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 to many employers. A prospective college mathematics major should. take as many mathematics courses as possible while in high school.

In 1996, 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.

Job Outlook

Employment of mathematicians is expected to increase more slowly than the average for all occupations through the year 2006. 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.

Earnings

According to a 1997 survey by the National Association of Colleges and Employers, starting salary offers for mathematics graduates with a bachelor's degree averaged about $31,800 a year and for those with a master's degree, $38,300.

In the Federal Government in 1997, the average annual salary for mathematicians in supervisory, nonsupervisory, and managerial positions was $62,000; for mathematical statisticians, $65,660; and for cryptanalysts, $56,160.

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. Related Occupations

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.

Sources of Additional Information

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 1996 resource guide on careers in mathematical sciences contact:

☛ Conference Board of the Mathematical Sciences, 1529 18th St. NW., Washington, DC 20036.

For specific information on careers in applied mathematics, contact:

☛ Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688.

Information on obtaining a mathematician position with the Federal Government may be obtained from the Office of Personnel Management through a telephone based system. Consult your telephone directory under U.S. Government for a local number or call (912) 757-3000 (TDD 912 744-2299). That number is not toll free and charges may result. Information also is available from their internet site: http:// www.usajobs.opm.gov

Operations Research Analysts

(D.O.T. 020.067-018)

Significant Points

Individuals with a master's or Ph.D. degree in management science or operations research should find good job prospects through the year 2006, despite projected slower than average employment growth.

Skills acquired by operations research analysts are useful for higher-level management jobs.

Nature of the Work

Efficiently running a complex organization such as a manufacturing plant or an airline requires the precise coordination of materials, equipment, and people. Operations research analysts help organizations coordinate and operate in the most efficient manner by applying mathematical principles to organizational problems. Managers then evaluate alternatives and choose the course of action that best meets their goals.

Operations research analysts tackle a whole host of problems facing large business and government organizations, including strategy, forecasting, resource allocation, facilities layout, inventory control, personnel schedules, and distribution systems. Their methods generally use a mathematical model consisting of a set of equations that describe how things happen within the organization. Use of models enables the analyst to break down problems into their component parts, assign numerical values to different components, and determine the mathematical relationships between them. These values can be altered to examine what will happen to the system under different circumstances. The situation under consideration determines the mathematical method used. Some of the methods

available include simulation, linear optimization, networks, waiting lines, and game theory.

Operations research analysts use computers extensively in their work. They are typically highly proficient in database collection and management, programming, and in the development and use of sophisticated software programs. Many of the models employed in operations research are so complicated that only a computer can solve them efficiently.

The type of problem they handle varies by industry. For example, a civilian analyst for the Armed Forces may coordinate flight and maintenance schedules to produce an optimal schedule for the safe deployment of troops and material. An analyst employed by a hospital concentrates on a different set of factors, such as scheduling admissions, managing patient flow, assigning shifts, monitoring use of pharmacy and laboratory services, and forecasting demand for hospital services.

The duties of the operations research analyst vary according to the structure and management philosophy of the employer or client. Some firms centralize operations research in one department, while others use operations research in all divisions. Firms may contract out operations research services to a consulting firm. Some operations research analysts specialize in one type of application, whereas others are generalists, especially at the beginning of their careers. In addition, economists, systems analysts, mathematicians, industrial engineers, and others may also apply operations research techniques to address problem areas within their respective fields.

The degree of supervision varies by organizational structure and experience. In some organizations, analysts have a great deal of professional autonomy, while in others, analysts are more closely supervised. Operations research analysts work closely with senior managers, who have a wide variety of support needs. Analysts must adapt their work to reflect these requirements.

Regardless of the industry or structure of the organization, operations research entails a similar set of procedures. Managers begin the process by describing the symptoms of a problem to the analyst, who then formally defines the problem. For example, an operations research analyst for an auto manufacturer may be asked to determine the best inventory level for each of the materials for a new production line or, more specifically, to determine how many windshields should be kept in inventory.

