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.

Salary at 10th Percentile: $52,860
Median Salary: $103,010
Salary at 90th Percentile: $161,900

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.

Technology
Example
Hot Technology
Graphics or photo imaging software
Adobe Systems Adobe Photoshop
Analytical or scientific software
Algae
Development environment software
C
Object or component oriented development software
C#
Enterprise application integration software
Extensible markup language XML
Web platform development software
JavaScript
Operating system software
Linux
Desktop publishing software
MicroPress VTeX
Data base user interface and query software
Microsoft Access
Spreadsheet software
Microsoft Excel
Office suite software
Microsoft Office
Electronic mail software
Microsoft Outlook
Presentation software
Microsoft PowerPoint
Word processing software
Microsoft Word
Data base management system software
MySQL
Internet browser software
Web browser software
Tool
Example
Hot Technology
Desktop computers
Desktop computers
Scientific calculator
Graphing calculators
Notebook computers
Laptop computers
Read write digital versatile disc DVD
Optical disk drives
Personal computers
Personal computers
Mainframe computers
Supercomputers
High capacity removable media drives
Universal serial bus USB flash drives
Mathematics
95%
Importance

Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.

Computers and Electronics
74%
Importance

Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.

English Language
71%
Importance

Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.

Physics
56%
Importance

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.

Education and Training
49%
Importance

Knowledge of principles and methods for curriculum and training design, teaching and instruction for individuals and groups, and the measurement of training effects.

Design
36%
Importance

Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models.

Administration and Management
35%
Importance

Knowledge of business and management principles involved in strategic planning, resource allocation, human resources modeling, leadership technique, production methods, and coordination of people and resources.

Customer and Personal Service
35%
Importance

Knowledge of principles and processes for providing customer and personal services. This includes customer needs assessment, meeting quality standards for services, and evaluation of customer satisfaction.

Telecommunications
32%
Importance

Knowledge of transmission, broadcasting, switching, control, and operation of telecommunications systems.

Communications and Media
30%
Importance

Knowledge of media production, communication, and dissemination techniques and methods. This includes alternative ways to inform and entertain via written, oral, and visual media.

Mathematics
100%
Importance

Using mathematics to solve problems.

Reading Comprehension
75%
Importance

Understanding written sentences and paragraphs in work related documents.

Critical Thinking
75%
Importance

Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.

Complex Problem Solving
75%
Importance

Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.

Active Learning
69%
Importance

Understanding the implications of new information for both current and future problem-solving and decision-making.

Active Listening
60%
Importance

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
60%
Importance

Communicating effectively in writing as appropriate for the needs of the audience.

Speaking
56%
Importance

Talking to others to convey information effectively.

Science
56%
Importance

Using scientific rules and methods to solve problems.

Learning Strategies
56%
Importance

Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.

Mathematical Reasoning
94%
Importance

The ability to choose the right mathematical methods or formulas to solve a problem.

Number Facility
81%
Importance

The ability to add, subtract, multiply, or divide quickly and correctly.

Deductive Reasoning
78%
Importance

The ability to apply general rules to specific problems to produce answers that make sense.

Written Comprehension
75%
Importance

The ability to read and understand information and ideas presented in writing.

Inductive Reasoning
75%
Importance

The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).

Information Ordering
75%
Importance

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
69%
Importance

The ability to listen to and understand information and ideas presented through spoken words and sentences.

Fluency of Ideas
66%
Importance

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
66%
Importance

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.

Category Flexibility
66%
Importance

The ability to generate or use different sets of rules for combining or grouping things in different ways.

Interacting With Computers
89%
Importance

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
87%
Importance

Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.

Making Decisions and Solving Problems
81%
Importance

Analyzing information and evaluating results to choose the best solution and solve problems.

Getting Information
80%
Importance

Observing, receiving, and otherwise obtaining information from all relevant sources.

Thinking Creatively
80%
Importance

Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.

Processing Information
78%
Importance

Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.

Updating and Using Relevant Knowledge
76%
Importance

Keeping up-to-date technically and applying new knowledge to your job.

