Mathematicians
Overview
Salary
Demand
Core Tasks
Technology Skills
Tools Used
Top 10 Knowledge Required
Top 10 Skills
Top 10 Abilities
Top 10 Work Activities
Detailed Work Activities
Work Context
Education
Majors
Interests
Top 10 Work Styles
Work Values
Related Careers
Overview
Job Zone Five: Extensive Preparation Needed
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.
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).
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.
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.
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 Salary
Salary at 10th Percentile: $61K
Salary at 25th Percentile: $79K
Median Salary: $110K
Salary at 75th Percentile: $134K
Salary at 90th Percentile: $170K
Demand
Core Tasks
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.
Assemble sets of assumptions and explore the consequences of each set.
Perform computations and apply methods of numerical analysis to data.
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.
Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
Technology Skills
Technology
Example
Hot Technology
Tools Used
Tool
Example
Top 10 Knowledge Required
Mathematics
100%
Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
English Language
76%
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
70%
Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
Education and Training
64%
Knowledge of principles and methods for curriculum and training design, teaching and instruction for individuals and groups, and the measurement of training effects.
Engineering and Technology
56%
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
55%
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.
Administration and Management
44%
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.
Foreign Language
40%
Knowledge of the structure and content of a foreign (non-English) language including the meaning and spelling of words, rules of composition and grammar, and pronunciation.
Design
39%
Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models.
Biology
38%
Knowledge of plant and animal organisms, their tissues, cells, functions, interdependencies, and interactions with each other and the environment.
Top 10 Skills
Mathematics
100%
Using mathematics to solve problems.
Critical Thinking
85%
Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
Complex Problem Solving
83%
Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
Active Learning
80%
Understanding the implications of new information for both current and future problem-solving and decision-making.
Reading Comprehension
80%
Understanding written sentences and paragraphs in work related documents.
Science
73%
Using scientific rules and methods to solve problems.
Judgment and Decision Making
70%
Considering the relative costs and benefits of potential actions to choose the most appropriate one.
Writing
70%
Communicating effectively in writing as appropriate for the needs of the audience.
Active Listening
68%
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
68%
Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
Top 10 Abilities
Mathematical Reasoning
100%
The ability to choose the right mathematical methods or formulas to solve a problem.
Number Facility
90%
The ability to add, subtract, multiply, or divide quickly and correctly.
Deductive Reasoning
83%
The ability to apply general rules to specific problems to produce answers that make sense.
Inductive Reasoning
83%
The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
Information Ordering
80%
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
80%
The ability to listen to and understand information and ideas presented through spoken words and sentences.
Written Comprehension
80%
The ability to read and understand information and ideas presented in writing.
Oral Expression
78%
The ability to communicate information and ideas in speaking so others will understand.
Category Flexibility
75%
The ability to generate or use different sets of rules for combining or grouping things in different ways.
Fluency of Ideas
75%
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).
Top 10 Work Activities
Analyzing Data or Information
97%
Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
Making Decisions and Solving Problems
95%
Analyzing information and evaluating results to choose the best solution and solve problems.
Processing Information
93%
Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
Getting Information
90%
Observing, receiving, and otherwise obtaining information from all relevant sources.
Interacting With Computers
90%
Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
Thinking Creatively
90%
Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.
Updating and Using Relevant Knowledge
90%
Keeping up-to-date technically and applying new knowledge to your job.
Interpreting the Meaning of Information for Others
80%
Translating or explaining what information means and how it can be used.
Communicating with Supervisors, Peers, or Subordinates
78%
Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
Training and Teaching Others
77%
Identifying the educational needs of others, developing formal educational or training programs or classes, and teaching or instructing others.
Detailed Work Activities
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.
Work Context
Electronic Mail
How often do you use electronic mail in this job?
Importance of Being Exact or Accurate
How important is being very exact or highly accurate in performing this job?
Indoors, Environmentally Controlled
How often does this job require working indoors in environmentally controlled conditions?
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?
Freedom to Make Decisions
How much decision making freedom, without supervision, does the job offer?
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?
Telephone
How often do you have telephone conversations in this job?
Contact With Others
How much does this job require the worker to be in contact with others (face-to-face, by telephone, or otherwise) in order to perform it?
Consequence of Error
How serious would the result usually be if the worker made a mistake that was not readily correctable?
Education
Majors
Major
Interests
Investigative
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
67%
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
58%
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.
Enterprising
24%
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.
Realistic
24%
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.
Social
15%
Social occupations frequently involve working with, communicating with, and teaching people. These occupations often involve helping or providing service to others.
Top 10 Work Styles
Analytical Thinking
100%
Job requires analyzing information and using logic to address work-related issues and problems.
Attention to Detail
95%
Job requires being careful about detail and thorough in completing work tasks.
Persistence
93%
Job requires persistence in the face of obstacles.
Achievement/Effort
89%
Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.
Innovation
86%
Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems.
Initiative
85%
Job requires a willingness to take on responsibilities and challenges.
Independence
84%
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
82%
Job requires being honest and ethical.
Dependability
81%
Job requires being reliable, responsible, and dependable, and fulfilling obligations.
Cooperation
71%
Job requires being pleasant with others on the job and displaying a good-natured, cooperative attitude.
Work Values
Achievement
86%
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%
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
77%
Occupations that satisfy this work value allow employees to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy.
Working Conditions
77%
Occupations that satisfy this work value offer job security and good working conditions. Corresponding needs are Activity, Compensation, Independence, Security, Variety and Working Conditions.
Support
34%
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%
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.
