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
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
- Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
- Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
- Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
- Assemble sets of assumptions and explore the consequences of each set.
- Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
- Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
- Perform computations and apply methods of numerical analysis to data.
- Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
- Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
Tools & Technology
Tools used in this occupation:
- Desktop computers
- High capacity removable media drives — Universal serial bus USB flash drives
- Mainframe computers — Supercomputers
- Notebook computers — Laptop computers
- Personal computers
- Read write digital versatile disc DVD — Optical disk drives
- Scientific calculator — Graphing calculators
Technology used in this occupation:
- Analytical or scientific software — SAS software; Symmetrica *; The MathWizards MathViews; The MathWorks MATLAB (see all 51 examples)
- Computer aided design CAD software — Mathsoft Mathcad
- Data base user interface and query software — Microsoft Access
- Desktop publishing software — MicroPress VTeX software
- Development environment software — C; Formula translation/translator FORTRAN; Microsoft Visual Basic
- Electronic mail software — Microsoft Outlook
- Graphics or photo imaging software — Adobe Systems Adobe Photoshop software
- Internet browser software — Web browser software
- Object or component oriented development software — C++; Python; R *; Sun Microsystems Java
- Presentation software — Microsoft PowerPoint
- Spreadsheet software — Microsoft Excel
- Word processing software — Microsoft Word
* Software developed by a government agency and/or distributed as freeware or shareware.
- Mathematics — Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
- Computers and Electronics — Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
- English Language — Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.
- 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.
- 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.
- Mathematics — Using mathematics to solve problems.
- Complex Problem Solving — Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
- Critical Thinking — Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
- Reading Comprehension — Understanding written sentences and paragraphs in work related documents.
- Active Learning — Understanding the implications of new information for both current and future problem-solving and decision-making.
- Active Listening — Giving full attention to what other people are saying, taking time to understand the points being made, asking questions as appropriate, and not interrupting at inappropriate times.
- Writing — Communicating effectively in writing as appropriate for the needs of the audience.
- Judgment and Decision Making — Considering the relative costs and benefits of potential actions to choose the most appropriate one.
- Learning Strategies — Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
- Science — Using scientific rules and methods to solve problems.
- 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.
- 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.
- 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).
- Written Comprehension — The ability to read and understand information and ideas presented in writing.
- Oral Comprehension — The ability to listen to and understand information and ideas presented through spoken words and sentences.
- 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).
- Near Vision — The ability to see details at close range (within a few feet of the observer).
- 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.
- Oral Expression — The ability to communicate information and ideas in speaking so others will understand.
- Written Expression — The ability to communicate information and ideas in writing so others will understand.
- 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.
- 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.
- 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.
- Selective Attention — The ability to concentrate on a task over a period of time without being distracted.
- Interacting With Computers — Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
- 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.
- 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.
- Processing Information — Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
- Updating and Using Relevant Knowledge — Keeping up-to-date technically and applying new knowledge to your job.
- Communicating with Supervisors, Peers, or Subordinates — Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
- Documenting/Recording Information — Entering, transcribing, recording, storing, or maintaining information in written or electronic/magnetic form.
- Estimating the Quantifiable Characteristics of Products, Events, or Information — Estimating sizes, distances, and quantities; or determining time, costs, resources, or materials needed to perform a work activity.
- Identifying Objects, Actions, and Events — Identifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events.
- Interpreting the Meaning of Information for Others — Translating or explaining what information means and how it can be used.
- Organizing, Planning, and Prioritizing Work — Developing specific goals and plans to prioritize, organize, and accomplish your work.
- Provide Consultation and Advice to Others — Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics.
- 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 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.
- Developing Objectives and Strategies — Establishing long-range objectives and specifying the strategies and actions to achieve them.
- Establishing and Maintaining Interpersonal Relationships — Developing constructive and cooperative working relationships with others, and maintaining them over time.
Detailed Work Activities
- Analyze data to identify trends or relationships among variables.
- Prepare analytical reports.
- Present research results to others.
- Develop computer or information security policies or procedures.
- Develop scientific or mathematical models.
- Apply mathematical principles or statistical approaches to solve problems in scientific or applied fields.
- Determine appropriate methods for data analysis.
- Update knowledge about emerging industry or technology trends.
- Analyze security of systems, network, or data.
- Design computer modeling or simulation programs.
- Electronic Mail — 88% responded “Every day.”
- Freedom to Make Decisions — 71% responded “A lot of freedom.”
- Importance of Being Exact or Accurate — 67% responded “Extremely important.”
- Structured versus Unstructured Work — 63% responded “A lot of freedom.”
- Duration of Typical Work Week — 75% responded “More than 40 hours.”
- Spend Time Sitting — 54% responded “Continually or almost continually.”
- Face-to-Face Discussions — 50% responded “Once a week or more but not every day.”
- Indoors, Environmentally Controlled — 75% responded “Every day.”
- Telephone — 63% responded “Once a week or more but not every day.”
- Impact of Decisions on Co-workers or Company Results — 42% responded “Moderate results.”
- Level of Competition — 38% responded “Highly competitive.”
- Work With Work Group or Team — 26% responded “Extremely important.”
- Contact With Others — 52% responded “Contact with others about half the time.”
|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)|
Percentage of Respondents
|Education Level Required|
This occupation may require a background in the following science, technology, engineering, and mathematics (STEM) educational disciplines:
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.
- 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.
- 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.
- Innovation — Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems.
- Achievement/Effort — Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.
- Integrity — Job requires being honest and ethical.
- Persistence — Job requires persistence in the face of obstacles.
- Independence — Job requires developing one's own ways of doing things, guiding oneself with little or no supervision, and depending on oneself to get things done.
- Initiative — Job requires a willingness to take on responsibilities and challenges.
- Dependability — Job requires being reliable, responsible, and dependable, and fulfilling obligations.
- 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.
- Cooperation — Job requires being pleasant with others on the job and displaying a good-natured, cooperative attitude.
- Stress Tolerance — Job requires accepting criticism and dealing calmly and effectively with high stress situations.
- Leadership — Job requires a willingness to lead, take charge, and offer opinions and direction.
- 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.
Wages & Employment Trends
|Median wages (2014)||$49.86 hourly, $103,720 annual|
|Employment (2012)||4,000 employees|
|Projected growth (2012-2022)||Much faster than average (22% or higher)|
|Projected job openings (2012-2022)||1,700|
|Top industries (2012)|
Source: Bureau of Labor Statistics 2014 wage data and 2012-2022 employment projections . "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.
Job Openings on the Web
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 . Bureau of Labor Statistics, U.S. Department of Labor. Occupational Outlook Handbook, 2014-15 Edition.