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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  |  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.
  • 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.

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Tools & Technology

Tools used in this occupation:

High capacity removable media drives — Universal serial bus USB flash drives
Mainframe computers — Supercomputers
Notebook computers — Laptop 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
Development environment software — C; Formula translation/translator FORTRAN; Microsoft Visual Basic
Electronic mail software — Microsoft Outlook
Object or component oriented development software — C++; Python; R *; Sun Microsystems Java
Spreadsheet software — Microsoft Excel

* 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.
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.

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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.

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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).

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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.
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.

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Work Context

Electronic Mail — How often do you use electronic mail in this job?
Freedom to Make Decisions — How much decision making freedom, without supervision, does the job offer?
Importance of Being Exact or Accurate — How important is being very exact or highly accurate in performing this job?
Structured versus Unstructured Work — To what extent is this job structured for the worker, rather than allowing the worker to determine tasks, priorities, and goals?
Duration of Typical Work Week — Number of hours typically worked in one week.
Spend Time Sitting — How much does this job require sitting?
Face-to-Face Discussions — How often do you have to have face-to-face discussions with individuals or teams in this job?
Indoors, Environmentally Controlled — How often does this job require working indoors in environmentally controlled conditions?
Telephone — How often do you have telephone conversations in this job?
Impact of Decisions on Co-workers or Company Results — How do the decisions an employee makes impact the results of co-workers, clients or the company?

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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

Find Training Find Certifications

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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.
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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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.

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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.
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 (2013) $49.25 hourly, $102,440 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 2013 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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