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Mathematics is one of the oldest and most basic sciences. Mathematicians create new mathematical theories and techniques involving the latest technology and solve economic, scientific, engineering, and business problems using mathematical knowledge and computational tools.
Mathematical work falls into two broad classes: theoretical (pure) mathematics and applied mathematics. However, these classes are not sharply defined and often overlap.
Theoretical mathematicians advance mathematical science by developing new principles and new relationships between existing principles of mathematics. Although they seek to increase basic knowledge without necessarily considering its practical use, this pure and abstract knowledge has been instrumental in producing or furthering many scientific and engineering achievements.
Applied mathematicians use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, engineering, and the physical, life, and social sciences. For example, they may analyze the mathematical aspects of computer and communications networks, the effects of new drugs on disease, the aerodynamic characteristics of aircraft, or the distribution costs or manufacturing processes of businesses. Applied mathematicians working in industrial research and development may develop or enhance mathematical methods when confronted with difficult problems. Some mathematicians, called cryptanalysts, analyze and decipher encryption systems designed to transmit national security-related information.
Mathematicians use computers extensively to analyze relationships among variables, solve complex problems, develop models, and process large amounts of data.
Much work in applied mathematics, however, is carried on by persons other than mathematicians. In fact, because mathematics is the foundation upon which many other academic disciplines are built, the number of workers using mathematical techniques is many times greater than the number actually designated as mathematicians. Engineers, computer scientists, physicists, and economists are among those who use mathematics extensively but have job titles other than mathematician. Some workers, such as statisticians, actuaries, and operations research analysts, actually are specialists in a particular branch of mathematics. (See statements on actuaries, operations research analysts, and statisticians elsewhere in the Handbook.)
Mathematicians working for government agencies or private firms usually have structured work schedules. They may work alone, in a small group of mathematicians, or as an integral part of a team that includes engineers, computer scientists, physicists, technicians, and others. Deadlines, overtime work, special requests for information or analysis, and travel to attend seminars or conferences may be part of their jobs.
Mathematicians held about 14,000 jobs in 1994. In addition, about 20,000 persons held mathematics faculty positions in colleges and universities, according to the American Mathematical Society. (See the statement on college and university faculty elsewhere in the Handbook.)
Many nonfaculty mathematicians work for either Federal or State governments. The Department of Defense is the primary Federal employer of mathematicians; more than three-fourths of the mathematicians employed by the Federal Government work for the Navy, Army, or Air Force. In the private sector, major employers include research and testing services, educational services, security and commodity exchanges, and management and public relations services. Within manufacturing, the drug industry is the key employer. Some mathematicians also work for banks, insurance companies, and public utilities.
A bachelor's degree in mathematics is the minimum education needed for prospective mathematicians. In the Federal Government, entry-level job candidates usually must have a 4-year degree with a major in mathematics or a 4-year degree with the equivalent of a mathematics major-24 semester hours of mathematics courses.
In private industry, job candidates generally need a master's or a Ph.D. degree to obtain jobs as mathematicians. Most of the positions designated for mathematicians are in research and development labs as part of technical teams. These research scientists engage in either pure mathematical, or basic, research; or in applied research focusing on developing or improving specific products or processes. The majority of bachelor's and master's degree holders in private industry work, not as mathematicians, but in related fields such as computer science, where they are called computer programmers, systems analysts, or systems engineers.
A bachelor's degree in mathematics is offered by most colleges and universities. Mathematics courses usually required for this degree are calculus, differential equations, and linear and abstract algebra. Additional coursework might include probability theory and statistics, mathematical analysis, numerical analysis, topology, modern algebra, discrete mathematics, and mathematical logic. Many colleges and universities urge or even require students majoring in mathematics to take several courses in a field that uses or is closely related to mathematics, such as computer science, engineering, operations research, a physical science, statistics, or economics. A double major in mathematics and another discipline such as computer science, economics, or one of the sciences is particularly desirable. A prospective college mathematics major should take as many mathematics courses as possible while in high school.