Analysts study the problem, then break it into its component parts. Then they gather information about each of these parts. Usually this involves consulting a wide variety of sources of information. To determine the most efficient amount of inventory to be kept on hand, for example, operations research analysts might talk with engineers about production levels, discuss purchasing arrangements with buyers, and examine data on storage costs provided by the accounting department.

With this information in hand, the analyst is ready to select the most appropriate analytical technique. There may be several techniques that could be used, but all techniques involve the construction of a mathematical model that explains the system and solves the problem. In almost all cases, the computer program used to solve the model must be modified repeatedly to reflect different solutions.

A model for airline flight scheduling, for example, might include variables for the cities to be connected, amount of fuel required to fly the routes, projected levels of passenger demand, varying ticket and fuel prices, pilot scheduling, and maintenance costs. The analyst then chooses values for these variables, enters them into a computer which is then programmed to solve the calculations, and runs the program to produce the best flight schedule consistent with various sets of assumptions.

At this point, the operations research analyst presents the final work to management along with recommendations based on the results of the analysis. Additional computer runs based on different assumptions may be needed to help in making the final decision between various options. Once a decision has been reached by management, the analyst may work with others in the organization to ensure the plan's successful implementation.

Operations research is performed by analysts who may hold a variety of job titles.

Working Conditions

Operations research analysts generally work regular hours in an office environment. Because they work on projects that are of immediate interest to management, analysts often are under pressure to meet deadlines and often work more than a 40-hour week.

Employment

Operations research analysts held about 50,000 jobs in 1996. They are employed in most industries. Major employers include telecommunication companies, air carriers, computer and data processing services, financial institutions, insurance carriers, engineering and management services firms, and the Federal Government. About 1 out of 5 analysts work for management, research, public relations, and testing agencies that do operations research consulting.

Most operations research analysts in the Federal Government work for the Armed Forces. In addition, many operations research analysts in private industry work directly or indirectly on national defense.

Training, Other Qualifications, and Advancement Employers generally prefer applicants with at least a master's degree in operations research, industrial engineering, or management science, coupled with a bachelor's degree in computer science or one of the quantitative disciplines like economics, mathematics or statistics.

Employers often sponsor skills-improvement training for experienced workers, helping them keep up with new developments in operations research techniques as well as advances in computer science. Some analysts attend advanced university classes on these subjects at their employer's expense.

Operations research analysts must be able to think logically and work well with people, so employers prefer workers with good oral and written communication skills. The computer is the most important tool for quantitative analysis, and both training and experience in programming is a must.

Beginning analysts usually do routine work under the supervision of more experienced analysts. As they gain knowledge and experience, they are assigned more complex tasks, with greater autonomy to design models and solve problems. Operations research analysts advance by assuming positions as technical specialists or supervisors. The skills acquired by operations research analysts are useful for higher-level management jobs, and experienced analysts may leave

the field to assume nontechnical managerial or administrative positions.

Job Outlook

Individuals seeking employment as operations research or management science analysts who hold master's or Ph.D. degrees in management science or operations research should find good opportunities through the year 2006 because the number of openings generated each year as a result of the slower than average employment growth expected and the need to replace those leaving the occupation is expected to exceed the number of persons graduating with these credentials. Graduates with only a bachelors degrees in operations research or management science should find opportunities as research assistants in a variety of related fields which allow them to use their quantitative abilities. Organizations are expected to use operations research and management science techniques to improve productivity and quality and to reduce costs. This reflects an acceptance of a systematic approach to decision making by top managers. This should result in a steady demand for workers knowledgeable in operations research techniques in the years ahead.

The importance of quantitative analysis in decision making ensures that training in operations research will continue to be valuable in obtaining employment. Employment opportunities will occur in the transportation, manufacturing, finance, and services sectors, where the use of quantitative analysis can achieve dramatic improvements in operating efficiency and profitability.

