Why
Major In
Mathematics?
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 paths. For a more complete
discussion of mathematical career options, see the
Handbook
for Mathematics Majors and Minors.
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 Langs
|
+5.7% |
+3.3% |
| History |
+2.9% |
+4.6% |
| Biology |
+4.0% |
+3.3% |
| Psychology |
+0.9% |
+0.8% |
| Political
Science |
-1.6% |
+.06% |
| Arts & Music |
-.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
Langs |
+5.1% |
| Poli. Sci. |
+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. In The Jobs
Rated Almanac (1999
edition),
Les Krantz ranks 250 jobs according to six criteria: income, stress,
physical demands, potential growth, job security and work
environment. Mathematician ranks 5th out of 250.
Moreover,
the jobs rated higher than mathematician, such as Actuary, also involve
significant mathematical reasoning and knowledge and therefore are
likely filled by math majors also. |
|
Job
|
Satisfaction
Ranking |
| Actuary |
2 |
| Mathematician |
5 |
| Biologist |
23 |
| Physicist |
42 |
| Mechanical Engineer |
45 |
| Economist |
50 |
| Electrical Engineer |
54 |
| Attorney |
60 |
| Chemist |
64 |
| Computer Consultant |
81 |
| General Practice
Physician |
82 |
| Dentist |
86 |
| Senior Corporate
Executive |
95 |
| Stockbroker |
124 |
| Surgeon |
135 |
|
|
Jobs
for Math Majors
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.
Now That You Are Interested...
If you want to learn more about
getting a major in mathematics, feel free to have a chat with
Prof. Bill Allard
(Director of Undergraduate Studies) or
Prof. Clark Bray
(Associate Director of Undergraduate Studies).