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 so 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, cryptography, and mathematics education, as well as prepare you 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. Below is a sample list of the many fields where math majors are in demand.
In mathematical modeling, equations are used to describe how a real world system behaves. Building a mathematical model involves a multi-stage process whereby you study a problem, write down the equations, use them to predict what will happen, see if your predictions agree with experiments, modify the equations if necessary, make new predictions, and so on.
The "system" can be applied to 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 investigate how heat is dissipated through the heat shield of a space vehicle. In physiology you may 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 predict how a strike in the automotive industry will affect other parts of the economy.
The model may be solved exactly (you may be able to write down a function that tells you the values you want to know), may be solved using approximated values because they can't be found exactly, or the model may have to be simulated on a computer (i.e., let the computer imitate the real system) to see what happens as you change the parameters. 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.
Wall Street has become a major employer of math majors. Trying to match the outstanding success of multi-billionaire 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.
The proliferation of statistics in everything ranging from business to government has induced many organizations to seek math majors for employment. Statisticians use surveys (e.g. 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.
Insurance is one business with an extreme interest in statistics. Actuaries are the (highly paid) specialists who are responsible for compiling and analyzing statistics to order to calculate insurance risks and premiums for a company.
The computer industry provides numerous 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. Plenty of sophisticated computer applications – such as creating computer graphics or compressing video and audio signals – involve a great deal of deep mathematics which, as a result, leads many computer companies to specifically hire math majors.
One area that is particularly "hot" these days is cryptography – the making and breaking of secret codes. The CIA, NSA, and other spy agencies aren't the only devotees. Numerous businesses also require cryptography. 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 and banks 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.
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.
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 so schools are in need of qualified math majors.
If at the end of your undergraduate years, you have fallen in love with the beauty of mathematics and want to learn more, graduate school in mathematics or a related field such as operation research, economics, computer science is an option. Graduate school students usually receive nominal compensation to pursue a Master's degree or PhD. With a graduate degree, you can find a teaching or research job in academia, or a leadership position in industry.