Earnings

In 1996, the median salary of operations and systems researchers and analysts was about $42,400 a year. The middle 50 percent earned between about $33,100 and $55,500; the lowest 10 percent were paid less than $24,300, while the highest 10 percent earned over $65,500 a year.

The average annual salary for operations research analysts in the Federal Government in nonsupervisory, supervisory, and managerial positions was $66,760 in 1997.

Related Occupations

Operations research analysts apply mathematical principles to large, complicated problems. Workers in other occupations that stress quantitative analysis include computer scientists, engineers, mathematicians, statisticians, and economists. Because its goal is improved organizational efficiency, operations research is closely allied to managerial occupations.

Sources of Additional Information

Information on career opportunities for operations research analysts is available from:

The Institute for Operations Research and the Management Sciences, 901 Elkridge Landing Rd., Suite 400, Linthicum, MD 21090.

For information on careers in the Armed Forces and Department of Defense, contact:

Military Operations Research Society, 101 South Whiting St., Suite 202, Alexandria, VA 22304.

Nature of the Work

Statistics is a science, applying mathematical tools, involved with the collection, analysis, interpretation, and presentation of numerical data. Many applications-including predicting population growth or economic conditions, providing quality control tests for manufactured products, and helping business managers and government officials make decisions-benefit from statistical techniques. Statisticians are the individuals who design surveys and experiments, collect data, and interpret the results. In doing so, they often apply their knowledge of statistical methods to a particular subject area, such as biology, economics, engineering, medicine, or psychology. Some statisticians develop new statistical methods.

Statisticians typically work with professionals in other fields to solve practical problems. For example, biostatisticians involved in clinical research have developed sequential procedures that minimize patients' exposure to harmful treatment and make beneficial treatments more rapidly accessible.

Often statisticians are able to obtain information about a group of people or things by surveying a small portion, called a sample, of the group. For example, to determine the size of the total audience for particular programs, television rating services ask only a few thousand families, rather than all viewers, which programs they watch. Statisticians decide where and how to gather the data, determine the type and size of the sample group, and develop the survey questionnaire or reporting form. They also prepare instructions for workers who will collect and tabulate the data. Finally, statisticians analyze,

Statisticians

(D.O.T. 020.067-022, .167-026)

Significant Points

Many with bachelors and master's degrees in statistics enter jobs in which they do not have the title of statistician. In private industry and colleges and universities, many positions require a graduate degree, often a doctorate, in statistics.

Good communications skills are important for prospective statisticians.

interpret, and summarize the data, usually using sophisticated statistical computer software.

In manufacturing industries, statisticians play an important role in the area of quality improvement. For example, a statistician in an automobile manufacturing company might design experiments using statistical models to estimate the failure time of an engine exposed to extreme weather conditions and to identify factors that can lead to improved performance. In chemical companies, statisticians might design experiments to determine what combination of chemicals would produce the best product for a specific purpose.

Because statistics are used in so many areas, specialists in other fields who use statistics often have other designations. For example, a person using statistical methods on economic data may have the title of econometrician. (See the statement on economists and marketing research analysts elsewhere in the Handbook).

Working Conditions

Statisticians usually work regular hours in offices. Some statisticians travel to provide advice on research projects, supervise or set up surveys, or to gather statistical data. Some may have fairly repetitive tasks, while others may have a variety of tasks, such as designing experiments.

Employment

Statisticians held about 14,000 jobs in 1996. Over one-fourth of these jobs were in the Federal Government, where statisticians were concentrated in the Departments of Commerce, Agriculture, and Health and Human Services. Most of the remaining jobs were in private industry, especially in the biopharmaceutical industry. In addition, many statisticians work in academia. (See the statement on college and university faculty elsewhere in the Handbook.)

