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Summary Report for:
15-2021.00 - Mathematicians

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 of reported 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

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Tasks  |  Tools & Technology  |  Knowledge  |  Skills  |  Abilities  |  Work Activities  |  Detailed Work Activities  |  Work Context  |  Job Zone  |  Education  |  Credentials  |  Interests  |  Work Styles  |  Work Values  |  Related Occupations  |  Wages & Employment  |  Job Openings  |  Additional Information

Tasks

  • Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry. See more occupations related to this task.
  • Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields. See more occupations related to this task.
  • Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation. See more occupations related to this task.
  • Assemble sets of assumptions and explore the consequences of each set. See more occupations related to this task.
  • Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences. See more occupations related to this task.
  • Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols. See more occupations related to this task.
  • Disseminate research by writing reports, publishing papers, or presenting at professional conferences. See more occupations related to this task.
  • Perform computations and apply methods of numerical analysis to data. See more occupations related to this task.
  • Develop new principles and new relationships between existing mathematical principles to advance mathematical science. See more occupations related to this task.
  • Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code. See more occupations related to this task.

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Tools & Technology

Tools used in this occupation:

  • Desktop computers See more occupations related to this tool.
  • High capacity removable media drives — Universal serial bus USB flash drives See more occupations related to this tool.
  • Mainframe computers — Supercomputers See more occupations related to this tool.
  • Notebook computers — Laptop computers See more occupations related to this tool.
  • Personal computers See more occupations related to this tool.
  • Read write digital versatile disc DVD — Optical disk drives See more occupations related to this tool.
  • Scientific calculator — Graphing calculators See more occupations related to this tool.

Technology used in this occupation:

  • Analytical or scientific software — SAS software; Symmetrica *; The MathWizards MathViews; The MathWorks MATLAB (see all 51 examples) See more occupations related to this technology.
  • Computer aided design CAD software — Mathsoft Mathcad See more occupations related to this technology.
  • Data base user interface and query software — Microsoft Access See more occupations related to this technology.
  • Desktop publishing software — MicroPress VTeX software See more occupations related to this technology.
  • Development environment software — C; Formula translation/translator FORTRAN; Microsoft Visual Basic See more occupations related to this technology.
  • Electronic mail software — Microsoft Outlook See more occupations related to this technology.
  • Graphics or photo imaging software — Adobe Systems Adobe Photoshop software See more occupations related to this technology.
  • Internet browser software — Web browser software See more occupations related to this technology.
  • Object or component oriented development software — C++; Python; R *; Sun Microsystems Java See more occupations related to this technology.
  • Presentation software — Microsoft PowerPoint See more occupations related to this technology.
  • Spreadsheet software — Microsoft Excel See more occupations related to this technology.
  • Word processing software — Microsoft Word See more occupations related to this technology.

* Software developed by a government agency and/or distributed as freeware or shareware.

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Knowledge

  • Mathematics — Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications. See more occupations related to this knowledge.
  • Computers and Electronics — Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming. See more occupations related to this knowledge.
  • English Language — Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar. See more occupations related to this knowledge.
  • 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. See more occupations related to this knowledge.
  • 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. See more occupations related to this knowledge.

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Skills

  • Mathematics — Using mathematics to solve problems. See more occupations related to this skill.
  • Complex Problem Solving — Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions. See more occupations related to this skill.
  • Critical Thinking — Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems. See more occupations related to this skill.
  • Reading Comprehension — Understanding written sentences and paragraphs in work related documents. See more occupations related to this skill.
  • Active Learning — Understanding the implications of new information for both current and future problem-solving and decision-making. See more occupations related to this skill.
  • 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. See more occupations related to this skill.
  • Writing — Communicating effectively in writing as appropriate for the needs of the audience. See more occupations related to this skill.
  • Judgment and Decision Making — Considering the relative costs and benefits of potential actions to choose the most appropriate one. See more occupations related to this skill.
  • Learning Strategies — Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things. See more occupations related to this skill.
  • Science — Using scientific rules and methods to solve problems. See more occupations related to this skill.
  • Speaking — Talking to others to convey information effectively. See more occupations related to this skill.
  • Systems Analysis — Determining how a system should work and how changes in conditions, operations, and the environment will affect outcomes. See more occupations related to this skill.
  • 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. See more occupations related to this skill.

