Mathematicians Go Back to List 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.

Technology used in this occupation:
	Graphics or photo imaging software

Tasks
	Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
	Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
	Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
	Perform computations and apply methods of numerical analysis to data.
	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.
	Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
	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.
	Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.

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.
	Reading Comprehension - Understanding written sentences and paragraphs in work related documents.
	Critical Thinking - Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
	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.
	Speaking - Talking to others to convey information effectively.
	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.

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.
	Education and Training - Knowledge of principles and methods for curriculum and training design, teaching and instruction for individuals and groups, and the measurement of training effects.
	Design - Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models.
	Administration and Management - 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 - 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 - Knowledge of transmission, broadcasting, switching, control, and operation of telecommunications systems.

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Education & Training   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.

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