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Mathematicians
SOC Code: 15-2021.00

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

  • 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.

Technology Skills

  • Analytical or scientific software - Minitab ; SAS ; StataCorp Stata ; The MathWorks MATLAB (see all 52 examples)
  • 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
  • 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
  • Object or component oriented development software - C++ ; Practical extraction and reporting language Perl ; Python ; R (see all 6 examples)
  • Office suite software - Microsoft Office
  • Operating system software - Linux ; UNIX
  • Presentation software - Microsoft PowerPoint
  • Spreadsheet software - Microsoft Excel
  • Web platform development software - JavaScript ; PHP: Hypertext Preprocessor
  • Word processing software - Microsoft Word

Tools Used

  • 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

Knowledge

  • 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.

Skills

  • 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.

Abilities

  • 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.

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.
    • 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.

Work Context

  • 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.”

Education

Percentage of RespondentsEducation Level Required
38%Master's degree
33%Doctoral degree
21%Bachelor's degree

Work Styles

  • 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.

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.
  • 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 & Trends

  • Median wages (2017)
    • $49.52 hourly, $103,010 annual
  • Employment (2016)
    • 3,000 employees
  • Projected growth (2016-2026)
    • Much faster than average (15% or higher)
  • Projected job openings (2016-2026)
    • 300

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