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: Computational Mathematician, Computational Scientist, Cryptographer, Cryptographic Vulnerability Analyst, Image Scientist, Knowledge Engineer, Mathematician, Research Computing Specialist, Research Scientist, Researcher
Tasks | Technology Skills | Tools Used | 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
- Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
- Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
- Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
- Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
- Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
- Perform computations and apply methods of numerical analysis to data.
- Assemble sets of assumptions and explore the consequences of each set.
- Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
- 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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- Analytical or scientific software — IBM SPSS Statistics ; Minitab ; SAS ; The MathWorks MATLAB (see all 53 examples)
- Business intelligence and data analysis software — Tableau
- Customer relationship management CRM software — Salesforce software
- Data base management system software — MySQL
- Data base user interface and query software — Microsoft Access ; Structured query language SQL
- Desktop publishing software — MicroPress VTeX
- Development environment software — C; Formula translation/translator FORTRAN; Microsoft Visual Basic ; Microsoft Visual Studio
- Electronic mail software — Microsoft Outlook
- Enterprise application integration software — Extensible markup language XML
- Graphics or photo imaging software — Adobe Systems Adobe Photoshop
- Internet browser software — Web browser software
- Network security or virtual private network VPN management software — Vormetric Application Encryption
- Object or component oriented development software — C# ; Oracle Java ; Perl ; R (see all 7 examples)
- Office suite software — Microsoft Office
- Operating system software — Apple macOS ; Bash ; Linux ; UNIX (see all 6 examples)
- Presentation software — Microsoft PowerPoint
- Program testing software — User interface design software
- Spreadsheet software — Microsoft Excel
- Transaction server software — Web server software
- Word processing software — Microsoft Word
Hot Technology — a technology requirement frequently included in employer job postings.
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- Mathematics — Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
- English Language — Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.
- Computers and Electronics — Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
- 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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- Mathematics — Using mathematics to solve problems.
- Critical Thinking — Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions, or approaches to problems.
- Complex Problem Solving — Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
- Active Learning — Understanding the implications of new information for both current and future problem-solving and decision-making.
- Reading Comprehension — Understanding written sentences and paragraphs in work-related documents.
- Science — Using scientific rules and methods to solve problems.
- Judgment and Decision Making — Considering the relative costs and benefits of potential actions to choose the most appropriate one.
- Writing — Communicating effectively in writing as appropriate for the needs of the audience.
- Active Listening — Giving full attention to what other people are saying, taking time to understand the points being made, asking questions as appropriate, and not interrupting at inappropriate times.
- Learning Strategies — Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
- Speaking — Talking to others to convey information effectively.
- Systems Analysis — Determining how a system should work and how changes in conditions, operations, and the environment will affect outcomes.
- Instructing — Teaching others how to do something.
- 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.
- Monitoring — Monitoring/Assessing performance of yourself, other individuals, or organizations to make improvements or take corrective action.
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- Mathematical Reasoning — The ability to choose the right mathematical methods or formulas to solve a problem.
- Number Facility — The ability to add, subtract, multiply, or divide quickly and correctly.
- Deductive Reasoning — The ability to apply general rules to specific problems to produce answers that make sense.
- Inductive Reasoning — The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
- Information Ordering — The ability to arrange things or actions in a certain order or pattern according to a specific rule or set of rules (e.g., patterns of numbers, letters, words, pictures, mathematical operations).
- Oral Comprehension — The ability to listen to and understand information and ideas presented through spoken words and sentences.
- Written Comprehension — The ability to read and understand information and ideas presented in writing.
- Oral Expression — The ability to communicate information and ideas in speaking so others will understand.
- Category Flexibility — The ability to generate or use different sets of rules for combining or grouping things in different ways.
- 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).
- 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 that there is a problem.
- Written Expression — The ability to communicate information and ideas in writing so others will understand.
- Near Vision — The ability to see details at close range (within a few feet of the observer).
- 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.
- 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.
- 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.
- Selective Attention — The ability to concentrate on a task over a period of time without being distracted.
- Speech Clarity — The ability to speak clearly so others can understand you.
- Speech Recognition — The ability to identify and understand the speech of another person.
- Speed of Closure — The ability to quickly make sense of, combine, and organize information into meaningful patterns.
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- Analyzing Data or Information — Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
- Making Decisions and Solving Problems — Analyzing information and evaluating results to choose the best solution and solve problems.
- Processing Information — Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
- Getting Information — Observing, receiving, and otherwise obtaining information from all relevant sources.
- Thinking Creatively — Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.
- Updating and Using Relevant Knowledge — Keeping up-to-date technically and applying new knowledge to your job.
- Working with Computers — Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
- Interpreting the Meaning of Information for Others — Translating or explaining what information means and how it can be used.
- Communicating with Supervisors, Peers, or Subordinates — Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
- Training and Teaching Others — Identifying the educational needs of others, developing formal educational or training programs or classes, and teaching or instructing others.
