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Very few people seem to know the type of work mathematicians do in government and industry, and therefore most people do not realize that mathematicians have wide employment opportunities beyond teaching. In fact, at the University of New Mexico, large percentage of mathematics graduates go into government or industry, whereas the remaining percentage is evenly split between graduate school and teaching. Our students are hired to do applied mathematics. This applied mathematics is sometimes called engineering, sometimes called computer science, sometimes called actuarial science, etc. In fact, the resulting job title may not even mention mathematics. Every task, however, that you may encounter in a scientific career can be attacked in a mathematical manner— an approach that requires both mathematical competence and perspective. Companies and agencies know this to be true, and place considerable value on having employees who can master this approach.
Companies hire mathematicians as well as particular types of scientists because both groups have something important to contribute. Typically, companies will have people of various backgrounds (engineers, mathematicians, computer scientists, etc.) grouped together to work on pertinent problems. These real-world problems are "word problems," e.g., the group leader wants a quantitative analysis to streamline a procedure, to make it more cost- efficient, etc. This is the type of analysis that must precede actual computation, i.e., the group must determine formulas and equations that accurately describe the actual phenomena being analyzed. Clearly, if a formula for the solution already existed, it would be already programmed on the computer, and there would be no need to hire an engineer or a mathematician to punch a button and retrieve the answer.
A typical applied problem resolution involves three phases:
- Build a mathematical model to describe the phenomena,
- Analyze the model, and
- Generate a computational approximation for the solution of the model.
Building the mathematical model requires the knowledge of the science of the problem plus the knowledge of how to use mathematics to describe the phenomenon quantitatively. Analysis of the model involves, among other things, evaluating the accuracy of approximations used to make the mathematical formulation tractable. Finally, one must determine the best computational approach to get a reasonable solution with respect to the particular computer environment of one's workplace. Each of these three aspects is very mathematical in nature and underscores the need for mathematical competence. In fact, the computer revolution has increased, rather than decreased, the role of applied mathematics, because many complex mathematical models until recently were computationally intractable.
The bottom-line in choosing a career comes down to two essentials:
It is absolutely imperative for your own happiness and well-being that you choose an area of work that you enjoy and for which you have considerable aptitude. Too many students whose first love is mathematics turn away to a side area just because they are not aware of the fine career opportunities available in applied mathematics. Such students are making a serious mistake. Applied mathematical career opportunities are sufficiently comparable to those in other areas that you can comfortably base your decision on these two primary factors, taste and talent.
The following organizations express an interest in hiring mathematics students:
- Central Intelligence Agency
- Defense Technology
- Department of Justice
- Digital Signal Corp.
- General Services Admin.
- IBM Corporation
- Internal Revenue Service
- Management Systems Labs
- Michelin Americas
- Mitre Corporation
- National Security Agency
- Naval Air Development Center
- Naval Surface Warfare Center
- TRW Systems Division
- USF&G Corporation
- U.S. Dept. of the Army
You are, of course, already aware of the increasing need for mathematics teachers. This profession yields a wonderful way to combine a love of mathematics and a love of working with young people.
Some of the other common occupations for mathematicians, which are much less well known, are the following.
The actuary deals in mathematical probabilities. He/she designs insurance and pension programs and analyzes and solves complex business and social problems. A large percentage of actuaries are employed in the insurance profession, but there are other areas of actuarial employment including consulting firms, state and local governments, banks, and academic institutions.
You do not need actuarial training to get a job in this field, but be prepared to invest many hours of concentrated study over several years to pass a series of nine or ten examinations given by the Society of Actuaries of the Casualty Actuarial Society.
The first two actuary exams should be taken while you are an undergraduate. The first exam is primarily calculus and some students who have taken the exam suggest you take it at the end of your sophomore year while the material is still fresh in your mind. The second exam is primarily probability and statistics and should be taken after you have completed some courses in this area. The exams may be scheduled through the counseling center. There are no special actuary course you need to take. On the other hand, related courses in business can be helpful in this profession. For more information visit our department website at http://www.stat.unm.edu/stats_actuarial.html.
Industrial engineering seems to be more engineering-oriented while operations research is more mathematics-oriented. In operations research, one is concerned with such concepts as maximization and mathematical models. Significant numbers of practicing operations-research analysts are trained (have at least one degree) as mathematicians and are quite successful in the field.
Most large corporations have operations research groups that are concerned with such parameters as costs, profits, and probabilities of various kinds of success or failure. You should have courses in probability and statistics, and you should be conversant with numerical analysis and computer methods. Furthermore, many smaller corporations, especially those performing quantitative studies and evaluations for federal government agencies, have a need for people with a sound math background. This type of company works in a variety of analytical areas and you may need courses in such areas as probability and statistics, physics, modeling, simulation, and operations research.
A math major with some computer science background is eligible for a wide variety of computer-oriented jobs, including systems analyst, programmer, data processing manager, and computer operations manager.
A systems analyst plans, helps design, and implements small- and large- scale computerized systems for a wide variety of business-oriented applications. A systems analyst might install systems in inventory control, purchasing, personnel, or truck-loading for a large company, or do systems planning for medical societies, municipal governments, and new town developers.
In the broader sense a systems analyst might not be concerned with the computer, although some computer background is helpful to communicate with the programmers. Courses in linear programming are helpful. Today's sophisticated industrial system needs to be balanced to make sure it is economically feasible. For example, how many of a certain style product should you produce to maximize profits. Every company with annual sales of over fifty million dollars has a computer-oriented cost system.
A math major can qualify for Civil Service positions as a Mathematician, Oceanographer, Operations Research Analyst, Physicist, or Statistician. For the physicist position, you must have 24 semester hours of physics, but most mathematics majors should have the background to apply for the other positions listed.
A math major does not have to take the Federal entrance exam, but you must get on the Federal register to be eligible, except in a few exempt agencies. One of the largest employer of mathematicians has been the National Security Agency. Their main work, of course, lies in cryptography. Mathematicians work at many other government agencies as well.
UNM mathematicians take jobs in many other areas, as well. In fact, it is fairly common for mathematics students to do graduate work in the area of their applied specialty. At a recent National Computer Conference, a panel discussed the contributions of the past and those anticipated for the future by mathematicians and computer scientists in the fields of sociology and education, urban emergency services, population biology, and energy-societal fields typical of those currently receiving wide attention. At Brown University in the graduate school there are interdepartmental standard concentrations in Applied Mathematics/Biomedicine, and Economics/Operations Research. The Society for Industrial and Applied Mathematics stated in a news release that health research needs mathematicians. Use your mathematics and your imagination and you can quickly think of a dozen more, although some of the newer areas may require graduate work.