Throughout history, mathematics has played a vital role in efforts to understand the world and control the environment. Not only the natural sciences, but also economics, political science, sociology, psychology and other social sciences rely on mathematics to understand, control and predict phenomena. Consequently, mathematics majors have many career opportunities open to them. Also, career opportunities of students who major in other subjects are enhanced by supporting courses in mathematics.
The mathematician in teaching has an extremely important job. Approximately 1/5 of all bachelor’s-level mathematicians work in education, but there is now a shortage of high school mathematics teachers. The most effective teachers have breadth in mathematics (a major) and understand how to pose and solve problems in mathematics applications. An internship (observing and teaching) and teacher certification are required for teaching in public schools.
University Professor: A Ph.D. degree in mathematics is required for this position. A university professor of mathematics teaches courses, mentors students, and provides service to the institution and the community. A university professor can also be considered a practitioner to the extent that he/she conducts research and develops new mathematical knowledge. A university professor may also engage in consulting activities.
College Teacher: College mathematics teachers may have a master's degree or a Ph.D., depending on the level and nature of the institution. Responsibilities may be exclusively instruction-related, as in the case of a community college, or may include some research.
High School Teacher: Well-qualified mathematics teachers are in high demand. A bachelor's degree is the minimum requirement for teaching in secondary schools. State requirements for certification, which usually include courses in education, must also be met. The traditional areas of secondary school mathematics--algebra, geometry, and trigonometry--have been augmented in many schools by analytic geometry and calculus and other courses that are intended to meet diverse student needs. Newer curricula include computer programming, probability and statistics, linear algebra, and applications. The prospective teacher who is familiar with these latter areas will have a competitive advantage.
The mathematician in government typically is solving algebraic or differential equations or analyzing statistical data. With some experience, the mathematician generally becomes a department-wide consultant. Many data-analysis problems involve matching data with imperfect mathematical models of physical, economic or sociological systems. The mathematician combines what can be observed, what can be modeled mathematically, and what can be solved mathematically in finite terms with finite resources to produce results upon which decisions are based.
The mathematician in industry is hired because he or she can contribute to some ongoing problem. Rarely does the mathematician work alone in industry, more often working as part of a team. Thus a fundamental requirement is the ability to communicate about and solve problems. Four broad categories of applied mathematicians are associated with four general classes of problems:
Computational Mathematicians interpret problems arising from the physical sciences and engineering in mathematical form and develops mathematical solutions to these problems. Very large and sophisticated computers are used intensively. Potential employers include government laboratories, the chemical industry, and the biotech industry. work with computer-related problems. Every industry in the world makes extensive use of computers. There is great demand for people who can efficiently communicate with computers. Computational Mathematicians can also work with software engineers to designs and writes software that performs nonnumerical functions, such as graphics. Employers include consulting firms and large corporations which do their own software development. There is also room in this field for the entrepreneur or consultant.
Operations Researchers also called management science analysts, help organizations coordinate activities and operate in the most efficient manner, by applying scientific methods and mathematical principles to organizational problems. Computers are used extensively in their work. Students interested in this career path should minor in Management Information Systems (MIS) or Systems and Industrial Engineering (SIE).build simple mathematical models of complex economic and business structures to help people plan a course of action.
Statisticians design experiments, plan data collection, and analyze data to forecast trends, reliability, etc. They also deal extensively with quality control issues. Statistics is both a very applied field and also a theoretical one. Many, but not all, statisticians are active in both applications and the development of new theory, but the greatest potential in terms of jobs is in applied statistics. Statisticians generally work with people in other fields, therefore communication skills are very important. Statistical applications nearly always include the analysis of data and hence some knowledge and experience in computing is very important. There are opportunities for statisticians in the government, in industry, business, medicine, and in academia. An area very closely related to Statistics is Actuarial Science. Actuaries are hired by insurance companies (life, health, casualty, etc.), pension plans, businesses, consulting firms (business and actuarial), and government agencies. To become an actuary (an Associate or a Fellow), one must pass a series of examinations administered by the Society of Actuaries. The initial exams are primarily mathematics, including probability and statistics, and can be taken while still an undergraduate student. Because actuarial science is a mixture of mathematics and business, the student should speak with an advisor about other course work needed to prepare for this career. For more more information about a career in the actuarial sciences, see www.beanactuary.org
Applied Mathematicians deal with industrial problems involving questions of chemistry or physics, problems in structure stability, wave propagation, etc. Applied Mathematicians may also engage in research in areas of interest to large corporations and various departments of government. These include the Department of Energy, various branches of the military, and security agencies. While the demand for non-academic research mathematicians has been shrinking in recent years, there still are positions available at national laboratories, the National Security Agency, and other government entities, as well as some large corporations. An advanced degree is usually required for these positions. The scientific publishing industry has a need for scientifically trained individuals for sales and editing. Excellent writing and oral communication skills are essential in this career field. Accurate and understandable technical writing is widely needed.