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Abilities

  • Mathematical Reasoning — The ability to choose the right mathematical methods or formulas to solve a problem. See more occupations related to this ability.
  • Number Facility — The ability to add, subtract, multiply, or divide quickly and correctly. See more occupations related to this ability.
  • Deductive Reasoning — The ability to apply general rules to specific problems to produce answers that make sense. See more occupations related to this ability.
  • Inductive Reasoning — The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events). See more occupations related to this ability.
  • 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). See more occupations related to this ability.
  • Written Comprehension — The ability to read and understand information and ideas presented in writing. See more occupations related to this ability.
  • Oral Comprehension — The ability to listen to and understand information and ideas presented through spoken words and sentences. See more occupations related to this ability.
  • Category Flexibility — The ability to generate or use different sets of rules for combining or grouping things in different ways. See more occupations related to this ability.
  • 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). See more occupations related to this ability.
  • Near Vision — The ability to see details at close range (within a few feet of the observer). See more occupations related to this ability.
  • 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. See more occupations related to this ability.
  • Oral Expression — The ability to communicate information and ideas in speaking so others will understand. See more occupations related to this ability.
  • Written Expression — The ability to communicate information and ideas in writing so others will understand. See more occupations related to this ability.
  • 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. See more occupations related to this ability.
  • Speech Clarity — The ability to speak clearly so others can understand you. See more occupations related to this ability.
  • Speech Recognition — The ability to identify and understand the speech of another person. See more occupations related to this ability.
  • 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. See more occupations related to this ability.
  • Selective Attention — The ability to concentrate on a task over a period of time without being distracted. See more occupations related to this ability.

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Work Activities

  • Interacting With Computers — Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information. See more occupations related to this activity.
  • Analyzing Data or Information — Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts. See more occupations related to this activity.
  • Making Decisions and Solving Problems — Analyzing information and evaluating results to choose the best solution and solve problems. See more occupations related to this activity.
  • Getting Information — Observing, receiving, and otherwise obtaining information from all relevant sources. See more occupations related to this activity.
  • Thinking Creatively — Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions. See more occupations related to this activity.
  • Processing Information — Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data. See more occupations related to this activity.
  • Updating and Using Relevant Knowledge — Keeping up-to-date technically and applying new knowledge to your job. See more occupations related to this activity.
  • Communicating with Supervisors, Peers, or Subordinates — Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person. See more occupations related to this activity.
  • Documenting/Recording Information — Entering, transcribing, recording, storing, or maintaining information in written or electronic/magnetic form. See more occupations related to this activity.
  • 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. See more occupations related to this activity.
  • Identifying Objects, Actions, and Events — Identifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events. See more occupations related to this activity.
  • Interpreting the Meaning of Information for Others — Translating or explaining what information means and how it can be used. See more occupations related to this activity.
  • Organizing, Planning, and Prioritizing Work — Developing specific goals and plans to prioritize, organize, and accomplish your work. See more occupations related to this activity.
  • Provide Consultation and Advice to Others — Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics. See more occupations related to this activity.
  • Training and Teaching Others — Identifying the educational needs of others, developing formal educational or training programs or classes, and teaching or instructing others. See more occupations related to this activity.
  • 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. See more occupations related to this activity.
  • Developing Objectives and Strategies — Establishing long-range objectives and specifying the strategies and actions to achieve them. See more occupations related to this activity.
  • Establishing and Maintaining Interpersonal Relationships — Developing constructive and cooperative working relationships with others, and maintaining them over time. See more occupations related to this activity.

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Detailed Work Activities

  • Analyze data to identify trends or relationships among variables. See more occupations related to this activity.
  • Prepare analytical reports. See more occupations related to this activity.
  • Present research results to others. See more occupations related to this activity.
  • Develop computer or information security policies or procedures. See more occupations related to this activity.
  • Develop scientific or mathematical models. See more occupations related to this activity.
  • Apply mathematical principles or statistical approaches to solve problems in scientific or applied fields. See more occupations related to this activity.
  • Determine appropriate methods for data analysis. See more occupations related to this activity.
  • Update knowledge about emerging industry or technology trends. See more occupations related to this activity.
  • Analyze security of systems, network, or data. See more occupations related to this activity.
  • Design computer modeling or simulation programs. See more occupations related to this activity.

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Work Context

  • Electronic Mail — 88% responded “Every day.” See more occupations related to this work context.
  • Freedom to Make Decisions — 71% responded “A lot of freedom.” See more occupations related to this work context.
  • Importance of Being Exact or Accurate — 67% responded “Extremely important.” See more occupations related to this work context.
  • Structured versus Unstructured Work — 63% responded “A lot of freedom.” See more occupations related to this work context.
  • Duration of Typical Work Week — 75% responded “More than 40 hours.” See more occupations related to this work context.
  • Spend Time Sitting — 54% responded “Continually or almost continually.” See more occupations related to this work context.
  • Face-to-Face Discussions — 50% responded “Once a week or more but not every day.” See more occupations related to this work context.
  • Indoors, Environmentally Controlled — 75% responded “Every day.” See more occupations related to this work context.
  • Telephone — 63% responded “Once a week or more but not every day.” See more occupations related to this work context.
  • Impact of Decisions on Co-workers or Company Results — 42% responded “Moderate results.” See more occupations related to this work context.
  • Level of Competition — 38% responded “Highly competitive.” See more occupations related to this work context.
  • Work With Work Group or Team — 26% responded “Extremely important.” See more occupations related to this work context.
  • Contact With Others — 52% responded “Contact with others about half the time.” See more occupations related to this work context.

