Majoring in Mathematics

Why Major in Mathematics?

One could say that mathematics is simply an exciting, fascinating, utterly satisfying, and rapidly expanding discipline. Many people are drawn to the level of challenge it presents, the creativity it requires, and the clarity it affords in knowing when you are right.

If you like solving puzzles and hunting for patterns and hidden structures -- if you enjoy logical analysis, deduction, and investigating the unknown -- if you want to understand the connections between seemingly widely different areas of science and technology, and how mathematics can be used to explain and control natural phenomena -- then being a math major might be a good choice for you.

That said, people sometimes worry about the practicalities of graduating with a major in math: What kinds of careers can they pursue? How much money will they be able to make? Will they like their job, once they have it? Is majoring in math helpful if you want to go to medical school, law school, or a graduate school in business?

A few years ago, Duke University compiled some amazingly compelling statistics that speak to each of these questions. You can find the bulk of what they wrote copied below -- or if you wish, you can read the original article here:

Entrance Exam Scores

Suppose you love mathematics, but ultimately see yourself pursuing a career as a doctor, lawyer, or businessman. Then you should be aware that professional graduate schools in business, law, and medicine think mathematics is a great major because it develops analytical skills and the ability to work in a problem solving environment. Their entrance tests support this bias.
A study of college students' scores on admission tests for graduate and professional schools showed that students majoring in mathematics received scores substantially higher than the average on each of the tests studied. The study, by the National Institute of Education, compared the scores of 550,000 college students who took the LSAT and GMAT with data collected over the previous eighteen years.

The table on the right excerpts some of this data from THE CHRONICLE OF HIGHER EDUCATION. The entries show the percentage by which the mean score of test takers from specific undergraduate majors differs from the mean score of all test takers.

Major LSAT GMAT
Mathematics +12.8% +13.3%
Philosophy +8.7% +11.0%
Economics +9.6% +7.3%
Chemistry +7.6% +7.5%
English +5.6% +4.1%
Foreign Languages +5.7% +3.3%
History +2.9% +4.6%
Biology +4.0% +3.3%
Psychology +0.9% +0.8%
Political Science -1.6% +0.06%
Arts & Music -0.05% -1.2%
Business -4.5% -0.8%
Sociology -7.0% -5.0%
Education -8.7% -4.2%

Salaries

For those of you who wish to take your undergraduate degree directly to the job market after graduation, the chart on the right, extracted from the National Association of Colleges and Employers 2005 salary survey, provides a comparison of average starting salaries for students by undergraduate major.
Note the statistics in the table to the right indicate the percentages by which the average salaries for specific undergraduate majors exceed that of an English major.

Major Salary Differential
Mathematics +37.7%
Economics +33.5%
Chemistry +22.8%
Foreign Languages +5.1%
Political Science +4.9%
History +0.9%
Biology +0.8%
English +0%
Sociology -0.3%
Psychology -4.4%

Job Satisfaction

In addition to higher pay, a math major's employment promises higher levels of job satisfaction. JobsRated.com ranks 200 jobs according to environment, income, outlook, physical demands, and stress. Based on these criteria, "Mathematician" takes the number one spot on the list -- outranking jobs in medicine, finance, engineering, and law.

Numbers two and three on the list, "Actuary" and "Statistician", are also careers for which an undergraduate degree in mathematics is extremely valuable.

Job Satisfaction Ranking
Mathematician 1
Actuary 2
Statistician 3
Biologist 4
Software Engineer 5
Economist 11
Physicist 13
Computer Programmer 18
Aerospace Engineer 33
Nuclear Engineer 41
Chemist 57
Electrical Engineer 62
Federal Judge 69
Civil Engineer 71
Mechanical Engineer 74
Attorney 82
Stockbroker 84
Senior Corporate Executive 88
Dentist 101
Orthodontist 103
General Practice Physician 142
Surgeon 156

Jobs for Math Majors

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.