Mathematicians
Overview
SaveJob 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, physician assistants, 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.
Yearly Salary
| High: | $170K |
| Median: | $110K |
| Low: | $61K |
Demand
Core Tasks
- Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
- Mentor others on mathematical techniques.
- Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
- Assemble sets of assumptions, and explore the consequences of each set.
- Perform computations and apply methods of numerical analysis to data.
- Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
- Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
- 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.
- 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
97%
Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
Education and Training
74%
Knowledge of principles and methods for curriculum and training design, teaching and instruction for individuals and groups, and the measurement of training effects.
Computers and Electronics
70%
Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
English Language
66%
Knowledge of the structure and content of the English language including the meaning and spelling of words, and rules of composition and grammar.
Physics
60%
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.
Engineering and Technology
58%
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.
Communications and Media
43%
Knowledge of media production, communication, and dissemination techniques and methods. This includes alternative ways to inform and entertain via written, oral, and visual media.
Administration and Management
41%
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.
Design
41%
Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models.
Administrative
40%
Knowledge of administrative and office procedures and systems such as word processing, managing files and records, stenography and transcription, designing forms, and workplace terminology.
Top 10 Skills
Mathematics
100%
Using mathematics to solve problems.
Critical Thinking
83%
Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions, or approaches to problems.
Active Learning
80%
Understanding the implications of new information for both current and future problem-solving and decision-making.
Complex Problem Solving
80%
Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
Reading Comprehension
80%
Understanding written sentences and paragraphs in work-related documents.
Judgment and Decision Making
75%
Considering the relative costs and benefits of potential actions to choose the most appropriate one.
Science
73%
Using scientific rules and methods to solve problems.
Writing
73%
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
65%
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
93%
The ability to add, subtract, multiply, or divide quickly and correctly.
Oral Comprehension
83%
The ability to listen to and understand information and ideas presented through spoken words and sentences.
Oral Expression
83%
The ability to communicate information and ideas in speaking so others will understand.
Written Comprehension
83%
The ability to read and understand information and ideas presented in writing.
Written Expression
83%
The ability to communicate information and ideas in writing so others will understand.
Deductive Reasoning
80%
The ability to apply general rules to specific problems to produce answers that make sense.
Category Flexibility
78%
The ability to generate or use different sets of rules for combining or grouping things in different ways.
Inductive Reasoning
78%
The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
Information Ordering
78%
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).
Top 10 Work Activities
Thinking Creatively
94%
Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.
Analyzing Data or Information
91%
Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
Updating and Using Relevant Knowledge
87%
Keeping up-to-date technically and applying new knowledge to your job.
Processing Information
86%
Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
Training and Teaching Others
85%
Identifying the educational needs of others, developing formal educational or training programs or classes, and teaching or instructing others.
Working with Computers
85%
Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
Making Decisions and Solving Problems
84%
Analyzing information and evaluating results to choose the best solution and solve problems.
Getting Information
83%
Observing, receiving, and otherwise obtaining information from all relevant sources.
Interpreting the Meaning of Information for Others
79%
Translating or explaining what information means and how it can be used.
Communicating with Supervisors, Peers, or Subordinates
70%
Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
Detailed Work Activities
- Collaborate on research activities with scientists or technical specialists.
- Provide technical guidance to other personnel.
- Update knowledge about emerging industry or technology trends.
- Develop scientific or mathematical models.
- Present research results to others.
- Prepare analytical reports.
- Analyze data to identify trends or relationships among variables.
- Review professional literature to maintain professional knowledge.
- Update professional knowledge.
- Design computer modeling or simulation programs.
- Apply mathematical principles or statistical approaches to solve problems in scientific or applied fields.
- Determine appropriate methods for data analysis.
- Analyze security of systems, network, or data.
- Develop computer or information security policies or procedures.
Education
Interests
Investigative
100%
Work involves studying and researching non-living objects, living organisms, disease or other forms of impairment, or human behavior. Investigative occupations are often associated with physical, life, medical, or social sciences, and can be found in the fields of humanities, mathematics/statistics, information technology, or health care service.
Conventional
76%
Work involves following procedures and regulations to organize information or data, typically in a business setting. Conventional occupations are often associated with office work, accounting, mathematics/statistics, information technology, finance, or human resources.
Artistic
47%
Work involves creating original visual artwork, performances, written works, food, or music for a variety of media, or applying artistic principles to the design of various objects and materials. Artistic occupations are often associated with visual arts, applied arts and design, performing arts, music, creative writing, media, or culinary art.
Realistic
43%
Work involves designing, building, or repairing of equipment, materials, or structures, engaging in physical activity, or working outdoors. Realistic occupations are often associated with engineering, mechanics and electronics, construction, woodworking, transportation, machine operation, agriculture, animal services, physical or manual labor, athletics, or protective services.
Social
29%
Work involves helping, teaching, advising, assisting, or providing service to others. Social occupations are often associated with social, health care, personal service, teaching/education, or religious activities.
Enterprising
17%
Work involves managing, negotiating, marketing, or selling, typically in a business setting, or leading or advising people in political and legal situations. Enterprising occupations are often associated with business initiatives, sales, marketing/advertising, finance, management/administration, professional advising, public speaking, politics, or law.
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.
Majors
Colleges
SAGE Scholars Member Schools that offer majors leading to this career.
Check out the College Search to see the full list of schools with majors for this career.