The work of mathematicians falls into two sometimes overlapping categories: applied and theoretical mathematics.
Theoretical, or pure, mathematicians develop new principles and seek new relationships between existing principles of mathematics. This basic knowledge is the foundation for much of the work in the second category, applied mathematics. In this area, mathematical theories are used to develop theories and techniques for solving practical problems in business, government, and the natural and social sciences. Mathematicians may work in statistics, actuarial jobs, computer programming, economics, or systems analysis.
Many mathematicians, usually theoretical mathematicians, work in colleges where they teach or do research. Mathematicians are found in the private sector in the aerospace, communications, machinery, and electrical equipment industries. The Department of Defense and National Aeronautics and Space Administration employ most of those who work for the federal government.
Places of Employment and Working Conditions
Mathematicians can be found working in government agencies, private firms, and as faculty members at colleges and universities. Some mathematicians work alone, and some work as members of research teams.
While those working for government agencies and private firms usually have structured work schedules, they may face deadlines, overtime work, and travel to seminars or conferences. College faculty have more flexible schedules, with their time devoted to teaching, research, consulting, and administrative responsibilities.
Qualifications, Education and Training
Mathematicians need good reasoning ability and persistence in solving problems. In applied mathematics especially, they should be able to communicate effectively with non-mathematicians in the discussion and solution of practical problems.
A prospective mathematician should take as many mathematics courses as possible while still in high school and should obtain a bachelor's degree that includes courses in analytical geometry, calculus, differential equations, probability and statistics, mathematics analysis, and modern algebra.
Most positions in research or in university teaching require an advanced degree, frequently a Ph.D. Private industry and the government also prefer those with advanced degrees.
For work in applied mathematics, a background in a specialty field such as engineering, economics, or statistics is also necessary. This can be accomplished by including a minor in one of these fields while in college. In modern industry, knowledge of computer programming also is essential since most complex problems are now solved with the aid of computers.
There are many colleges and universities that offer a master's degree program in mathematics and a lesser number that also offer a Ph.D. program. Candidates for graduate degrees in mathematics concentrate on a specific field such as algebra, geometry, or mathematical analyses and conduct research in addition to taking advanced courses.
Potential and Advancement
Mathematicians work in the federal government and in private science and engineering research companies. They work on teams with engineers, scientists, and other professionals and consequently must often work around others' schedules.
Mathematicians who work in postsecondary education usually have a blend of teaching and research duties. Collaborators work together at the same institution or from different locations, communicating electronically. Mathematicians in academia often have help from graduate students.
A majority of the mathematicians in the United States hold mathematics faculty positions in colleges and universities.
The Bureau of Labor Statistics estimates that the demand for mathematicians will grow by 21% between 2014 and 2024, as businesses will need employees who can analyze growing quantities of data. Holders of a doctorate in applied mathematics will be in greater demand in industry than those who specialize in theoretical mathematics. However, theoretical mathematicians with a Ph.D. should find many opportunities for teaching and research jobs in colleges and universities.
Mathematicians with a master's degree will face competition for research and teaching jobs, but there will be many opportunities in applied mathematics fields. Holders of a bachelor's degree with some experience in computer science will have good opportunities in computerized data processing activities. Those who fulfill the necessary requirements may become high school mathematics teachers.
Income
According to the Bureau of Labor Statistics, the median annual wage of mathematicians was $111,110 in 2015 College and university teachers are paid at the same rate as other faculty members; salaries tend to be lower than in private industry or government.
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