Mathematics is the most rigorous and demanding of all intellectual
pursuits. Why should a student major in it? For some, the joy of
attacking the intellect's most extreme sport is sufficient justification. We
all need to eat, however, and so on this page we note how a mathematics
major helps provide for your daily bread. We begin by looking at the
significance of the math major for several non-mathematical career
path.
Careers related to Mathematics
Studying Mathematics develops such skills as arguing logically and rigorously, thinking abstractly, formulating and solving problems, analyzing data, and creating and analyzing mathematical models. Employers value these skills; consequently, math majors find themselves in demand by employers for careers in a wide spectrum of fields.
A bachelor's degree in mathematics will prepare you for jobs in statistics, actuarial sciences, mathematical modeling, and cryptography, mathematics education, as well as for graduate school leading to a research career in engineering, mathematics or statistics. A strong background in mathematics is also necessary for research in many areas of computer science and social science. We describe below a few of the many fields where mathematics majors are in demand.
Mathematical Modeling
In mathematical modeling, you write down equations to describe how a real world system behaves. The "system" might be drawn from many different fields. For example, most financial companies hire mathematicians to study financial models and make predictions based on statistical evidence. In physics or engineering you might be interested in how heat is dissipated through the heat shield of a space vehicle. In physiology you might want to apply the laws of fluid dynamics to describe how blood flows in vessels and what happens when blood pressure is increased. In economics you might want to predict how a strike in the automotive industry will affect other parts of the economy.
Building a mathematical model is usually a multi-stage process: you study the problem, write down the equations, use them to predict what will happen, see if your predictions agree with experiments, modify your equations if necessary, make new predictions, and so on.
The model may be solved exactly (you may be able to write down a function that tells you the values you want to know), or you may have to approximate the values because they can't be found exactly, or you may have to simulate the model on a computer -- i.e., let the computer imitate the real system to see what happens as you change some of the parameters.
As usual, the power of mathematics comes from its ability to handle general abstract problems and then to apply these general methods to an enormous variety of problems.
Finance
Wall Street has become a major employer of math majors. Trying to match the outstanding success of multibillionaire Differential Geometer, James Simons (founder of the Renaissance Technologies Corporation and the top hedge fund, the Medallion Fund), many investment and financial firms consider mathematicians prized hires.
Statistics
The proliferation of statistics in everything ranging from business to government has induced many organizations to seek math majors. Statisticians use surveys -- for example, opinion polls -- to predict the patterns of behavior of large groups based on relatively small samples. They ask questions such as: How can we be sure that what we predict from our small sample is true of the population being sampled? Probability theory provides the theoretical foundation for statistics.
One business with an extreme interest in statistics is insurance. The (highly paid) professionals responsible for computing insurance rates are specialist statisticians called actuaries.
Where Mathematics Meets Computer Science
The computer industry provides many lucrative jobs for math majors. Beyond mere proficiency in computer programming, math majors are trained to address the more fundamental issues involved in the creation of new algorithms. Furthermore, many sophisticated applications of computers such as creation of computer graphics and the compression of video and audio signals (to name a few examples) involve a great deal of deep mathematics, and as a result, many computer companies specifically hire math majors.
Cryptography
One area that is particularly "hot" these days is cryptography - the making and breaking of secret codes. Not only the CIA, NSA, and other spy agencies are devotees. Numerous businesses also require cryptography. For example, the cable TV companies encode their signals, forcing the viewer to rent their decoding devices in order to turn the signals back into a television picture. Banks also employ cryptography in order to protect the privacy and integrity of their transactions. Number theory is the branch of pure mathematics which provides the theoretical underpinnings for much of the recent progress in cryptography.
Biotech
Recent breakthroughs in the study of DNA and proteins have generated a great deal of interest in mathematical biology. Many biotech companies hire mathematics majors because of the high (and growing) mathematical content of the field.
Teaching
If you would like to give back to your community and serve children, teaching mathematics at the secondary school level can be very rewarding. Every year, roughly half of the positions advertised for secondary school teachers in math go unfilled. Schools are desperate for qualified math majors.
Graduate School
At the end of your undergraduate years, you may have fallen in love with the beauty of mathematics and want to learn more. You may wish to go to graduate school in mathematics or a related field (e.g., operation research, economics, computer science, etc.). In graduate school, students typically get paid (albeit not much) to pursue a Master or PhD degree. With a graduate degree, you may find a teaching or research job in academia, or a leadership position in industry.
Source: Duke Mathematics Department
