Opposed to Others
How important are interactions requiring the worker to: Take a position opposed to coworkers or others?
12 (I) Pace Determined by Speed of Equipment
How important is it to this job that the pace is determined by the speed of equipment or machinery? (This does not refer to keeping busy at all times on this job.)
12 (I) Persuade Someone to a Course of Action
How important are interactions requiring the worker to: Persuade someone to a course of action (informally) or influence others to buy something (to sell)?
10 (F) Walking or Running
How much time in a usual work period does the worker spend: Walking or running?
5 (F) Special Uniform
How often does the worker wear: A special uniform, such as that of a commercial pilot, nurse, police officer, or military personnel?
5 (F) Kneeling, Crouching or Crawling
How much time in a usual work period does the worker spend: Kneeling, stooping, crouching or crawling?
5 (F) Bending or Twisting the Body
How much time in a usual work period does the worker spend: Bending or twisting the body?
5 (F) Frequency in Conflict Situations
How frequently do the job requirements place the worker in conflict situations?
INTERESTS:
Interest elements are ranked by occupational interest.
100 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.
61 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.
50 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.
44 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.
28 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.
17 Social
Social occupations frequently involve working with, communicating with, and teaching people. These occupations often involve helping or providing service to others.
WORK VALUES:
Work values elements are ranked by extent.
83 Achievement-Mean Extent
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.
82 Independence-Mean Extent
Occupations that satisfy this work value allow employs to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy.
68 Working Conditions-Mean Extent
Occupations that satisfy this work value offer job security and good working conditions. Corresponding needs are Activity, Compensation, Independence, Security, Variety and Working Conditions.
56 Recognition-Mean Extent
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.
46 Support-Mean Extent
Occupations that satisfy this work value offer supportive management that stands behind employees. Corresponding needs are Company Policies, Supervision: Human Relations and Supervision: Technical.
46 Relationships-Mean Extent
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.
94 Autonomy
Workers on this job plan their work with little supervision
91 Ability Utilization
Workers on this job make use of their individual abilities
81 Working Conditions
Workers on this job have good working conditions
81 Independence
Workers on this job do their work alone
78 Responsibility
Workers on this job make decisions on their own
75 Achievement
Workers on this job get a feeling of accomplishment
75 Creativity
Workers on this job try out their own ideas
75 Security
Workers on this job have steady employment
72 Moral Values
Workers on this job are never pressured to do things that go against their sense of right and wrong
66 Social Status
Workers on this job are looked up to by others in their company and their community
66 Company Policies and Practices
Workers on this job are treated fairly by the company
66 Activity
Workers on this job are busy all the time
63 Recognition
Workers on this job receive recognition for the work they do
59 Compensation
Workers on this job are paid well in comparison with other workers
53 Advancement
Workers on this job have opportunities for advancement
50 Supervision, Human Relations
Workers on this job have supervisors who back up their workers with management
47 Co-workers
Workers on this job have co-workers who are easy to get along with
44 Authority
Workers on this job give directions and instructions to others
44 Variety
Workers on this job have something different to do every day
22 Supervision, Technical
Workers on this job have supervisors who train their workers well
19 Social Service
Workers on this job have work where they do things for other people
CROSSWALKS:
| DOT91 (Dictionary of Occupational Titles): |
020067014 Mathematician |
| AIM97 (Apprenticeship Information Management): |
No crosswalks |
| CEN90 (1990 Census Occupations): |
068 Mathematical Scientists, N.E.C. |
| CIP90 (Classification of Instructional Programs): |
400810 Theoretical and Mathematical Physics 400801 Physics, General 270301 Applied Mathematics, General 270101 Mathematics |
| GOE93 (Guide for Occupational Exploration): |
020101 Physical Sciences: Theoretical Research |
| MOC97 (Military Occupational Codes): |
2050 Mathematics Research Officer 49E Operations Research, Test, and Evaluation 49D Operations Research, Planning, Programming and Resource Management 49B Operations Research, Personnel 49C Operations Research, Combat Operations/Materiel Systems 49A Operations Research, General 61S3E Scientist 61S1E Scientist |
| OES98 (Occupational Employment Statistics): |
25319 All Other Mathematical Scientists |
| OPM97 (Office of Personnel Management Occupations): |
1520 Mathematics 1540 Cryptography |
| SOC98 (Standard Occupational Classification): |
15-2021 Mathematicians |
