Mathematics
is one of the oldest and most fundamental sciences. Mathematicians use
mathematical theory, computational techniques, algorithms, and the
latest computer technology to solve economic, scientific, engineering,
physics, and business problems. The work of mathematicians falls into
two broad classes  theoretical (pure) mathematics and applied
mathematics. These classes, however, are not sharply defined and often
overlap.
Theoretical
mathematicians advance mathematical knowledge by developing new
principles and recognizing previously unknown relationships between
existing principles of mathematics. Although these workers seek to
increase basic knowledge without necessarily considering its practical
use, such pure and abstract knowledge has been instrumental in producing
or furthering many scientific and engineering achievements. Many
theoretical mathematicians are employed as university faculty, dividing
their time between teaching and conducting research.
Applied mathematicians
use theories and techniques, such as mathematical modeling and
computational methods, to formulate and solve practical problems in
business, government, engineering, and the physical, life, and social
sciences. For example, they may analyze the most efficient way to
schedule airline routes between cities, the effects and safety of new
drugs, the aerodynamic characteristics of an experimental automobile, or
the costeffectiveness of alternative manufacturing processes.
Applied mathematicians
working in industrial research and development may develop or enhance
mathematical methods when solving a difficult problem. Some
mathematicians, called cryptanalysts, analyze and decipher encryption
systems—codes—designed to transmit military, political, financial, or
lawenforcementrelated information.
Applied mathematicians
start with a practical problem, envision its separate elements, and then
reduce the elements to mathematical variables. They often use computers
to analyze relationships among the variables, and they solve complex
problems by developing models with alternative solutions.
Individuals
with titles other than mathematician also do work in applied
mathematics. In fact, because mathematics is the foundation on which so
many other academic disciplines are built, the number of workers using
mathematical techniques is much greater than the number formally called
mathematicians. For example, engineers, computer scientists, physicists,
and economists are among those who use mathematics extensively. Some
professionals, including statisticians, actuaries, and operations
research analysts, are actually specialists in a particular branch of
mathematics. Applied mathematicians frequently are required to
collaborate with other workers in their organizations to find common
solutions to problems.
The world is full of places to do
rigorous mathematics. As you begin to identify potential outlets for your
talent, it may be useful to get a sense of the dimensions of the 'field'
in its entirety. Business, industry, and
government use mathematical expertise, often in the context of
applications.
However, the job titles often do not include the word
"mathematics" or "mathematician," but do involve significant use of
mathematics and/or quantitative reasoning. For people with advanced degrees in mathematics, careers
involve development of new mathematical methods and theories and
application to almost every area of science, engineering, industry and
business. Those who major in mathematics in undergraduate institutions
find a broad variety of opportunities. Some use their mathematical
training directly and some use their training in rigorous thinking and
analysis indirectly to solve problems in the business sector.
Many
of the contributions and uses of mathematics are closely related to the
need for mathematical modeling and simulation of physical phenomena on the
computer. In addition, the analysis and control of processes, and
optimization and scheduling of resources use significant mathematics. For
example, the finance industry uses sophisticated mathematical models for
pricing of securities, while the petroleum industry models the flow of oil
in underground rock formations to help in oil recovery. Image processing,
whether producing clear pictures from satellite imagery or making medical
images (CAT, MRI) to detect and diagnose, all use significant mathematics.
Industrial design, whether structural components for airplanes or
automobile parts, uses a tremendous amount of mathematical modeling; much
of which is embodied in CAD/CAM computer software. Such techniques were
used in the design of the Boeing 777, as well as in the design of
automobiles. Computational modeling is also used in airplane and
automobile design to analyze the flow of air over vehicles to determine
fuel economy and efficiency.
The
use of mathematics is pervasive in modern industry. The result is that
mathematicians are found in almost every sector of the job market,
including engineering research, telecommunications, computer services and
software, energy systems, computer manufacturers, aerospace and
automotive, chemicals and pharmaceuticals, and government laboratories,
among others.
Note:
Some resources in this section are provided by the
American Mathematical Society,
Mathematical Association of America,
Society for Industrial and Applied
Mathematics,
and the US Department
of Labor, Bureau of Labor Statistics.