Training, Other Qualifications, and Advancement

A bachelor's degree with a major in statistics or mathematics is the minimum educational requirement for some beginning jobs in statistics. The training required for employment as an entry level statistician in the Federal Government is a college degree including at least 15 semester hours of statistics-or a combination of 15 hours of mathematics and statistics if at least 6 semester hours are in statistics. An additional 9 semester hours in another academic discipline, such as economics, physical or biological science, medicine, education, engineering, or social science, are also required. To qualify as a mathematical statistician in the Federal Government requires 24 semester hours of mathematics and statistics with a minimum of 6 semester hours in statistics and 12 semester hours in advanced mathematics, such as calculus, differential equations, or vector analysis. Research positions in institutions of higher education and many positions in private industry require a graduate degree, often a doctorate, in statistics.

About 80 colleges and universities offered bachelor's degrees in statistics in 1996. Many other schools also offered degrees in mathematics, operations research, and other fields which included a sufficient number of courses in statistics to qualify graduates for some beginning positions, particularly in the Federal Government. Required subjects for statistics majors include differential and integral calculus, statistical methods, mathematical modeling, and probability theory. Additional courses that undergraduates should take include linear algebra, design and analysis of experiments, applied multivariate analysis, and mathematical statistics. Because computers are used extensively for statistical applications, a strong background in computer science is highly recommended. For positions involving quality and productivity improvement, training in engineering or physical science is useful. A background in biological, chemical, or health science is important for positions involving the preparation and testing of pharmaceutical or agricultural products. For many jobs in market research, business analysis, and forecasting, courses in economics and business administration are helpful.

In 1996, approximately 110 universities offered a master's degree program in statistics, and 58 had statistics departments which offered

a doctoral degree program. Many other schools also offered graduate-level courses in applied statistics for students majoring in biology, business, economics, education, engineering, psychology, and other fields. Acceptance into graduate statistics programs does not require an undergraduate degree in statistics although a good mathematics background is essential.

Good communications skills are important for prospective statisticians, not only for those who plan to teach, but also to qualify for many positions in industry, where the need to explain technical processes to those who are not statisticians is common. A solid understanding of business and the economy is important for those who plan to work in private industry.

Beginning statisticians who have only the bachelor's degree often spend much of their time doing routine work supervised by an experienced statistician. With experience, they may advance to positions of greater technical and supervisory responsibility. However, opportunities for promotion are best for those with advanced degrees. Master's and Ph.D. degree holders enjoy greater independence in their work and are qualified to engage in research, to develop statistical methods, or, after a number of years of experience in a particular area, to become statistical consultants.

Job Outlook

Although employment of statisticians is expected to grow little through the year 2006, job opportunities should remain favorable for individuals with statistical training. Many individuals at the bachelor's degree level, and some at the master's degree level, will find positions in which they do not have the title of statistician. This is especially true for those involved in analyzing and interpreting data from other disciplines such as economics, biological science, psychology, or engineering.

Among graduates with a bachelor's degree in statistics, those with a strong background in mathematics, engineering, or computer science should have the best prospects of finding jobs related to their field of study. Federal Government agencies will need statisticians in fields such as demography, agriculture, consumer and producer surveys, Social Security, health care, education, energy conservation, and environmental quality. However, competition for entry level positions in the Federal Government is expected to be strong for those just meeting the minimum qualification standards for statisticians. Those who meet State certification requirements may become high school statistics teachers, a newly emerging field. (For additional information, see the statement on kindergarten, elementary, and secondary school teachers elsewhere in the Handbook.)

Private industry will continue to require statisticians, especially at the master's and Ph.D. degree levels, to monitor and improve productivity and quality in the manufacture of various products including pharmaceuticals, motor vehicles, chemicals, and food products. For example, pharmaceutical firms will need statisticians to assess the safety and effectiveness of the rapidly expanding number of drugs. To counter stiff competition, motor vehicle manufacturers will need statisticians to improve the quality of automobiles, trucks, and their components by developing and testing new designs. Some statisticians with a knowledge of engineering and the physical sciences will find jobs in research and development, working with teams of scientists and engineers to help improve design and production processes in order to ensure consistent quality of newly developed products. Business firms will rely more heavily on workers with a background in statistics to forecast sales, analyze business conditions, and help solve management problems. In addition, sophisticated statistical services will increasingly be contracted out to consulting firms.