In 1994, about 240 colleges and universities offered a master's degree as the highest degree in either pure or applied mathematics; 195 offered a Ph.D. in pure or applied mathematics. In graduate school, students conduct research and take advanced courses, usually specializing in a subfield of mathematics. Some areas of concentration are algebra, number theory, real or complex analysis, geometry, topology, logic, and applied mathematics.
For work in applied mathematics, training in the field in which the mathematics will be used is very important. Fields in which applied mathematics is used extensively include physics, actuarial science, engineering, and operations research; of increasing importance are computer and information science, business and industrial management, economics, statistics, chemistry, geology, life sciences, and the behavioral sciences.
Mathematicians should have substantial knowledge of computer programming because most complex mathematical computation and much mathematical modeling is done by computer.
Mathematicians need good reasoning ability and persistence in order to identify, analyze, and apply basic principles to technical problems. Communication skills are also important, as mathematicians must be able to interact with others, including nonmathematicians, and discuss proposed solutions to problems.
Employment of mathematicians is expected to change or grow more slowly than the average for all occupations through the year 2005. The number of jobs available for workers whose educational background is solely mathematics is not expected to increase significantly. Many firms engaged in civilian research and development that use mathematicians are not planning to expand their research departments much, and, in some cases, may reduce them. Expected reductions in defense-related research and development will also affect mathematicians' employment, especially in the Federal Government. Those whose educational background includes the study of a related discipline will have better job opportunities. However, as advancements in technology lead to expanding applications of mathematics, more workers with a knowledge of mathematics will be required. Many of these workers have job titles which reflect the end product of their work rather than the discipline of mathematics used in that work.
Bachelor's degree holders in mathematics are usually not qualified for most jobs as mathematicians. However, those with a strong background in computer science, electrical or mechanical engineering, or operations research should have good opportunities in industry. Bachelor's degree holders who meet State certification requirements may become high school mathematics teachers. (For additional information, see the statement on kindergarten, elementary, and secondary school teachers elsewhere in the Handbook.)
Holders of a master's degree in mathematics will face very strong competition for jobs in theoretical research. However, job opportunities in applied mathematics and related areas such as computer programming, operations research, and engineering design in industry and government will be more numerous.
According to a 1995 survey by the National Association of Colleges and Employers, starting salary offers for mathematics graduates with a bachelor's degree averaged about $30,300 a year and for those with a master's degree, $35,600. Starting salaries were generally higher in industry and government than in educational institutions. For example, the American Mathematical Society reported that, based on a 1994 survey, median annual earnings for new recipients of doctorates in research were $35,000; for those in government, $45,500; and for those in business and industry, $52,500.
In the Federal Government in 1995 the average annual salary for mathematicians in supervisory, nonsupervisory, and managerial positions was $58,150; for mathematical statisticians, $60,510; and for cryptanalysts, $52,840.
Benefits for mathematicians tend to be similar to those offered to most professionals who work in office settings: Vacation and sick leave, health and life insurance, and a retirement plan, among others.
Other occupations that require a degree in or extensive knowledge of mathematics include actuary, statistician, computer programmer, systems analyst, systems engineer, and operations research analyst. In addition, a strong background in mathematics facilitates employment in fields such as engineering, economics, finance, and physics.
For more information about the field of mathematics, including career opportunities and professional training, contact:
American Mathematical Society, Department of Professional Programs and Services, P.O. Box 6248, Providence, RI 02940-6248.
Mathematical Association of America, 1529 18th St. NW., Washington, DC 20036.
For a 1995 resource guide on careers in mathematical sciences, send a self-addressed envelope with two first-class stamps to:
Conference Board of the Mathematical Sciences, 1529 18th St. NW., Washington, DC 20036.
For specific information on careers in applied mathematics, contact:
Information on Federal job opportunities is available from area offices of the State employment service and the U.S. Office of Personnel Management's Federal Job Information Centers located in various large cities throughout the country.
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