- Communicating with People Outside the 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.
- Identifying Objects, Actions, and Events — Identifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events.
- Developing Objectives and Strategies — Establishing long-range objectives and specifying the strategies and actions to achieve them.
- Providing Consultation and Advice to Others — Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics.
- Establishing and Maintaining Interpersonal Relationships — Developing constructive and cooperative working relationships with others, and maintaining them over time.
- Coaching and Developing Others — Identifying the developmental needs of others and coaching, mentoring, or otherwise helping others to improve their knowledge or skills.
- Documenting/Recording Information — Entering, transcribing, recording, storing, or maintaining information in written or electronic/magnetic form.
- Estimating the Quantifiable Characteristics of Products, Events, or Information — Estimating sizes, distances, and quantities; or determining time, costs, resources, or materials needed to perform a work activity.
- Organizing, Planning, and Prioritizing Work — Developing specific goals and plans to prioritize, organize, and accomplish your work.
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Detailed Work Activities
- Analyze data to identify trends or relationships among variables.
- Prepare analytical reports.
- Present research results to others.
- Update knowledge about emerging industry or technology trends.
- Apply mathematical principles or statistical approaches to solve problems in scientific or applied fields.
- Design computer modeling or simulation programs.
- Determine appropriate methods for data analysis.
- Develop scientific or mathematical models.
- Analyze security of systems, network, or data.
- Develop computer or information security policies or procedures.
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- Electronic Mail — 92% responded “Every day.”
- Importance of Being Exact or Accurate — 79% responded “Extremely important.”
- Duration of Typical Work Week — 78% responded “More than 40 hours.”
- Structured versus Unstructured Work — 58% responded “A lot of freedom.”
- Freedom to Make Decisions — 48% responded “A lot of freedom.”
- Face-to-Face Discussions — 57% responded “Once a week or more but not every day.”
- Spend Time Sitting — 42% responded “Continually or almost continually.”
- Indoors, Environmentally Controlled — 63% responded “Every day.”
- Telephone — 35% responded “Once a week or more but not every day.”
- Contact With Others — 38% responded “Contact with others most of the time.”
- Work With Work Group or Team — 42% responded “Very important.”
- Level of Competition — 38% responded “Highly competitive.”
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|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 pharmacists, lawyers, astronomers, biologists, clergy, neurologists, and veterinarians.|
|SVP Range||(8.0 and above)|
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Percentage of Respondents
|Education Level Required|
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Interest code: ICA Want to discover your interests? Take the O*NET Interest Profiler at My Next Move.
- 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.
- 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.
- 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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- Analytical Thinking — Job requires analyzing information and using logic to address work-related issues and problems.
- Attention to Detail — Job requires being careful about detail and thorough in completing work tasks.
- Persistence — Job requires persistence in the face of obstacles.
- Achievement/Effort — Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.
- Innovation — Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems.
- Initiative — Job requires a willingness to take on responsibilities and challenges.
- 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.
- Integrity — Job requires being honest and ethical.
- Dependability — Job requires being reliable, responsible, and dependable, and fulfilling obligations.
- Cooperation — Job requires being pleasant with others on the job and displaying a good-natured, cooperative attitude.
- Adaptability/Flexibility — Job requires being open to change (positive or negative) and to considerable variety in the workplace.
- Self-Control — Job requires maintaining composure, keeping emotions in check, controlling anger, and avoiding aggressive behavior, even in very difficult situations.
- Leadership — Job requires a willingness to lead, take charge, and offer opinions and direction.
- Stress Tolerance — Job requires accepting criticism and dealing calmly and effectively with high-stress situations.
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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.
- 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.
- Independence — Occupations that satisfy this work value allow employees to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy.
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Wages & Employment Trends
|Median wages (2020)||$53.30 hourly, $110,860 annual|
|Employment (2020)||2,700 employees|
|Projected growth (2020-2030)||Slower than average (1% to 5%)|
|Projected job openings (2020-2030)||200|
|Top industries (2020)||
Professional, Scientific, and Technical Services
Source: Bureau of Labor Statistics 2020 wage data and 2020-2030 employment projections . “Projected growth” represents the estimated change in total employment over the projections period (2020-2030). “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.
- American Mathematical Association of Two-Year Colleges
- American Mathematical Society
- American Physical Society
- American Statistical Association
- Association for Computing Machinery
- Association for Women in Mathematics
- Conference Board of the Mathematical Sciences
- Institute for Operations Research and the Management Sciences
- International Association for Cryptologic Research
- Mathematical Association of America
- Mathematical Programming Society
- National Association of Mathematicians
- Occupational Outlook Handbook: Mathematicians and statisticians
- Society for Industrial and Applied Mathematics
- Society for Mathematical Biology
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