Earnings

The average annual salary for statisticians in the Federal Government in nonsupervisory, supervisory, and managerial positions was $61,030 in 1997; mathematical statisticians averaged $65,660.

Statisticians who hold advanced degrees generally earn higher starting salaries.

Agricultural science is closely related to biological science, and agricultural scientists use the principles of biology, chemistry, physics, mathematics, and other sciences to solve problems in agriculture. They often work with biological scientists on basic biological research and in applying to agriculture the advances in knowledge brought about by biotechnology.

Many agricultural scientists work in basic or applied research and development. Others manage or administer research and development programs or manage marketing or production operations in companies that produce food products or agricultural chemicals, supplies, and machinery. Some agricultural scientists are consultants to business firms, private clients, or to government.

Depending on the agricultural scientist's area of specialization, the nature of the work performed varies.

Food science. Food scientists or technologists are usually employed in the food processing industry, universities, or the Federal Government, and help meet consumer demand for food products that are healthful, safe, palatable, and convenient. To do this, they use their knowledge of chemistry, microbiology, and other sciences to develop new or better ways of preserving, processing, packaging, storing, and delivering foods. Some engage in basic research, discovering new food sources; analyzing food content to determine levels of vitamins, fat, sugar, or protein; or searching for substitutes for harmful or unde

sirable additives, such as nitrites. Many food technologists work in product development. Others enforce government regulations, inspecting food processing areas and ensuring that sanitation, safety, quality, and waste management standards are met.

Plant science. Agronomy, crop science, entomology, and plant breeding are included in plant science. Scientists in these disciplines study plants and their growth in soils, helping producers of food, feed, and fiber crops to continue to feed a growing population while conserving natural resources and maintaining the environment. Agronomists and crop scientists not only help increase productivity, but also study ways to improve the nutritional value of crops and the quality of seed. Some crop scientists study the breeding, physiology, and management of crops and use genetic engineering to develop crops resistant to pests and drought. Entomologists conduct research to develop new technologies to control or eliminate pests in infested areas and prevent the spread of harmful pests to new areas, and which are compatible with the environment. They also do research or engage in oversight activities aimed at halting the spread of insectborne disease.

Soil science. These workers study the chemical, physical, biological, and mineralogical composition of soils as they relate to plant or crop growth. They study the responses of various soil types to fertilizers, tillage practices, and crop rotation. Many soil scientists who work for the Federal Government conduct soil surveys, classifying and mapping soils. They provide information and recommendations to farmers and other landowners regarding the best use of land and how to avoid or correct problems such as erosion. They may also consult with engineers and other technical personnel working on construction projects about the effects of, and solutions to, soil problems. Since soil science is closely related to environmental science, persons trained in soil science also apply their knowledge to ensure environmental quality and effective land use.

Animal science. Developing better, more efficient ways of producing and processing meat, poultry, eggs, and milk is the work of animal scientists. Dairy scientists, poultry scientists, animal breeders, and other related scientists study the genetics, nutrition, reproduction, growth, and development of domestic farm animals. Some animal scientists inspect and grade livestock food products, purchase livestock, or work in technical sales or marketing. As extension agents or consultants, animal scientists advise agricultural producers on how to upgrade animal housing facilities properly, lower mortality rates, or increase production of animal products, such as milk or eggs.

Working Conditions

Agricultural scientists involved in management or basic research tend to work regular hours in offices and laboratories. The working environment for those engaged in applied research or product development varies, depending on the discipline of agricultural science and the type of employer. For example, food scientists in private industry may work in test kitchens while investigating new processing techniques. Animal scientists working for Federal, State,