Communicating with Supervisors, Peers, or Subordinates
72%
Importance

Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.

Identifying Objects, Actions, and Events
70%
Importance

Identifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events.

Estimating the Quantifiable Characteristics of Products, Events, or Information
70%
Importance

Estimating sizes, distances, and quantities; or determining time, costs, resources, or materials needed to perform a work activity.

Present research results to others.

Prepare analytical reports.

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 data to identify trends or relationships among variables.

Design computer modeling or simulation programs.

Develop scientific or mathematical models.

Analyze security of systems, network, or data.

Develop computer or information security policies or procedures.

Importance of Being Exact or Accurate

How important is being very exact or highly accurate in performing this job?

Freedom to Make Decisions

How much decision making freedom, without supervision, does the job offer?

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?

Electronic Mail

How often do you use electronic mail in this job?

Spend Time Sitting

How much does this job require sitting?

Indoors, Environmentally Controlled

How often does this job require working indoors in environmentally controlled conditions?

Face-to-Face Discussions

How often do you have to have face-to-face discussions with individuals or teams in this job?

Impact of Decisions on Co-workers or Company Results

What results do your decisions usually have on other people or the image or reputation or financial resources of your employer?

Telephone

How often do you have telephone conversations in this job?

Level of Competition

To what extent does this job require the worker to compete or to be aware of competitive pressures?

Major
Mathematics, General
Analysis and Functional Analysis
Mathematics, Other
Applied Mathematics, General
Computational Mathematics
Mathematics and Statistics, Other
Investigative

Score: 100 / 100

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

Score: 67 / 100

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

Score: 57 / 100

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.

Realistic

Score: 24 / 100

Realistic occupations frequently involve work activities that include practical, hands-on problems and solutions. They often deal with plants, animals, and real-world materials like wood, tools, and machinery. Many of the occupations require working outside, and do not involve a lot of paperwork or working closely with others.

Enterprising

Score: 24 / 100

Enterprising occupations frequently involve starting up and carrying out projects. These occupations can involve leading people and making many decisions. Sometimes they require risk taking and often deal with business.

Social

Score: 14 / 100

Social occupations frequently involve working with, communicating with, and teaching people. These occupations often involve helping or providing service to others.

Analytical Thinking
98%
Importance

Job requires analyzing information and using logic to address work-related issues and problems.

Attention to Detail
93%
Importance

Job requires being careful about detail and thorough in completing work tasks.

Innovation
87%
Importance

Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems.

Integrity
85%
Importance

Job requires being honest and ethical.

Achievement/Effort
85%
Importance

Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.

Persistence
85%
Importance

Job requires persistence in the face of obstacles.

Independence
84%
Importance

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
80%
Importance

Job requires a willingness to take on responsibilities and challenges.

Dependability
78%
Importance

Job requires being reliable, responsible, and dependable, and fulfilling obligations.

Adaptability/Flexibility
66%
Importance

Job requires being open to change (positive or negative) and to considerable variety in the workplace.

Achievement
86%
Importance

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
81%
Importance

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.

Working Conditions
76%
Importance

Occupations that satisfy this work value offer job security and good working conditions. Corresponding needs are Activity, Compensation, Independence, Security, Variety and Working Conditions.

Independence
76%
Importance

Occupations that satisfy this work value allow employees to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy.

Support
33%
Importance

Occupations that satisfy this work value offer supportive management that stands behind employees. Corresponding needs are Company Policies, Supervision: Human Relations and Supervision: Technical.

Relationships
29%
Importance

Occupations that satisfy this work value allow employees to provide service to others and work with co-workers in a friendly non-competitive environment. Corresponding needs are Co-workers, Moral Values and Social Service.

Career
Operations Research Analysts
Biostatisticians
Political Scientists
Sociologists
Geographers
Statisticians
Computer Programmers
Actuaries
Geoscientists, Except Hydrologists and Geographers
Geospatial Information Scientists and Technologists