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Job Zone

Title Job Zone Five: Extensive Preparation Needed
Education Most of these occupations require graduate school. For example, they may require a master's degree, and some require a Ph.D., M.D., or J.D. (law degree).
Related Experience Extensive skill, knowledge, and experience are needed for these occupations. Many require more than five years of experience. For example, surgeons must complete four years of college and an additional five to seven years of specialized medical training to be able to do their job.
Job Training Employees may need some on-the-job training, but most of these occupations assume that the person will already have the required skills, knowledge, work-related experience, and/or training.
Job Zone Examples These occupations often involve coordinating, training, supervising, or managing the activities of others to accomplish goals. Very advanced communication and organizational skills are required. Examples include librarians, lawyers, sports medicine physicians, wildlife biologists, school psychologists, surgeons, treasurers, and controllers.
SVP Range (8.0 and above)

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Education


Percentage of Respondents
Education Level Required
38   Master's degree
33   Doctoral degree
21   Bachelor's degree

This occupation may require a background in the following science, technology, engineering, and mathematics (STEM) educational disciplines:

Mathematics — Algebra and Number Theory; Analysis and Functional Analysis; Applied Mathematics; Computational Mathematics; Geometry/Geometric Analysis; Mathematical Statistics and Probability (see all 11 programs)

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Credentials

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Interests

Interest code: ICA

  • 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. See more occupations related to this interest.
  • 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. See more occupations related to this interest.
  • 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. See more occupations related to this interest.

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Work Styles

  • Analytical Thinking — Job requires analyzing information and using logic to address work-related issues and problems. See more occupations related to this work style.
  • Attention to Detail — Job requires being careful about detail and thorough in completing work tasks. See more occupations related to this work style.
  • Innovation — Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems. See more occupations related to this work style.
  • Achievement/Effort — Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks. See more occupations related to this work style.
  • Integrity — Job requires being honest and ethical. See more occupations related to this work style.
  • Persistence — Job requires persistence in the face of obstacles. See more occupations related to this work style.
  • 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. See more occupations related to this work style.
  • Initiative — Job requires a willingness to take on responsibilities and challenges. See more occupations related to this work style.
  • Dependability — Job requires being reliable, responsible, and dependable, and fulfilling obligations. See more occupations related to this work style.
  • Adaptability/Flexibility — Job requires being open to change (positive or negative) and to considerable variety in the workplace. See more occupations related to this work style.
  • Self Control — Job requires maintaining composure, keeping emotions in check, controlling anger, and avoiding aggressive behavior, even in very difficult situations. See more occupations related to this work style.
  • Cooperation — Job requires being pleasant with others on the job and displaying a good-natured, cooperative attitude. See more occupations related to this work style.
  • Stress Tolerance — Job requires accepting criticism and dealing calmly and effectively with high stress situations. See more occupations related to this work style.
  • Leadership — Job requires a willingness to lead, take charge, and offer opinions and direction. See more occupations related to this work style.

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Work Values

  • 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. See more occupations related to this work value.
  • 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. See more occupations related to this work value.
  • Independence — Occupations that satisfy this work value allow employees to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy. See more occupations related to this work value.

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Related Occupations

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Wages & Employment Trends

Median wages (2014) $49.86 hourly, $103,720 annual
State wages Local Salary Info
 
Employment (2012) 4,000 employees
Projected growth (2012-2022) Much faster than average (22% or higher) Much faster than average (22% or higher)
Projected job openings (2012-2022) 1,700
State trends Employment Trends
 
Top industries (2012)

Source: Bureau of Labor Statistics 2014 wage data external site and 2012-2022 employment projections external site. "Projected growth" represents the estimated change in total employment over the projections period (2012-2022). "Projected job openings" represent openings due to growth and replacement.

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Job Openings on the Web

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Sources of Additional Information

Disclaimer: Sources are listed to provide additional information on related jobs, specialties, and/or industries. Links to non-DOL Internet sites are provided for your convenience and do not constitute an endorsement.

  • Mathematicians external site. Bureau of Labor Statistics, U.S. Department of Labor. Occupational Outlook Handbook, 2014-15 Edition.

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