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Career Description

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.

What Job Titles Mathematicians Might Have

• Agent-Based Modeler
• Lead Simulation Modeling Engineer
• Research Scientist
• Scientist

What Mathematicians Do

• 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.

What Mathematicians Should Be Good At

• Mathematical Reasoning - The ability to choose the right mathematical methods or formulas to solve a problem.
• Deductive Reasoning - The ability to apply general rules to specific problems to produce answers that make sense.
• Written Comprehension - The ability to read and understand information and ideas presented in writing.
• 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).
• Oral Comprehension - The ability to listen to and understand information and ideas presented through spoken words and sentences.
• 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).
• Problem Sensitivity - 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 - The ability to generate or use different sets of rules for combining or grouping things in different ways.
• Near Vision - The ability to see details at close range (within a few feet of the observer).
• Oral Expression - The ability to communicate information and ideas in speaking so others will understand.
• Written Expression - The ability to communicate information and ideas in writing so others will understand.

What Mathematicians Should Be Interested In

• 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.

What Mathematicians Need to Learn

• 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.